Handling Qualities of Large Rotorcraft in Hover and Low Speed

compensation strategy for the higher response frequency. As a corollary to this result, for the low-frequency attitude responses, it can be inferred that the pilots tend to “over-drive” the aircraft to compensate for the slow response. As indicated by the results from the previous section, this is not a unique characteristic of the extended (i.e., 40 ft) pilot offset location.

Rather, it confirms a normal compensation technique adaptation of the pilot in line with the classical crossover model [51].

The significance of the results in Figures 52 and 53 is they confirmed a direct link between the second-order command model system natural frequency parameter and quantifiable metrics of pilot compensation, independent of time delay. This key result suggests pilot compensation frequency was inherently governed by the aircraft equivalent second-order natural dynamics.

Effectively, it could be argued that task bandwidth was set by the aircraft natural response dynamics, mainly the natural frequency. As the command model second-order natural frequency increased, pilots appeared to become more comfortable with increasing the frequency of their inputs. This trend was naturally limited by the objectionable flying/ride qualities that emerged for higher bandwidth configurations, where it eventually exceeded the compensation ability of the pilot, in particular when coupled with large delays.

The grouping of better HQRs near 2.1 rad/s in Figure 54(a) suggests pilots consistently preferred the vehicle roll dynamics that allowed them to operate at this frequency. Pilots appeared to be more tentative in pitch, with the mean longitudinal control cutoff frequency for these optimal control system configurations dropping to about 1.6 rad/s (Figure 54(b)). In general, operating at higher frequencies excited objectionable deficiencies in the aircraft response qualities, especially with large added delay. One particular case stands out in Figure 54(b) as an exception where pilots, on average, used a higher crossover frequency of about 2.85 rad/s, yet rated this configuration to have borderline Level 1–Level 2 handling qualities.

However, a large standard deviation of 0.89 rad/s in the longitudinal control cutoff frequency, along with a 1.72 rad/s minimum and 4.27 rad/s maximum, indicate significant variability in the control techniques. Reviewing pilot comments, it is evident that ride quality, though described as “very rough,” was not weighed into the HQR score for this particular configuration. Pilots indicated they could operate the aircraft with continuous, but small amplitude, control inputs.

This is consistent with the quantitative pilot input cutoff frequency measurements. While pilots disliked the ride qualities of the aircraft, they liked the fact that the particular control system allowed them, under the appropriate control technique, to achieve reasonable accuracy in task performance.

Pilot Evaluations of LCTR Short-Term Yaw Response in Hovering Turn MTE Analysis of the effect of pilot offset on the yaw handling qualities presented above showed that Level 1 handling qualities requirements in hover might not be applicable to vehicles where the pilot station is 30 ft, or farther, from the center of rotation of the aircraft. The analysis presented here focuses on the evaluation of yaw short-term response requirements for an LCTR configuration. The results in this section are from two separate assessments of the LCTR.

Early assessments of the LCTR aircraft found that the initial design yaw bandwidth, based on the ADS-33 requirements, was extremely obtrusive to the pilot, and therefore, disruptive of the normal execution of the experiment. This process provided some insight into the adequate amount of control authority required for this type of aircraft. There are two basic elements that define overall yaw control authority: first, the control power or maximum yaw rate, and second, the precision required in capturing a target heading. The first element is not in question in this case, because it was generally possible to reach maximum yaw rates up to about 27.5 deg/s with the yaw-rate command system implemented. This surpasses the ADS-33 Level 1 minimum achievable yaw rate for Moderate Agility. With the pilot sitting almost 40 ft ahead of the center of gravity, it became apparent that bandwidth requirements for future large rotorcraft of this type would need to be balanced from a human factors and ride quality perspective. The bandwidth is closely related to the angular yaw acceleration, and at the large longitudinal offset location the pilot was subjected to highly objectionable peak lateral accelerations in excess of 0.6 ݃ Ǥ Current ADS-33 bandwidth requirements are minimums and are unbounded on the high side. The current exercise illustrates the potential necessity to curtail or modify current requirements, to account for aircraft size. The maneuver performed in this yaw bandwidth investigation loosely resembled the Hovering Turn MTE specified in ADS-33. No restrictions were placed on the aggressiveness and agility of the maneuver. The maneuver consisted of the pilot aligning the aircraft along the runway centerline, at an arbitrary altitude, and then executing 180 or 360 deg turns in an attempt to recapture the aircraft-runway alignment. Phase delay Time delay (s) 0.05 0.13 0.2 Level 3 0.28 Level 2 HQR Level 1 0 1 2 3 4 Cut-off frequency (rad/s) (a) Time delay (s) 0.05 0.09 0.15 Level 3 0.25 Level 2 HQR Level 1 0 1 2 3 4 Cut-off frequency (rad/s) (b) Figure 54. Correlation of HQRs with pilot cutoff frequency: (a) lateral axis and (b) longitudinal axis.

values for all control system configurations were around 0.15 s, placing the ADS-33 yaw bandwidth requirements approximately at 0.5 rad/s for the Level 2 minimum and 2 rad/s for the Level 1 minimum. The original design was set at 2 rad/s, with the intent that the design point be on the Level 1 boundary.

Figure 55 summarizes the pilot commentary for the different bandwidth and phase delay design points tested. The configurations that nominally fell within the ADS-33 Level 3 handling qualities region (for All Other MTEs ) were, not surprisingly, found to be lacking in terms of yaw bandwidth. However, design points that should theoretically possess Level 2 properties were unexpectedly characterized as having a major deficiency. The design points at 1.5 and 2 rad/s were reported to have very degraded characteristics. The latter 2 rad/s configuration, in particular, being the initial design bandwidth, was immediately considered unacceptable by pilots upon going into motion with this configuration. Response to pedal inputs for the three control system configurations with bandwidth values under 0.5 rad/s was described by the pilot as being too sluggish. All of these configurations required some level of pilot shaping of the pedal inputs in order to capture the desired heading accurately. In particular, the lowest bandwidth case, i.e., 0.1 rad/s, was deficient in the ability to capture a desired heading, and highly prone to PIO, as well. Additionally, a larger pedal input was required in order to achieve the desired initial response (understood as yaw rate). Pilot comments seem to support the assertion that yaw performance is not adequate enough for these cases to be considered to have Level 2 handling qualities; the 0.5 rad/s case was considered to be equivalent to a borderline Level 2/Level 3 situation .

Yaw response bandwidths of 0.8, 1, and 1.5 rad/s possessed markedly quicker response characteristics, and therefore tended, up to a point, to lead to more predictable configurations.

The 0.8 rad/s point was deemed to be the best compromise value by the project test pilot. A second pilot confirmed this as the best trade-off. At higher bandwidth values (i.e., 1 through 2 rad/s), the effects of the large distance between pilot station and axis of rotation manifested a sharpness of the response that was characterized as a major deficiency, with controllability even put into question for the initial design configuration of 2 rad/s.

0.4 Level 2 Level 3 0.3 Sluggish, control shaping required, (s) PIO prone Level 1 p τ 0.2 Optimal Not tolerable, unpredictable Phase delay, 0.1 Very crisp, very Too crisp, objectionable objectionable, predictable 0 1 2 3 4 5 Bandwidth, (rad/s) ω BW Figure 55. Pilot commentary for LCTR yaw bandwidth and phase delay design points.

After this initial exploratory phase of the yaw characteristics, the simple pedal hover turn task that was developed from the ADS-33 Hovering Turn MTE was employed for the subsequent evaluations. Regarding the task itself, it is noted that although pilots were able to push for much higher aggressiveness than needed, the task was considered representative of an actual mission an aircraft of this size would be required to perform. Based on this Hovering Turn MTE, the average HQR scores shown in Figure 56 indicate there is a broad yaw axis bandwidth range where the aircraft will prove satisfactory. HQR 3.5 and 6.5 contour lines for the surface interpolation of the average HQRs demarcate the Level1, Level 2, and Level 3 handling qualities regions for the available data.

A minimum bandwidth of 0.25 rad/s was required to generate satisfactory yaw control for precise heading capture maneuvers. The HQR surface interpolation contour line distinguishing the Level 1 and Level 2 ratings correlates approximately with the first-order yaw rate command model 3.6 s time constant ( ߬ ) isoline, highlighting that, at these timescales, the handling ௣௘ௗ qualities are largely insensitive to delay. Below these frequencies, the yaw response becomes unsatisfactory for precision capture of a desired heading. It is expected that yaw control will eventually be lost in the limit when bandwidth approaches zero, as the time to build up desired rates becomes excessive and meeting the performance metrics impossible. A Level 3 boundary was not identified, but extrapolation would put it below 0.1 rad/s. It is noted that while the current ADS-33 short-term yaw response boundaries are not supported for the yaw task defined for this experiment, the same trends are observed for bandwidths less than 1 rad/s, mainly that increasing yaw bandwidth results in improving handling qualities.

The size of the LCTR presents issues when configured for high yaw bandwidths not anticipated in the current ADS-33 specifications. As indicated by the contour boundary lines, degradation into Level 2 of the short-term response handling qualities was observed for bandwidth and phase delay pairs beyond a line defined approximately by rate response time constants in the order of 0.45–0.5 s. Increasing the quickness of response further to response time constants of 0.1 s or less resulted in major control deficiencies that put the aircraft with the ~40 ft pilot offset, squarely in Level 3 handling qualities. Delay in the response has significant 0.4 =3.6 s τ ped 0.3 Level 2 HQR 6.5 (s) contour fit p 4.8 2.7 τ 3.2 3.8 (5) (5) Level 3 (5) 5.1 (4) 0.2 (5) HQR 3.5 7.2 contour fit (5) 3.5 2.4 2.6 2.6 4.5 (5) (6) (5) Phase delay, τ =0.1 s (5) ped (4) Level 1 τ =0.2 s 0.1 ped Response delay 5.7 3.3 2.6 2.3 0.05 s 2.7 3.3 τ =0.4 s (5) (4) (4) (3) (3) (4) ped 0.16 s τ =0.6 s 0.28 s ped 0 1 2 3 4 5 Bandwidth, ω (rad/s) BW Figure 56. Short-term yaw response handling qualities evaluations for a 40 ft pilot offset.

impact on the handling qualities at bandwidths over 1.5 rad/s. All three configurations with bandwidths between 2.5 and 2.7 rad/s jumped one full handling qualities Level for every 110– 120 ms of time delay added to the commanded response dynamics. Pilots consistently described the extreme (i.e., Level 3) case as having a highly unpredictable initial response to input.

A contributing factor to the degraded handling qualities, and likely to the general sense of unpredictability of the initial yaw response, for these configurations commanding fast yaw rate dynamics, was related to a degraded ability of the control system to track aggressive pilot commanded responses because of increased actuator rate saturation.

It is further suspected that some of the issues with the predictability of the response are related to a fundamental distortion of the initial response, where pilots observed a “sudden” or “sharp,” but somewhat delayed response occurring sometime after application of the input.

Several pilots identified this type of characteristic response, where they would apply an input expecting an immediate response, which would then occur very suddenly a fraction of a second later. This would be the case where the time scales associated with the dynamics, or the dynamic response, are of the same order of magnitude as the time delay. Take a first-order rate response time constant of 0.4 s or lower, for example. A time delay in the order of 0.1–0.25 s represents a comparable time scale resulting in the type of distorted initial response characteristic discussed above. This discussion is somewhat academic, of course, because the evaluations in the Hovering Turn MTE have confirmed there is no practical need to design the yaw control axis to such high bandwidths for these types of large rotorcraft.

Analogous to the results from the pitch and roll short-term response evaluations discussed previously, where the HQRs showed a close dependency to the second-order command model natural frequency, results shown in Figure 57 from the yaw-axis evaluations in the Hovering Turn MTE illustrate the direct impact of the command model first-order yaw rate response time constant on the handling qualities. Major handling qualities improvements are shown in Figure 57 for a very modest increase in the time constant reciprocal. Also, the HQRs degrade again for the increasing response quickness, crossing the Level 1 handling qualities boundary for a first- -1 order rate response reciprocal of 2.5 s (i.e., 0.4 s time constant), according to the deficiencies and issues discussed above. The better handling qualities seem to be found between 0.5 and -1 1.5 s , independent of the time delay.

Time delay (s) 0.05 0.16 0.28 Level 3 Level 2 HQR Level 1 0 1 2 3 4 5 Time constant reciprocal (1/s) Figure 57. Correlation of average HQRs with reciprocals of the time constants of the commanded first-order rate response for a 40 ft offset.

Handling Qualities for Large Tiltrotor Using Translational Rate Command Rationale of Investigation The experimental results from the piloted simulations presented in the previous sections have demonstrated how an ACAH response type was insufficient to confer Level 1 handling qualities for a large tiltrotor in the Hover and Lateral Reposition Mission Task Elements (MTEs).

The primary issues were related to the objectionable motion induced at the pilot station because of the offset location from the center of gravity when rotating. Using a Translational Rate Command (TRC) control that eliminated the need to pitch or roll to maneuver was a natural progression. Furthermore, the tiltrotor configuration offers a solution that enables TRC without attitude changes, which helicopters cannot provide. This section presents analysis of results from further piloted simulations that apply a form of TRC, described above, that makes particular use of the tiltrotor control devices to enable maneuvering in translation with almost no angular (attitude) motion. This is achieved by using nacelle tilt to effect longitudinal translation and lateral rotor cyclic tilt for lateral translation. These were designed to act in conjunction with the conventional use of longitudinal cyclic and differential rotor thrust on the left and right rotors to regulate and maintain the pitch and roll attitude at the nominal “deck-level” datum position.

The control law was designed to the TRC criteria specified in ADS-33, and although there is no requirement to apply the military-focused ADS-33 specifications to the civilian LCTR2, it is considered the de-facto design standard for rotorcraft handling qualities and therefore a good basis for the control law design. This section also presents a brief description of the current criteria and background information, and an alternative short-term position response frequency- domain characterization proposed in this investigation.

ADS-33 TRC requirements. The ADS-33 TRC design criterion consists of two quantitative parameters, an equivalent rise time and a steady-state stick to control response sensitivity.

Further criteria specify “a qualitative first-order appearance” of the translational rate response to a step controller input is required [10]: • The pitch and roll attitudes shall not exhibit objectionable overshoots in response to a step cockpit controller input.

• Zero cockpit control force and deflection shall correspond to zero translational rate with respect to fixed objects, or to the landing point on a moving ship.

• There shall be no noticeable overshoots in the response of translational rate to control inputs. The gradient of translational rate with control input shall be smooth and continuous.

The ADS-33 criteria encompass a significant amount of research in their foundation, and it is useful to review this body of work to understand how they were established and also to compare the earlier analysis to results in this section.

ADS-33 criteria definition. The ADS-33 design criteria is built on data from a variety of sources, including some of the important work described in references [52,53,54] that contributed largely to the criteria selection. In particular, this work led to the established respective minimum and maximum rise times of 2.5 and 5 s that are recommended for the desired first-order translational response. The reason for a maximum limit is intuitive; if the rise time is too long, the aircraft response will be too sluggish for precise maneuvering. The cause for the minimum rise time is less obvious, but it is fundamentally linked to an implementation of TRC where an inner attitude loop is enclosed by an outer translational motion loop, and the translation is caused by changing the attitude of the aircraft. A minimum rise time is a compromise between achieving a quick enough translational response and mitigating abrupt attitude changes that would be induced by a high-bandwidth TRC response.

The other key TRC requirement in ADS-33 is the “Control Response,” which is the steady- state translational velocity response per unit stick. Again, reference [52] was the key source for establishing the boundaries. They consist of an upper and lower limit for a nonlinear shaping of the control sensitivity in ft/s/in. The shaping confers reduced control sensitivity between 3 and 6 ft/s/in for speeds of up to ∼ 10 knots and higher sensitivity for larger velocity commands.

The supporting data for the ADS-33 TRC criteria were a number of experimental analyses of TRC conducted in flight test, and in motion- and fixed-base simulation, on a variety of platforms including the X-22A ducted fan V/STOL aircraft [54,55,56], the AV-8B jet aircraft [57], and the XV-15 tiltrotor [45,58], as well as other generic types. Studies in references [54,55] reported on an in-flight simulation experiment using the X-22A variable stability aircraft. Highlights included the use of an inner/outer loop-style TRC control law using attitude changes. The experiment examined equivalent translational response rise times in the range of 1.5 to 4 s, and variation of the control response sensitivity in the range of 3 to 12 ft/s/in. Similar conclusions to reference [52] were arrived at, in that pilots did not like the attitude changes that came with this form of TRC.

Reference [54] describes how different pilots reacted to attitude changes in TRC. The results from the experiment were used to create a TRC handling qualities criterion that was reappraised in an analysis in reference [56]. The purpose of this follow-up study was to validate the use of fixed-base simulation for the prediction of the X-22A in-flight simulation TRC handling qualities. A key premise of the paper was that TRC criteria based on correlating regions of cross-plots of the equivalent rise time and the control/response sensitivity parameter (linear constant) were inconsistent in predicting the piloted handling qualities.

The alternate criteria in reference [56] used a frequency-domain approach of regions of predicted Level 1 and Level 2 handling qualities on a Bode plot of the translational velocity response to stick input. The envelopes were applied to both the magnitude and phase plots of the frequency response, and the different regions of the plot were annotated to indicate possible handling qualities problems if a system frequency response curve entered that region.

The study in reference [56] showed that this frequency-domain approach was superior in predicting the handling qualities, especially when used in conjunction with a secondary criterion that included a measure of the magnitude and abruptness of the attitude response. The paper reported that this attitude sensitivity aspect was an area of “critical concern” for pilots.

This secondary criterion was based on a similar sensitivity criterion from a study in reference [58] that investigated TRC using an XV-15 simulation. In this work, the TRC system sensitivity, stiffness, and damping were varied parametrically using simplified linear models. Here, the stiffness was akin to the rise-time parameter as it effectively determined the quickness of the response and, as it was an attitude-based TRC, it also consequently governed the magnitude and abruptness of the attitude response. Again, optimum values for the translational response sensitivity and stiffness featured a trade-off between fine control and attaining adequate translational response in gross maneuvering, as well as between having low enough time constants to provide precise, responsive control without large or abrupt attitude changes. The pilots preferred a TRC response that was more first-order in nature with less oscillations and overshoots in the velocity.

Reference [53] highlights the importance of this first-order characteristic that describes the use of Lower-Order Equivalent System (LOES) models to characterize the TRC response.

Reference [53] reports that better handling qualities were obtained where the translational ሶ response fit well to a first-order form such as in Eq. (37). In Eq. (37) ܺ represents the translational rate, ߜ is the pilot stick input, and ܭ and ܶ are the control response ௣௜௟௢௧ ௑ሶ ௑ሶ sensitivity and equivalent rise time, respectively. Degraded handling qualities were reported in reference [53] when the aircraft response characteristics required a third-order form to capture higher-order dynamics (i.e., the attitude dynamics were significantly affecting the TRC response). This reinforced the observation that these configurations are unacceptable because of the excessive attitude responses.

ሶ ܺ ܭ ܶ௑ሶ (37) ൌ ߜ ݏ൅ ͳ ௣௜௟௢௧ ௑ሶ The study in reference [53] also assesses the equivalent rise time and steady-state velocity response sensitivity of the TRC control laws. Their analysis (based on results from reference [45]), is in alignment with the others reported in that they identified an optimum rise time for handling qualities in the 2.5 to 5 s range. For the sensitivity characteristics, there was a general complaint that the maximum speed attainable ( ∼ 24 knots) in TRC was too low. However, one interesting observation made is that a trend of higher control sensitivity for attitude-based TRC can be accepted when the rise time increased, i.e., when more sluggish. The hypothesis derived from this observation was that the pilot ratings somewhat aligned with curves of constant attitude change per unit stick in TRC (this ratio being a function of both the rise time and sensitivity).

The underpinning aspect of all of this previous evidence was that attitude-based TRC was used, and that some characteristics of that approach bring limitations. This is a point not completely disregarded in the literature, as references [53,57] both discuss the possibilities of TRC using Direct Force Control (DFC) through forms of thrust vectoring. An analysis of DFC- based response types is presented in reference [59], which compares acceleration and translational rate response types using both DFC and attitude-based approaches. The study in reference [57] reports on a fixed-base simulation study based on the AV-8B aircraft. It highlights how DFC decouples the attitude response from the translational response and how the experiment compared TRC based on attitude changes, DFC, and a combination of the two. A key result was that the pilots liked the attitude-only TRC systems the least and unanimously preferred the DFC systems. The HQRs recorded in the experiment were plotted against the criteria from both the previous Calspan X-22A [54] and the Systems Technology, Inc. (STI) XV-15-based studies [53]. The ratings for the attitude TRC did not match well with either criteria, predominantly because the ratings were mostly connected with the attitude changing aspect, something that the rise-time vs. steady-state velocity sensitivity criteria do not explicitly cover.

When the DFC ratings were compared, much better correlation was achieved, particularly with the Calspan boundaries.

Another important experimental result achieved using the DFC-based TRC was that increasingly better HQRs were obtained with increasingly quicker (shorter) rise times. Rise times down to 0.7 s were examined, which conferred Level 1 (HQR ” 3) ratings. This is an important result, as the 2.5 s minimum acceptable level reported in a number of the attitude- based TRC studies (and ADS-33) was no longer appropriate because the attitude changes were no longer a factor.

This conclusion of the superiority of DFC TRC response type is not, however, universal. The study in reference [53] also briefly discusses DFC vs. attitude TRC and states, “There is some evidence that complete decoupling between attitude and horizontal translation is not necessarily superior.” It goes on to refer to the study in reference [59] and another using the X-14A V/STOL aircraft. Reference [59] reports that the prime reason that the DFC-based TRC was rated worse was because of negative ride quality effects caused by the generation of “non-gravitational” reaction forces acting on the pilot when maneuvering. It is important to note that the study in reference [59] featured motion cueing as opposed to the fixed-base simulation in reference [57].

Another study of TRC using DFC is a simulation experiment in the NASA VMS of an Advanced STOVL (ASTOVL) aircraft [60,61]. This study has a number of useful parallels with the current research in this paper, i.e., it is a motion-based study in the NASA VMS, and it features an analysis of a hovering vehicle using a DFC form of TRC (in the longitudinal axis). The discussion of the performance of the TRC control law focused much more on frequency-domain parameters such as bandwidth and phase delay.

For longitudinal control, the results in references [60,61] showed that bandwidths (based on the í 45 deg phase margin frequency from the translational velocity to stick input frequency response) of between 0.4 and 0.9 rad/s conferred consistently satisfactory handling qualities, whereas values below 0.22 rad/s and above 1.1 rad/s were only adequate. The authors refer to the ADS-33 rise-time criteria of 2.5 and 5 s and compute that for an equivalent first-order response, these equate to bandwidths of 0.4 and 0.2 rad/s respectively. The authors note that the 0.2 rad/s value agrees well with their results while, at the other end of the range, their results indicate an ability to accept much quicker (higher bandwidth/short rise-time) TRC response with acceptable handling qualities. This discrepancy is attributed to “differences in implementation of the longitudinal velocity command systems,” which alludes to the previously discussed issues connected with attitude-based TRC. Another insight brought to the fore was through the use of the phase delay parameter, which highlighted that delays as high as 0.78 s could be tolerated before the handling qualities degraded to adequate. It was reported that the pilots could sense the delay but were able to compensate without too much effort until the delays became extreme.

The authors suggested the Level 1–2 boundary based on phase delay is in the region of 0.4– 0.6 s.

Some of the TRC research literature presented has included tiltrotors, which are of particular relevance to the current research. However, the tiltrotor research has not reported any experimentation with the DFC form of TRC using nacelle tilt to vector the thrust (for longitudinal translation). The only mention of such an approach was a consideration in reference [45] to implement a “mast-angle controller” for the XV-15 simulation. This proposed development was abandoned when it became apparent that, as a consequence of the limited performance of the nacelle actuators, the system would possess a very low ߜȀݑ bandwidth of around 0.7 rad/s, ௟௢௡ although it is not apparent which measure of bandwidth was used.

The key issues of how the ADS-33 TRC criteria were established have been discussed, as well as the implementation-specific aspects that underpin them. It has been shown that there are a number of useful similarities in the body of work in the literature to the current LCTR2 research. However, there are a number of aspects of the LCTR2 control architecture that are unaddressed in the current literature that require new research, including the influence of nacelle actuation characteristics on this form of nacelle-based TRC and its impact on large tiltrotor handling qualities.

Short-term position response characterization of nacelle-based TRC. As described in the preceding discussion, the TRC response characteristics have been defined and specified using a mixture of qualitative descriptions and quantitative time- and frequency-domain response criteria. The research presented in the following sections shows that the current ADS- 33 criteria does not satisfactorily predict the handling qualities for the TRC control laws developed for the LCTR2 configuration. It also shows that response delays due to actuator dynamics, as well as implementation-specific aspects, mean that although a particular configuration meets the Level 1 Handling Qualities (HQ) requirements, other factors affecting the slope of the frequency response phase curve at high frequencies lead to degraded handling qualities. Frequency-domain characterization using parameters such as bandwidth and phase delay is a robust way of defining response characteristics for good handling qualities using rate and attitude response types, and in most cases supersedes the use of time-domain parameters in up-to-date rotary and fixed-wing HQ requirements. For the TRC response, the longitudinal axis (the equivalent inceptor/response variable pairs would be appropriate for the lateral case) could be potentially characterized either by the ߜȀݑ or the ܺ ߜȀ frequency response, an ௟௢௡ ௟௢௡ extension of the definitions employed in ADS-33 for attitude responses applied to the translational response. While ߜȀݑ at first may seem a more natural representation of the ௟௢௡ aircraft TRC response, neither the gain or phase bandwidth definitions are representative of pilot-in-the-loop operating frequencies for position regulation tasks, according to the discussion above. Herein, the ܺ ߜȀ frequency response was chosen to characterize the TRC response, ௟௢௡ for the different experimental variants, as it was deemed to be a more suitable characterization for pilot-in-the-loop position control tasks, paralleling the approach by Franklin et al. [61] presented previously. Sections below, which consider the TRC control laws, demonstrate that the combination of ܺ ߜȀ phase delay and bandwidth correlate well with the piloted handling ௟௢௡ qualities and, therefore, offer useful metrics for future TRC design specifications.

Figures 58 and 59 show the relationship of the closed-loop ܺ ߜȀ frequency response ௟௢௡ phase bandwidth and delay values for the linearized model with the TRC control law command model equivalent rise times set at 2.5 and 5 s, and various nacelle actuator natural frequencies.

Also shown are the phase bandwidth and delay for the cyclic-augmented control law, described above, which uses a 3 rad/s bandwidth nacelle actuator, and the corresponding lateral response ω ≈ 0.5-0.8 rad/s BWgain 3 rad/s -20 4 rad/s 8 rad/s -40 Magnitude (dB) 16 rad/s -60 -90 -135 Φ ≈ 45 deg M -180 ω ≈ 0.2 rad/s BWphase -225 -270 Phase (deg) ω ≈ 0.8-1.1 rad/s -315 -360 0.1 1 10 Frequency (rad/s) Τ Figure 58. Closed-loop ࢾ ࢄ frequency response for varying actuator bandwidth (5 s ࢔࢕࢒ equivalent rise time).

1.0 BW for nominal BW for nominal 5 s rise time 2.5 s rise time Nacelle 0.8 actuator bandwidth (3 rad/s) (s) (3 rad/s) p 0.6 τ (4 rad/s) (4 rad/s) (3 rad/s) Lateral 0.4 TRC Phase delay, Cyclic- augmented (8 rad/s) 0.2 (8 rad/s) (16 rad/s) 0 0.1 0.2 0.3 0.4 0.5 Bandwidth, ω (rad/s) BW Figure 59. Closed-loop ࢾ ࢄ Τ bandwidth and phase delay for experimental TRC ࢔࢕࢒ configurations.

specification based on the ܻ ߜȀ transfer function. The latter illustrates the typical phase delays ௟௔௧ attainable with rotor-effected TRC.

Equivalent rise time has a fundamental relationship with the phase bandwidth, ߱ , as ஻ௐ ౦౞౗౩౛ defined from the Bode plot of the ܺ ߜȀ transfer function shown in Figure 58, but has much less ௟௢௡ effect on the phase delay, ߬ . The cases with equivalent rise time of 5 s shown in Figure 58 all ௣ ೉ had a nominal phase bandwidth of approximately 0.2 rad/s, whereas the 2.5 s equivalent rise time conferred a phase bandwidth closer to 0.36 rad/s (Figure 59). The actuator bandwidth, conversely, predominantly influenced the phase delay. The 3 rad/s actuator, for example, confers a phase delay in the order of 650 ms, but its bandwidth is basically unaffected. A progressive reduction in the phase delay is shown for increasing actuator bandwidths, down to about 200 ms for the 8 and 16 rad/s actuator configurations. The 16 rad/s actuator configuration displays a prominent phase recovery in Figure 58 but conveys minimal phase delay improvements over the 8 rad/s actuator configuration (Figure 59). These issues are further discussed below. Finally, the cyclic-augmented configuration confers a 200 ms phase delay reduction over the baseline configuration with the 3 rad/s actuator. Phase bandwidth was still led by the equivalent rise time and was accordingly close to 0.2 rad/s for this configuration.

Figures 60 and 61 use the qLPV LCTR2 model with nonlinear actuators and show the results of changing the nacelle actuator rate limits on the ܺ ߜȀ short-term dynamic response ௟௢௡ 0.1-inch input amplitude 0.5-inch input amplitude 0.2 0.2 Nacelle bandwidth point designs 0.15 0.15 3 rad/s 3 rad/s 8 rad/s 8 rad/s 0.1 0.1 4 rad/s 4 rad/s Bandwidth (rad/s) Bandwidth (rad/s) lon lon 0.05 0.05 δ δ X/ X/ 0 0 0 2 4 6 8 10 0 2 4 6 8 10 Nacelle Rate-limit (deg/s) Nacelle Rate-limit (deg/s) or Nacelle Actuator BW (rad/s) or Nacelle Actuator BW (rad/s) 1.0-inch input amplitude 2.0-inch input amplitude 0.2 0.2 Nacelle Actuator BW Nacelle Rate-limit 0.15 0.15 3 rad/s 3 rad/s 8 rad/s 8 rad/s 0.1 0.1 4 rad/s 4 rad/s Bandwidth (rad/s) Bandwidth (rad/s) lon lon 0.05 0.05 δ δ X/ X/ 0 0 0 2 4 6 8 10 0 2 4 6 8 10 Nacelle Rate-limit (deg/s) Nacelle Rate-limit (deg/s) or Nacelle Actuator BW (rad/s) or Nacelle Actuator BW (rad/s) Figure 60. ࢾ ࢄ Τ bandwidth from varying amplitude frequency sweeps for varying ࢔࢕࢒ nacelle actuator rate limits and bandwidths (10 (ft/s)/in control/response sensitivity).

0.1-inch input amplitude 0.5-inch input amplitude 2.0 2.0 1.5 1.5 1.0 1.0 Phase Delay (s) Phase Delay (s) 3 rad/s 3 rad/s lon lon 0.5 δ 0.5 δ 4 rad/s 4 rad/s X/ X/ 8 rad/s 8 rad/s 0 0 0 2 4 6 8 10 0 2 4 6 8 10 Nacelle Rate-limit (deg/s) Nacelle Rate-limit (deg/s) or Nacelle Actuator BW (rad/s) or Nacelle Actuator BW (rad/s) 1.0-inch input amplitude 2.0-inch input amplitude 2.0 2.0 Nacelle Actuator BW Nacelle Rate-limit 1.5 1.5 Actuator point designs 1.0 1.0 3 rad/s Phase Delay (s) Phase Delay (s) 3 rad/s 4 rad/s lon lon 0.5 δ 0.5 δ 8 rad/s 4 rad/s X/ X/ 8 rad/s 0 0 0 2 4 6 8 10 0 2 4 6 8 10 Nacelle Rate-limit (deg/s) Nacelle Rate-limit (deg/s) or Nacelle Actuator BW (rad/s) or Nacelle Actuator BW (rad/s) Τ Figure 61. ࢾ ࢄ phase delay from varying amplitude frequency sweeps for varying ࢔࢕࢒ nacelle actuator rate limits and bandwidths (10 (ft/s)/in control/response sensitivity).

parameters: bandwidth, ߱ , and phase delay, ߬ , and compares it to the effect of varying ஻ௐ ௣ ೉ ೉ the nacelle bandwidth by independently sweeping over a range of nacelle actuator natural frequencies or rate limits. These were computed using frequency sweeps at four different input amplitudes of the longitudinal stick input, ߜ , shown in each of the subplots. The sweeps were ௟௢௡ performed on the baseline configuration (8 rad/s bandwidth, 7.5 deg/s rate limit) with one of the two parameters held constant at these values while the other was varied. On each of the charts the 3, 4, and 8 rad/s point design configurations from the piloted experiment are also plotted for comparison; the key difference between these cases and the sweep results is that their control law gains have been optimized for a specific combination of actuator bandwidth and rate-limit point designs.

The effect on the longitudinal position response bandwidth shown in Figure 60 is minimal from either parameter variation except at very low actuator bandwidth or rate limits, where there are some variations. The longitudinal position response phase delay results for the same rate- limit and bandwidth variations are shown in Figure 61. Here there are continuous trends of increasing delay with both bandwidth and rate limit, with both trends showing differing amounts of sensitivity to the input amplitude. At low amplitudes the rate limit does not influence the phase delay until it gets very low, whereas bandwidth has an effect at all amplitudes. As the amplitude increases, the effect of the variation in the two parameters becomes almost indistinguishable for the range examined, despite the rate-limiting being a nonlinear discontinuity and the bandwidth being entirely a linear dynamic parameter. It is also useful to note that the experimental point designs all have smaller phase delays than the sweep analysis points, implying that the optimization of the TRC gains appears to bring some noticeable benefit. Further discussion of results from the effects in Figures 60 and 61 are provided in subsequent sections.

Overview of results. The handling qualities of various LCTR2 TRC control configurations encompassing variations of the nacelle actuation rate limit and natural frequency, and other design aspects of the control law, are assessed. TRC configurations are compared against each other and to the best-performing ACAH in the Lateral Reposition and Hover MTEs in further piloted simulation experiments in the NASA Ames Vertical Motion Simulator (VMS). The TRC discussion concludes with analysis of a “cyclic-augmented TRC” design that uses additional longitudinal cyclic inputs as part of the TRC control law to address concerns that only lower nacelle actuator bandwidths may be possible to alleviate the demand on the primary nacelle actuators to create the translational response. Results show that the TRC control system design did not confer consistent Level 1 handling qualities. This study called for the fundamental review of the ADS-33 design criteria to understand their relationship with the handling qualities with this type of TRC control law configuration, and ultimately identify design characteristics conducive to Level 1 handling qualities.

The second-order nacelle actuator dynamics was commonly fixed with a value of 8 rad/s for the natural frequency/bandwidth. This was identified as a potentially unfeasibly high value for such a large actuator. Therefore, further research was also required to investigate the handling qualities trends when reducing this actuator bandwidth. This analysis, reported below, sought to identify the minimum bandwidth required to maintain Level 1 handling qualities with this type of TRC control system.

Small non-minimum phase pitch changes in response to longitudinal stick inputs were found to negatively impact the handling qualities of this TRC control system design. Depending on the actuator rate limits, the aircraft response had a coupled pitch motion that was counterintuitive in direction sense and often obtrusive. Reducing rate limits reduced this problem but at the cost of degrading the overall TRC response quickness (or bandwidth). The discussion below describes the results of varying rate limit on the initial TRC control laws.

Further experimentation showed that handling qualities improvements could be achieved by simply reducing the tendency to pitch in TRC mode. This was achieved by developing a TRC control law that incorporated a crossfeed signal between nacelle rate and longitudinal cyclic.

The intent was to achieve a “purer” response, i.e., translational motion only with no coupled attitude perturbations. Better ride qualities were not the only advantage of this system. The flight dynamics aspects of this improvement are discussed in detail further below. Analysis of the influence of rotor longitudinal flapping dynamics, nacelle actuator limits, and piloted input amplitude showed that the crossfeed-improved TRC not only reduced the pitching response to almost zero, but also improved the TRC position response phase delay characteristics.

Appendix B describes how the key effect of this crossfeed gain was to reduce the tendency for the rotor flapping to lag behind the nacelle rotations.

Finally, the analysis reported below sought to investigate techniques to maintain the Level 1 handling qualities at lower nacelle actuator bandwidths, i.e., second-order dynamics and (equivalently) rate limits, through additional control law modifications.

Improvement of LCTR2 Handling Qualities With TRC Results for select ACAH and TRC configurations chosen for comparison in the Lateral Reposition and Hover MTEs are presented in this section. When selecting the LCTR2 short- term attitude response characteristics for comparison, care was taken to ensure sensible ride qualities, thus precluding higher bandwidth control response configurations. A methodical verification of various configurations was conducted with the project pilot prior to the commencement of the experiment. This process confirmed the trends from previous experiences, i.e., that higher response bandwidths result in negative ride qualities. The comparison ACAH therefore represents the best trade-off between handling and ride qualities.

The TRC control system used the conventional center stick controller. The inceptor gradient and break-out force-feel characteristics were configured for ACAH at 0.9 lb/in and 1 lb in the longitudinal direction and 0.7 lb/in and 0.6 lb in the lateral direction. Given these force-feel characteristics, center stick TRC control sensitivities were adjusted to provide the best-expected task performance with acceptable forces for the required inceptor displacements. The evaluation maneuver had constraints for this center stick TRC implementation that required a minimum translational velocity of 25 ft/s (~15 knots). Only directly proportional variations in translational rate with control deflection were investigated (i.e., constant sensitivity gains).

Lateral Reposition MTE. Piloted evaluations in the Lateral Reposition MTE showed that significant handling qualities improvements were conferred with TRC, when compared to the ACAH and “Hybrid” response types (Figure 62). The TRC configuration in Figure 62 employed a 15 ft/s/in sensitivity and a 5 s rise time. As shown, this configuration was consistently rated HQR 2–3. In contrast, ACAH was mostly rated HQR 4 (with a few HQR 3 marks and one HQR 6).

Finally, the Hybrid mode fell somewhere in between the TRC and the ACAH response types in terms of their handling qualities (most configurations were rated HQR 3). Recall that the “Hybrid” system was mechanized such that a center stick displacement greater than 1 inch from center would command roll attitude at a 3.45 deg/in sensitivity (0.3 of the baseline ACAH command model) in addition to the normal translational lateral rate commanded. Within this 1-inch displacement range, the system behaved identically to the TRC control system.

Unsurprisingly, the experimental observations suggested that longitudinal position control with the ACAH response type was challenging because of the pitch/heave coupling of pilot control activity associated with the significantly forward position of the pilot station. A survey of the pilot evaluation comments indicated that high workload in the longitudinal axis and altitude maintenance were contributing reasons for the elevated handling qualities ratings (HQRs) assigned to the ACAH mode. Moreover, the high bank angles associated with the ACAH configuration in the Lateral Reposition MTE were a major cause of performance degradation, initiating a sequence of events, to include the loss of usable visual cues, which significantly Level 3 Level 2 HQR 3.9 3.3 Level 1 2.4 ACAH TRC Hybrid Configuration Figure 62. Comparison of the HQRs for the ACAH, TRC, and Hybrid response type control configurations in the Lateral Reposition MTE.

increased the pilot workload. Pilots tended to lose sight of the longitudinal position cueing, especially during the deceleration when commanding large bank angles to arrest the lateral rates at the hover point. Additionally, a tendency to pitch up could cause the pilots to lose the lateral position cue.

It should be noted that the absence of an Altitude Hold mode contributed to a tendency to “balloon,” or gain altitude easily, during the deceleration phase of the maneuver. When decelerating aggressively the control system would see the sudden change in the body ݖ -axis velocity component as an un-commanded sink rate. Differences in the commanded and actual rates, if not adjusted quickly by the pilot, would result in the control system increasing power rather suddenly. This, in conjunction with the sudden change in aerodynamic angle of attack, naturally caused the aircraft to climb.

By reducing the bank angle changes, the TRC control response, and to a lesser degree the Hybrid response type, conferred notable improvements to the handling qualities in the Lateral Reposition MTE. Without the large bank angle changes, pilots did not lose sight of the runway as readily. Also the aircraft did not experience significant changes in altitude, such that the power/altitude maintenance did not require attention. Minimization of pitch attitude changes also curtailed the compelling pitch/heave perception issues associated with the center of gravity offset. Pilots described the lack of bank as “odd,” but agreed it was possibly the right way to fly this type of aircraft, and the HQRs confirmed their preference and better performance. Less significantly, compared to ACAH, the TRC and Hybrid configurations required larger lateral input. Pilots often mentioned that stick forces generated with these configurations were a little high. With the Hybrid mode, some of the issues related to the high bank angles, such as the loss of visual cues and the power management requirements, were lessened, but not entirely eliminated. Also, the Hybrid mode was not without its own faults, and issues with the phasing in and out of the bank angle felt somewhat unpredictable to two of the evaluation pilots.

Hover MTE. Ratings comparing select ACAH and TRC configurations in the Hover MTE are shown in Figure 63. It shows drastic improvements in the average ratings for the two TRC configurations (5.2 for ACAH, 2.1 for a TRC variant with 8 rad/s bandwidth nacelle actuators, and 2.8 for the so-called “cyclic-augmented” TRC). The TRC results presented in Figure 63 are for a 10 ft/s/in sensitivity and a 5 s first-order response equivalent rise time. These results illustrate the substantial, potential handling qualities improvements that are attainable with a * Cyclic-Augmented TRC Level 3 Level 2 3 rad/s nacelle act.

5.2 HQR 8 rad/s nacelle act.

Level 1 2.8 2.1 ACAH TRC TRC* Configuration Figure 63. Comparison of LCTR2 handling qualities for select TRC implementations relative to ACAH in the Hover MTE.

Table 14. TRC response parameters.

Control Nominal rise sensitivity time ((ft/s)/in) (s) 15 5.0 10* 5.0* 5 5.0 15 2.5 10 2.5 5 2.5 * Baseline TRC response type, provided necessary nacelle actuator bandwidth is installed, and how good handling qualities can be retained by quickening of the TRC response via rotor cyclic inputs with a reduced nacelle bandwidth. The cyclic-augmented TRC control law generated a sharp longitudinal cyclic pulse in response to the velocity command generated by the pilot. This provided the crucial initial longitudinal acceleration desired for the short-term TRC response quickening. As the pitch attitude built up, and once the nacelle actuator caught up with the command, the controller would effectively resume the attitude regulation role removing the initial cyclic input.

The outcome of a systematic analysis of the ADS-33 TRC design criteria and various fundamental design aspects of the nacelle actuators, encompassing a range of control sensitivity, equivalent rise time, and nacelle actuator bandwidth and saturation limit variants, led to the result that handling qualities improvements for the various TRC versions were generally not as definitive as those shown in Figure 63. Many of these results are shown in the subsequent discussions. An average improvement of the ratings suggested a general increased weighting of the HQRs towards Level 1 with the TRC configurations, compared to ACAH.

However, a handling qualities cliff was exposed, evidenced by the fact that a number of pilots rated the handling qualities with TRC to be either worse or equal to those with ACAH control mode. This is the focus of discussion further below. Consequently, minimum and maximum ratings for the various TRC versions conferred a range of ratings, a range equivalent or even greater than that for ACAH.

Despite the variability in the TRC HQRs, on closure of the velocity feedback loops, all TRC configurations showed a notable reduction in the turbulence-generated motion of the aircraft.

Once pilots had stabilized in the hover, workload ceased being a major factor, and pilots reported the aircraft appeared to reject turbulence very effectively. The critical sub-phase of the maneuver was consistently observed to be the deceleration into the hover, which appeared in some occasions to drive aggressive pilot compensation and thus expose the handling qualities cliff.

Effect of Control Sensitivity and Equivalent Rise Time The control sensitivity and equivalent rise time parameters are the focus of this section.

These parameters define the fundamental behavior of the TRC response and form the core of the ADS-33 HQ specifications for TRC as described in the rationale of investigation section. In the control law for the LCTR2 nacelle-based TRC, these parameters were used directly in the model-following command model blocks to specify the desired first-order response type, which the aircraft then attempted to track as closely as possible via the feedback control loops.

Table 14 lists the TRC control system parameters tested, including the control/response sensitivity gradients and nominal equivalent rise times. The baseline TRC control system case consisted of a 10 (ft/s)/in control/response sensitivity, a 5 s equivalent rise time, and a 0.0735 in/(deg/s) nacelle rate to longitudinal cyclic crossfeed. This control system also employed high bandwidth actuators (8 rad/s) to avoid cutoff of control inputs. Additional control system gain sets basically enforce variations in the control/response parameter and the equivalent rise time.

Summarized in Figure 64, HQRs for the varying control/response sensitivity and equivalent rise-time cases highlight two salient results: first, that 10 (ft/s)/in was the preferred sensitivity, and second, that the increased phase bandwidth associated with the 2.5 s rise time conferred only a slight improvement in the HQRs over the 5 s cases. Consequently, the experimental baseline design conferred the best handling qualities of the range of configurations selected.

Pilots generally indicated that the high stick sensitivity value resulted in the aircraft response being “too jerky.” High control sensitivity also made this configuration much more susceptible to rate-limiting. On the other hand, low stick control sensitivity elicited complaints that excessively large inputs were required. The control sensitivity did, however, offer an added protection against rate-limiting of the nacelle actuators. In interpreting these results, it is important to note that while the control/response sensitivity was varied, the control stick force gradient was left invariant. The potential effect of this parameter should not be discounted when establishing overarching conclusions about the control sensitivity, since it has a direct effect on the forces and thus the dynamic response of the stick. The differences between the VMS and flight motion cueing may also need to be considered before reaching a final conclusion on the appropriate control sensitivities.

A ܺ ߜȀ phase bandwidth improvement from just below 0.2 rad/s to 0.36 rad/s due to a ௟௢௡ smaller rise time did not appear to confer significant improvements in the handling qualities, although it did appear to improve the worst case scenarios. The reduced rise time did convey to the pilots a slight sense of increased quickness in the response when decelerating, and thus improved the ability to decelerate within the required time constraints.

A more detailed analysis of the piloted evaluations indicates that three pilots rated the 15 ft/s/in (high) sensitivity, 5 s rise time case in Level 2 (HQR 5/4/4). Comments from these pilots about the deficiencies pointed to, first, a tendency to over-control in the longitudinal axis, and second, a sharp lateral response. In particular, two of the pilots, and importantly, the pilot who rated the aircraft configuration HQR 5, indicated a tendency to over-control in the longitudinal axis; this became apparent during the deceleration and hover stabilization phase of Equivalent rise time 2.5 s 5 s Level 3 Level 2 HQR Level 1 5 10 15 Control sensitivity ((ft/s)/in) Figure 64. HQRs for varying equivalent rise times and steady-state control response sensitivities (8 rad/s actuator).

the maneuver. Other comments pointed to a very sharp lateral response, to the point of feeling disharmonious with the longitudinal response, but this did not necessarily intimate there was a deficiency in the longitudinal axis per se.

This disharmony observation was even more prevalent for the 15 ft/s/in sensitivity, which, when combined with the 2.5 s equivalent rise time, was greatly exacerbating the sharpness of the initial response. This configuration was often described as “uncomfortable,” and pilots consistently felt they could not be aggressive with it because of the “choppy” nature of the response. A “noticeable and distracting” strong heave perception described as “objectionable” was also reported by some pilots. This configuration, however, presented no tendency to over- control as the 5 s rise time/15 ft/s/in sensitivity case did, which made it perform quite well, especially in the deceleration and hover stabilization phase. The lower rise time fundamentally allowed pilots to achieve desired precision in capturing the hover position simply by releasing the stick and bringing back to center, or with very minimal required input reversal to stop.

The opposite (low) end of the control sensitivity range saw deficiencies in the aircraft characteristics of a different nature. The main objectionable characteristics were all derived from the fact that pilots now had to employ larger displacements, both steady and dynamic, in order to get a response of the aircraft. Associated with the large displacements were large forces, since stick force gradients were left unchanged for all configurations. Steady displacements were uncomfortable because of the large forces being sustained for prolonged periods of time, but these did not necessarily have an impact on the handling qualities. More importantly, in dynamic situations this combination of displacement and force gave the aircraft response a “false sense of sluggishness,” almost as if the aircraft felt “heavier.” This frequently induced some pilots to increase their aggressiveness in order to achieve the desired deceleration performance requirements. It also made velocity maintenance more difficult for some pilots.

None of these issues were significantly improved by using the lower equivalent rise time, although this did slightly improve the ability to capture a stable hover.

Nacelle Bandwidth Effects Another key parameter assessed was the nacelle actuator bandwidth, characterized by the natural frequency of the second-order actuator dynamics. Four values of natural frequency were chosen, summarized in Table 15. The selection of these values was driven by the experimental handling qualities and flight control requirements. A rigid wing structure was assumed, and any potential structural implications were disregarded at this stage. A preliminary assessment in piloted simulation with the experimental project pilot suggested that a 3 rad/s bandwidth represented the lowest practicable value for the baseline TRC control system design used in this research. Lower bandwidths led to severe controllability issues. A baseline damping ratio of 1 was chosen to ensure the quickest nacelle response for a given bandwidth, but without displaying any natural oscillatory behavior.

Table 15. Nacelle actuator configurations.

Bandwidth Rate Limits (rad/s) (deg/s) 3 5.0 4 5.0 8 7.5 16 7.5 Control implications of nacelle actuator bandwidth. Inclusion of nacelle-tilt actuator dynamics with increasingly higher actuation bandwidth (natural frequency) may cause potentially undesirable excitations of higher frequency dynamics in the longitudinal velocity open-loop response. This impacts the stability margin characteristics, as well as the closed-loop end-to-end response. Excitations in the pitch response are also expected because of the coupled nature of the longitudinal dynamics, leading to a range of handling and ride qualities issues that may impact the control system feedback design. While only the rigid body fuselage dynamics have been considered in this study, airframe structural modes have been recently found to impact the various aspects of control system design [62], making these considerations increasingly relevant.

Stability and performance design trade-off . Given a constant crossover frequency, an increment in the actuator bandwidth directly translates into an increase of the phase stability margin and the open-loop í 180 deg phase crossover frequency. This is, of course, assuming the actuator bandwidth is greater than the open-loop crossover frequency. In this particular problem, this was also accompanied by a slight reduction of the gain margins. A control system design optimization, again using CONDUIT [46], was performed for each actuator natural frequency value to determine a set of feedback gains that would ensure 45 deg stability phase margins in both the lateral and longitudinal translational axes, and 38 deg stability phase margins in the pitch and roll axes, as per the findings of the investigation of stability margins for large rotorcraft presented previously. The optimization strategy was to maximize the disturbance rejection bandwidth (DRB) in the longitudinal translational axis for a given set of actuator dynamics, while minimizing the margins to the allowable extent (Figure 65).

Open-loop frequency responses shown in Figure 66 corresponding to the 4, 8, and 16 rad/s nacelle actuator bandwidth configurations illustrate the gain margin reduction trend and also the increasing values of the open-loop crossover frequency. This positive crossover frequency trend was indicative of the closed-loop performance improvements of the velocity feedback regulator, such as tracking performance and disturbance rejection, that were afforded by increasing the nacelle actuator bandwidth. Incidentally, note that additional lead compensation is required to improve tracking of the command model output beyond these open-loop crossover frequencies.

4 rad/s 3 rad/s 2 rad/s 8 rad/s Gain Margin (dB) 16 rad/s 0 0.2 0.4 0.6 0.8 1.0 Disturbance Rejection Bandwidth (rad/s) Figure 65. Longitudinal velocity disturbance rejection bandwidth and gain margin feedback characteristics for varying actuator bandwidths.

ω ≈ 2.4 rad/s c GM ≈ 6 dB ω ≈ 0.5 rad/s c -20 -40 Magnitude (dB) -60 -80 Increasing ω ( ω ≈ 1.7-7.7 rad/s) 180 180 -90 PM ≈ 45 deg -180 Actuator Bandwidth 2 rad/s -270 4 rad/s Phase (deg) -360 8 rad/s 16 rad/s -450 0.1 1 10 Frequency (rad/s) Figure 66. Velocity open-loop frequency response for varying actuator bandwidth.

Model-following performance . In this model-following control system, the required additional lead compensation was provided by the feedforward controller. The overall influence of the nacelle actuator bandwidth on the command model-following performance, with the added lead compensation of the feedforward inverse model controller, is illustrated in Figure 67, which shows the frequency responses of the closed-loop transfer function relating the longitudinal velocity to the velocity command ( ݑ in Figure 9) for the various configurations. Inspection of ௖௠ௗ the frequency responses in Figure 67 suggested that a configuration using the 2 rad/s bandwidth actuator would track the command model output in a satisfactory manner at frequencies below 0.8 rad/s (defined by the point where the response phase is 45 deg off the commanded input). This configuration was ultimately deemed unacceptable on preliminary assessment by the project pilot. Instead, a configuration using a 3 rad/s actuator, offering a model-following bandwidth of 1.2 rad/s, was tested. By comparison, the configuration using the 4 rad/s actuator had a model-following bandwidth of 1.5 rad/s, and this increased to 4.8 rad/s for the configuration with an 8 rad/s actuator bandwidth.

The differences in the frequency-response magnitude (and phase) at the higher excitation frequencies for the various nacelle actuator bandwidths were attributed mainly to unmodeled actuator dynamics in the inverse model used in the feedforward control. To understand the impact of these unmodeled dynamics it was instructive to look at the analytical expression of the transfer function of the frequency responses in Figure 67. Comprising the feedforward controller inverse model dynamics in addition to those of the closed-loop feedback controller, this transfer function can be expressed, generally, as: ଵ ఛ ௦ ෨ ೐೜ ܩ ܩሻݏሺ ሻݏሺ ܩሻݏሺ ି݁ሻݏሺ ݑ ܭ ௨ఉ ௨ఉ ௨ ௨ఉ ೎೘೏ ೘ି ೎೘೏ (38) ൌ ൅  ݑ ͳ ൅ ܭ ܩሻݏሺ ሻݏሺ ͳ ൅ ܭ ܩሻݏሺ ሻݏሺ ௖௠ௗ ௨ ௨ఉ ௨ ௨ఉ ೎೘೏ ೎೘೏ Actuator Bandwidth -20 2 rad/s Effect of feedforward control 4 rad/s Effect of feedforward control -40 8 rad/s Magnitude (dB) 16 rad/s -60 -45 -90 -180 Phase (deg) -270 -360 0.1 1 10 Frequency (rad/s) Τ Figure 67. Closed-loop ࢛࢛ frequency response for varying actuator bandwidth.

ࢊ࢓ࢉ ଵ ఛ ௦ ೐೜ ෨ ݁ሻݏሺ Here, the transfer function ܩ represents the inverse model dynamics of Eq. (26).

௨ఉ ೘ି ఛ ௦ ೐೜ Barring the ି݁ factor that arises from the equivalent time delay of the dynamic inverse model implementation, the transfer function of the feedforward controller effectively approximates the closed-loop sensitivity transfer function: ͳ ሺݏሻ ൌ ܵ , ܩሻݏሺ ͳ ൅ ܭ ሻݏሺ ௨ ௨ఉ ೎೘೏ hence, providing the lead compensation necessary to improve the tracking performance for input frequencies above the open-loop crossover frequency. The nacelle actuator dynamics were not accounted for in the inverse model. Therefore, they were not adequately eliminated from the feedforward controller and thus reflect in the frequency responses of Figure 67 at these higher frequencies.

Incidentally, the frequency responses in Figure 67 approximate the theoretical pure time delay response behavior expected of the model-following control system architecture. The closest approximation, for a ߬ of 0.293 s, was achieved with the 8 rad/s configuration, ௘௤ because the bare-airframe dynamics for this actuator configuration were more accurately modeled by the approximation of Eq. (26). Indeed, if a perfect inversion of the dynamics were attainable, such that: ଵ ݏ ݍ ෨ ܩ ܩሻݏሺ ݁߬݁ሻݏሺ ൌ ͳ , ௨ఉ ௨ఉ ೎೘೏ ೘ି then the transfer function of Eq. (38) would simplify to the pure time delay transfer function ఛ ௦ ೐೜ ି݁ , independent of nacelle actuator bandwidth. A corollary to this result is that the theoretical model-following performance is a function only of the equivalent time delay, ߬ . Presumably ௘௤ some amount of delay would still be required in the approximation of the bare-airframe dynamics, but what this value of ߬ would be in this scenario is unclear.

௘௤ This was a key result, suggesting that a more sophisticated feedforward control system may achieve improved model-following performance, even with low-bandwidth actuators. This is a largely hypothetical question, beyond the scope of this study, however. The current approach offered a conservative, tractable control system design approach suitable for investigating these fundamental handling qualities issues.

Effect on short-term TRC response characterization. From an experimental standpoint, the more important effect of the nacelle actuator dynamics on the phase characteristics of Figure 67 was the effect on the phase delay of the position response to pilot input. This was illustrated by the longitudinal position response ܺ ߜȀ Bode plot in Figure 58 for the four primary actuator ௟௢௡ configurations. Incidentally, the closed-loop response for the 16 rad/s actuator configuration had a marked phase recovery due to the extra lead compensation afforded by the feedforward controller. Despite this recovery, the 16 rad/s actuator bandwidth did not confer significant phase delay reductions over the 8 rad/s case, suggesting no further advantage is gained by increasing the actuator bandwidth.

It is further noted that the í 180 deg phase curve crossover point for the closed-loop ܺ ߜȀ ௟௢௡ response shown in Figure 58 was between 0.74 and 1.1 rad/s, with values monotonically increasing as a function of actuator bandwidth, except for the 16 rad/s actuator case displaying a crossover at 0.8 rad/s. This later result was attributed to a slight resonance near the open-loop í 180 deg phase crossover frequency causing the phase curve to dip between 0.5 and 2.6 rad/s.

However, since phase delay was small, the particular characteristics of the TRC configuration with the 16 rad/s actuator were considered minor issues.

The differences in this frequency where the phase was í 180 deg were simply a function of the small variations in the closed-loop frequency responses of Figure 67 below 2 rad/s. The general existence and approximate location of this crossing, however, was considered an inherent characteristic of TRC control, and fundamentally independent of the nacelle actuator bandwidth. While a pure first-order velocity response yielded an undefined í 180 deg phase crossing, additional phase in the frequency response, due to the added dynamics and delays in the control system, ensured the longitudinal position response ܺ ߜȀ phase was í 180 deg for a ௟௢௡ frequency between the phase bandwidths of the TRC command model bandwidth and the model-following control system (defined by the frequency such that the phase is í 45 deg).

Based on the ideal transfer function response (with a ߬ of 0.293 s), this point was predicted to ௘௤ be 1.15 rad/s for the 2.5 s equivalent first-order TRC response time, and 0.82 rad/s for the 5 s case, which was consistent with the phase curves shown in Figure 58. In ideal settings this frequency could be stretched out to 2–2.5 rad/s (perfect inversion and equivalent time delays lower than 0.1 s), but for representative second-order approximations of the closed-loop model- following transfer function and time delays this í 180 deg phase crossing would normally be expected to be in the 0.5 to 1.2 rad/s range.

Significantly, for the TRC control system design as a whole, these values are well within the frequency range of pilot control and may be a possible indication of limited control margins being available to the pilots. This characteristic also highlights the impact of the shape of the phase curve beyond the í 180 deg crossover frequency, which the phase delay tries to represent. Should pilots be required to operate beyond the installed bandwidth, particularly for the low actuator bandwidth cases, this would easily lead them to be out of phase with the desired position response, and consequently at risk of entering PIO.

Disturbance rejection. Based on the control system optimization strategy that was adopted, it was expected that configurations with higher actuator bandwidth would possess improved rejection of atmospheric turbulence disturbances. Spectral analysis of the aircraft response, in a turbulent atmospheric field, shown in Figure 68 suggested marked horizontal motion reductions in the longitudinal axis with the higher actuator bandwidths. For example, below 1 rad/s there was an approximate 17 dB reduction in the auto-spectra of the longitudinal velocity between the 3 and 16 rad/s actuators. In terms of the RMS of the longitudinal position, this translated into an 80-percent reduction down from ~0.2 to 0.04 ft. This was consistent with the progressive 3 rad/s 4 rad/s 8 rad/s -20 uu 16 rad/s G -40 10log -60 -80 -100 0.1 1 10 100 Frequency (rad/s) Figure 68. Auto-spectrum comparison of the turbulence response for varying nacelle actuator bandwidths: longitudinal velocity (units of ࢛ are in ft/s).

increase of DRB in the longitudinal translational axis afforded by the higher actuator bandwidths, as shown in Figure 65.

Pitch coupling aspects of high crossover frequency design. A physical coupling of the pitch and velocity control loop dynamics, for the configuration with the 16 rad/s actuator, was hinted at by the approximate match between the open-loop crossover frequencies, at 2.4 rad/s, in both control loops (Figure 69). By comparison, the open-loop crossover frequencies for the TRC control system with the 8 rad/s bandwidth actuator were 3.4 and 1.6 rad/s in the pitch attitude and longitudinal velocity loops, respectively. The remaining TRC configurations were ensured to ω ≈ 2.4 rad/s c GM ≈ 6 dB -20 Lon. velocity loop Magnitude (dB) -40 Pitch loop -60 -90 -180 -270 ω ≈ 7.7 rad/s Phase (deg) -360 -450 0.1 1 10 Frequency (rad/s) Figure 69. Open-loop frequency responses for the configuration with 16 rad/s actuator bandwidth.

have even larger crossover frequency separations by factors of 3.5 or greater, and importantly, retained approximately the same pitch loop crossover frequencies (~3.4 rad/s). Naturally, this higher crossover frequency (1 rad/s difference) was associated with better pitch disturbance rejection characteristics, and would be expected to exhibit less pitch motion in response to turbulence or pilot input disturbances.

Incidentally, spacing of the open-loop crossover frequencies had not been seen as a critical design aspect for this form of TRC, since the two loops relied on independent actuation mechanisms. Indeed, results of the piloted evaluations presented below show this to be only a very minor, although perceptible, deficiency from a handling qualities perspective.

This coupling of the pitch and velocity control loops resulted, however, in measureable off- axis pitch motions in response to both atmospheric turbulence and pilot input. In Figure 70, for example, the configuration with the 16 rad/s actuator was noticeably more active in pitch as it reacted to atmospheric turbulence. This behavior extended to the piloted input response.

Inspection of Figure 71 indicates the pitch response is roughly 3.5 dB higher magnitude for input frequencies below 1 rad/s. This long-term response characteristic of the closed-loop TRC 3 rad/s 4 rad/s 8 rad/s -20 qq 16 rad/s G -40 10log -60 -80 -100 0.1 1 10 100 Frequency (rad/s) Figure 70. Auto-spectrum comparison of the turbulence response for varying nacelle actuator bandwidths: pitch rate (units of ࢗ in rad/s).

-20 Consequence of feedforward control -40 -60 Actuator Bandwidth 3 rad/s Magnitude (dB) -80 4 rad/s 8 rad/s 16 rad/s -100 0.1 1 10 Frequency (rad/s) Figure 71. Closed-loop ࣂ ࢾ Τ frequency-response magnitude for varying nacelle ࢔࢕࢒ actuator bandwidths (5 s rise time).

system with the 16 rad/s nacelle actuator bandwidth was attributed to the coupling of the nacelle-actuated velocity feedback loop and the rotor-actuated attitude feedback loop, and is shown from the piloted evaluations discussed below to be a perceptible aspect of this control system.

A further consequence of this off-axis coupling was the dependency of the pitch response on the nacelle actuator bandwidth. As shown by the ߜȀߠ Bode diagram in Figure 71, this ௟௢௡ configuration in particular also exhibited a distinct pitch response magnitude increase above the 3 rad/s point, noticeably exceeding the magnitude of the 8 rad/s bandwidth case for input frequencies greater than 5 rad/s. These off-axis pitch responses were attributed to the excitation of higher frequency dynamics by the feedforward control, and were accompanied, accordingly, by notably higher frequency angular nacelle accelerations (and corresponding pitching moments due to the torque reactions) in response to pilot input. With these response dynamics being within the frequency range of pilot control, they would also likely generate a series of ride qualities issues at high frequency if disturbed by the pilot, through off-axis couplings in addition to the primary longitudinal control axis response issues.

Piloted evaluations in the Hover MTE and rate-limiting considerations. The handling qualities ratings (HQRs) shown in Figure 72 for the baseline TRC implementation indicate that with nacelle-only actuation (i.e., no cyclic augmentation) Level 1 handling qualities are possible with actuator bandwidths greater than 4 rad/s. The phase delay for the 4 rad/s case was in the order of 480–500 ms. With this in consideration, the results in Figure 72 indicate there is a good correlation of the handling qualities with the ܺ ߜȀ phase delay, with the 480–500 ms of the ௟௢௡ 4 rad/s actuator configuration conferring borderline Level 1–2 handling qualities, on average, for a TRC phase bandwidth of 0.2 rad/s. These results are consistent with those of Franklin et al.

[61], which proposed a Level 1–2 boundary at 0.4–0.6 s for a similar (non-attitude based) TRC response type implementation.

Note that although the 3 and 4 rad/s actuators had lower rate limits than the 8 and 16 rad/s actuator configurations, rate-limiting was carefully monitored throughout the experiment and was not judged to be a major factor in the piloted experiments. As suggested by Figure 73, these lower bandwidth configurations would have only experienced gradual degradation of the effective phase delay for control amplitudes (in terms of RMS) up to 1 in. Rate-limiting certainly compounded the problems encountered when very large control inputs were required by the pilot, but it was never the precipitator of the initial handling qualities problem, which was a fundamental phase delay due to the low actuator bandwidth.

As shown in Figure 60, the effect on the longitudinal position response bandwidth is minimal from either parameter variation except at very low actuator bandwidth or rate limit, where there are some variations. The value of the bandwidth is already a very low frequency and is essentially governed by the translational response rise time, which was 5 s for the cases shown.

The results for the phase delay of the ܺ ߜȀ response in Figure 61 are more informative.

௟௢௡ The nonlinear trends with input amplitude varied from configuration to configuration. Figure 73 illustrates the variation of the longitudinal position response phase delay with longitudinal stick amplitude represented in RMS of the sinusoidal input used in the automated frequency sweeps.

For the lower bandwidth cases (3 and 4 rad/s), the phase delay starts at higher values at small amplitudes and increases almost immediately with increased RMS input. The higher actuator bandwidth cases (8 and 16 rad/s) have much lower minimum phase delays at low input and actually maintain that value constant up until a given input amplitude after which there is a rapid rise in the phase delay. The trend appears to be that the breakpoint for the rising phase delay is at higher amplitudes for higher actuator bandwidth but with a more aggressive increase.

The response lag in the longitudinal axis associated with the actuator bandwidth of 3 rad/s was consistently deemed by the evaluation pilots to be excessive and PIO conducive. Phase delay was in the order of 650 ms (Figure 59). This configuration was rated Level 2 by all evaluating pilots (Figure 72). The handling qualities improved significantly with the 4 rad/s actuator, with the perceived response lag being less objectionable, but still problematic when subjected to aggressive control. Comments generally pointed to mid-term or residual oscillations, particularly after an aggressive deceleration, which implies that pilots could not relax after achieving a stable hover. The initial response was not crisp, but was still predictable.

This amounted to an inability to be aggressive with the aircraft, but allowed for desired performance to be achieved if employing a low gain control technique. Consistent with these comments, HQR scores indicate borderline Level 1–2 handling qualities were conferred with this configuration.

Level 3 Level 2 HQR 4.9 Level 1 3.2 2.9 2.1 3 4 8 16 Actuator bandwidth (rad/s) Figure 72. HQRs for varying actuator bandwidth configurations (5 s rise time).

2.0 3 rad/s actuator 4 rad/s 1.6 8 rad/s 16 rad/s Limiting 1.2 phase delay (s) 0.8 lon δ X/ Sudden 0.4 limiting 0 1 2 3 4 Longitudinal stick RMS (in) Figure 73. ࢾ ࢄ Τ phase delay for varying frequency sweep amplitude.

࢔࢕࢒ The higher bandwidth actuators (8 and 16 rad/s), conferring low phase delay values (under 200 ms for both), consistently gave “very predictable” and “crisp” responding qualities, offering “very good speed control” with “precise and low workload hover stabilization.” Only passing mentions of a slight tendency to oscillate longitudinally from aggressive deceleration attempts were made by one pilot. Most pilots indicated that these configurations were quite insensitive to aggressiveness.

Although rated as conferring Level 1 handling qualities, the 16 rad/s actuator unexpectedly conferred slightly degraded handling qualities compared to the 8 rad/s actuator. Consistent with the analysis documented previously showing the increased off-axis pitch responses (Figs. 68 and 69), this configuration was persistently felt by the pilots to be notably more active in the pitch axis in response to both turbulence gusts and pilot inputs. In line with this assessment, the pilots indicated the presence of noticeable heave accelerations due to pitch that affected the compensation required. The 3.5 dB difference in the pitch response for input frequencies below 1 rad/s, indicated by the ߜȀߠ Bode diagram shown in Figure 69, implied that the rate and ௟௢௡ amplitude of oscillation would be about 50 percent larger for a given size of input. It is noted that while the amplitude of oscillation may be small, for a pilot station located 32 ft in front of the center of rotation, even a fraction of a degree of pitch results in a perceptible vertical displacement of the cockpit. This is consistent with pilot evaluation comments. Other issues reported in the piloted evaluations were also attributable to the high gain feedback design and manifested primarily in ride quality deficiencies: a “snappy” response, large lateral accelerations, etc.

Nacelle Rate-Limit Effects Although a nonlinear phenomenon, actuator rate-limiting is seen from the short-term position response characterization discussion presented previously, to have a similar effect on the ܺ ߜȀ characteristics to that of actuator bandwidth. Specific fundamental underlying aspects of ௟௢௡ this nonlinearity are further examined in this and subsequent sections.

HQRs for evaluations in the Hover MTE of four nacelle conversion actuator rate limits for a control sensitivity of 15 (ft/s)/in, and zero nacelle rate to longitudinal cyclic crossfeed, are shown in Figure 74. Error bars indicate the maximum and minimum values. This control sensitivity was not optimal, as seen from the results of Figure 64, which explains the average Level 2 ratings.

Indeed, this higher sensitivity tended to exacerbate the effects of these nonlinearities. Also, absence of the nacelle rate to longitudinal cyclic crossfeed, the purpose of which is to eliminate small “non-minimum phase” pitch attitude changes with this TRC system, was an important aspect, and its effect will be discussed further below. As such, the results suggest that 10 deg/s was found consistently to be the least objectionable of the nacelle actuator rate-limit configurations. Lower rate limits (5 and 7.5 deg/s) were too restrictive of pilot input and resulted in PIO more frequently. The 5 deg/s rate limit in particular was rated at least one HQR higher than the others. The 7.5 deg/s rate limit did confer the lowest individual rating, however.

Interestingly, the 12.5 deg/s rate limit, which was expected to be less restrictive and receive better ratings, was found to possess unsatisfactory deficiencies due to “obtrusive pitch perturbations” and was thus awarded Level 3 ratings. This pitch response is directly tied to the “non-minimum phase” pitch attitude changes associated with nacelle rate. Looking at this configuration more closely, the control system was observed to command nacelle rates near the 12.5 deg/s limit, but frequently without reaching the rate limit.

The interconnected factors of nacelle rate limit and coupled pitching led to conflicting trends for the HQRs for the various TRC rate-limit configurations—both increasing and decreasing the rate limit could cause a reduction in HQR. For some of the TRC configurations the non- minimum phase pitch response appeared only to be a minor “nuisance” factor, especially as several pilots did not comment or notice it at all as the amount of pitching is dependent on the pilot input magnitude—something that was somewhat dependent on pilot technique. Some pilots did comment on the perceivable aforementioned “opposite sense” pitching that would occur with any longitudinal stick input. The scenarios where it became more obvious were where a PIO occurred, with a large amount of fore-aft motions, large stick inputs, and the nacelle actuators reaching their limits.

Level 3 Level 2 HQR Level 1 5.0 7.5 10.0 12.5 Nacelle rate limit (deg/s) Figure 74. HQRs for varying nacelle actuator rate limits in the Hover MTE (5 s rise time and 8 rad/s actuator bandwidth).

2.0 5 deg/s 7.5 deg/s 10 deg/s 1.6 12.5 deg/s 1.2 phase delay (s) 0.8 lon δ X/ 0.4 0 1 2 3 4 Longitudinal stick RMS (in) Figure 75. Nonlinear phase delay effect of rate limits for varying pilot control input.

Notwithstanding the pitch coupling effects, the relationship of the rate limit on the TRC handling qualities can mostly be explained using the results in Figure 75. Here the ܺ ߜȀ phase ௟௢௡ delay is compared for the four nacelle actuator rate-limit configurations tested in the piloted simulation. At small pilot input RMS values, the systems are effectively linear, and there is no perceivable difference in the phase delay. However, for larger RMS inputs, the rate-limiting effect becomes prevalent, with the lower rate-limit cases exhibiting an earlier phase delay increase “breakpoint” as well as a steeper gradient. The ܺ ߜȀ phase delay strongly correlated ௟௢௡ with the HQRs for the Hover MTE for TRC control. A high phase delay value alone is poor, but a strong dependency of worsening phase delay on the pilot input amplitude leads to a highly nonlinear and negative control characteristic. If the input amplitude can be kept small, then the poor handling qualities are “avoided.” This is the core reason for the handling qualities cliff; if the input is too large, a large amount of delay is experienced and thus likely to increase the pilot gain to compensate, induce further large inputs, and exacerbate the problem. This HQ cliff is borne out by the ratings shown in Figure 74 where the different rate-limit cases showed a high degree of variability, even when the pitch attitude issues connected with rotor flapping were eliminated by the crossfeed (see section below).

Application of Open-Loop Onset Point (OLOP) design criteria. The correlation of the degradation of the handling qualities with reduced rate limit described in the previous section is not an unexpected outcome, albeit in a novel application of nacelle-actuated TRC. What is useful is to determine how to predict limiting in such a control architecture where rate-limiting might impact the handling qualities. The OLOP design criteria [50] was used in this case to predict the potential handling qualities impact associated with rate-limiting of the nacelle actuator. Figure 76 shows the effect of the experimental nacelle rate limits on the OLOP phase and amplitude criteria assuming a maximum control input amplitude of 1 in. The extra margins offered by the larger rate limits are clearly illustrated. For comparison, Figure 76 also illustrates the effect of pilot maximum input amplitude on the OLOP criteria. Center stick maximum displacement range was ±5 in, allowing the handling qualities impact of piloted input frequency and amplitude to be freely evaluated.

4.5 in 7.5 deg/s limit 1 in max. input Level 3 2.5 in 1.6 in Level 2 5 deg/s 1.0 in 7.5 deg/s Amplitude (dB) -5 10 deg/s 0.5 in 12.5 deg/s Level 1 -10 -15 -180 -160 -140 -120 -100 Phase (deg) Figure 76. OLOP specifications for varying nacelle rate limits (15 ft/s/in sensitivity and 1.0 in maximum pilot input).

OLOP uses linear analysis to predict the onset of rate-limiting; typically the input to compute the result is the maximum input but in some respects that determines an unrealistic scenario.

Figure 76 shows that increasing the input to 2.5 in from the nominal 1 in used for the 7.5 deg/s rate-limit case pushes the result into Level 3 handling qualities. This somewhat correlates with the result in Figure 75 where the same case at an equivalent RMS amplitude has a phase delay of around 0.6 s, which exceeds the Level 1 HQR boundary values proposed in the summary and discussion section below.

Effect of Crossfeed In the previous section it was shown that for the TRC control law without the nacelle rate to longitudinal cyclic crossfeed, relatively subtle variations in nacelle actuator dynamics, and how aggressively the pilot flew, led to a large variability in the handling qualities. A non-minimum phase pitch response was most evident in the 12.5 deg/s rate-limit case shown in Figure 74 because of the larger nacelle rates commanded by the TRC control system. Pilot comments for this configuration consistently mentioned the presence of a notable pitch oscillation accompanied by what was described as an unsettling heaving motion. While this oscillation was described as annoying, or bothersome, it did not appear to compromise the ability to meet the targeted performance standards. A few evaluation comments hinted to a quick pitch reversal in response to rapid input, and more interestingly, indicated that this pitch motion could be cueing them on to a false sense of aircraft response because the pitch response was opposite to the expected response pilot control input (e.g., nose-up pitch for a forward stick displacement). It was purported that this opposite pitch response to pilot input may have falsely cued the pilots into overcorrecting after an initial input. Additionally, this pitch oscillation appeared to affect the altitude maintenance because of the presence of an obvious heave motion perception at the pilot station.

The analysis in Appendix B illustrates the mechanics that cause this non-minimum phase response characteristic and the beneficial effect of the crossfeed. The oscillations were induced by the angular rate of the nacelles causing rotor flapping opposite to their rotation through the air, which in turn generated pitching moments on the aircraft body. To compound matters, these pitching moments are opposite in sense to the pilot input, i.e., stick forward commanded a forward rotation of the nacelles to accelerate forward and the rotors flap aft in response and cause a nose-up pitch. The larger the allowable nacelle rate, the larger the pitch disturbances became.

Figures 64 and 72 also show that the relatively simple crossfeed gain improved all the configurations, becoming less sensitive to a variety of pilot techniques and aggression levels and, in some instances, virtually eliminating the PIO tendency that had previously existed. This was a major factor in the large spread in the HQRs in Figure 74. The crossfeed is able to minimize the lagging effects on the longitudinal velocity of both rotor flap-back to nacelle rate and the subsequent pitching motions by effectively keeping the rotor disc plane perpendicular to the nacelle/shaft axis (Appendix B). The resulting effect of the crossfeed is well illustrated in Figure 77. It shows the same ܺ ߜȀ phase delay with pilot input RMS in Figure 75, but ௟௢௡ compares the rate-limit configurations with and without the crossfeed improvement. The solid (black) lines indicate the cases without crossfeed, and the effect of adding the crossfeed is indicated by the dashed (blue) lines. The main effect is an overall downward shift in the curves to lower phase delays. At small amplitudes, the difference is small, but as the RMS increases, inferring larger amplitude nacelle rates (and thus more rotor flapping), the crossfeed effect becomes more significant. At RMS amplitudes of 1 in and above, the phase delay reduction is in the order of 30 ms up to 100–150 ms for the lower rate-limit configurations. This across-the- board improvement was reflected in the HQRs. Also the worse (low rate-limit) configurations were improved more than the higher rate-limit cases—bringing them all closer together in performance.

The OLOP criterion shown in Figure 78 similarly predicts an improvement in the handling qualities from the addition of the crossfeed. The predicted improvement is fairly small and is indicated by the curve shifting to a location such that any given input amplitude point is moved further toward the Level 1 handling qualities region. This is likely the equivalent of the small delta observed in the ܺ ߜȀ phase delay curves for small RMS amplitudes where the system is ௟௢௡ effectively linear.

2.0 5 deg/s 7.5 deg/s 1.6 10 deg/s 12.5 deg/s Baseline Crossfeed 1.2 phase delay (s) 0.8 lon δ X/ 0.4 0 1 2 3 4 Longitudinal stick RMS (in) Figure 77. Effect of crossfeed on nonlinear phase delay of rate limits for varying pilot control input.

4.5 in 4.5 in Baseline Crossfeed Level 3 2.5 in 2.5 in 1.6 in Level 2 1.6 in 1.0 in 1.0 in Amplitude (dB) -5 0.5 in Level 1 -10 0.5 in -15 -180 -160 -140 -120 -100 Phase (deg) Figure 78. Effect of crossfeed on OLOP specifications for TRC control (15 ft/s/in control sensitivity and ±7.5 deg/s rate limits).

Cyclic Augmentation—Response Quickening The analysis of the results from the previous sections has established the necessary levels of nacelle actuator bandwidth required for Level 1 handling qualities to be achieved with this particular implementation of the TRC control. Whether these Level 1 handling qualities can be maintained for reduced actuator bandwidths by introducing other control mechanisms remains unanswered. It would be advantageous if additional longitudinal bandwidth or “quickening” of the longitudinal velocity response could be achieved through other methods to reduce the nacelle bandwidth requirements. TRC response augmentation by employing longitudinal rotor cyclic actuation in addition to nacelle actuation was a scheme tested.

The longitudinal cyclic rotor actuation “augmentation” in addition to nacelle actuation was demonstrated to confer significant handling qualities improvements to the equivalent nacelle actuation-only bandwidth cases, specifically the lower 3 rad/s actuator case, shown in Figure 79. All three cases shown were identically configured with the nacelle rate to cyclic crossfeed.

The results for these three control cases are that the small increase in phase bandwidth and reduction in phase delay attained with the case with the lower 2.5 s equivalent rise time, but nacelle-only actuation, did not confer a significant improvement in the handling qualities (see Figure 59). By comparison, referring to Figure 59, the phase delay improvement of the cyclic- augmented control system to the baseline 3 rad/s case was in the order of 200 ms (down to ~450 from 650 ms), resulting in a marked improvement in HQRs. With all other parameters remaining unchanged, this again indicated a strong correlation of the phase delay with the handling qualities. Although the cyclic-augmented configuration only used a 5 s rise time and thus had a lower bandwidth than the 2.5 s rise-time case, its bandwidth was sufficient (following the ADS-33 criteria definition), and crucially it had better phase delay characteristics as very little noticeable lag in the response was apparent. As such, the initial response was generally considered to be predictable and speed control easy. Only two pilots observed a slight amount of lag in the response, but considered it to be manageable and definitely not conducive to PIO.

Again these issues all point to the reduced phase delay being the cause for the handling qualities improvements.

Also playing a potentially beneficial role, as illustrated by the analysis of the qLPV and nonlinear actuator model used in the pilot experiments in Figure 80, the system overall phase delay is not only lower than both unaugmented cases, but notably, the rise in phase delay with amplitude is also eliminated. The vehicle dynamics effectively “appear” much more “linear” with no changes in response characteristics with changing pilot input amplitude—a significantly improved handling qualities characteristic.

In summary, these results suggest that while high by ACAH standards, a phase delay requirement of around 450 ms or lower in the context of this TRC implementation would be sufficient to achieve desired precision in the Hover MTE, a result that tracks the TRC research results published in reference [61].

It was recognized that the cyclic augmentation approach would reintroduce a certain amount of pitching motion, which although now in the right directional sense (i.e., pitch forward for forward stick input), might bring back undesirable vertical accelerations for crew and passengers. Only one pilot out of seven rated this cyclic-augmented control system Level 2 for this reason. Trying to compensate for a perceived heave motion was not conducive to good handling qualities, forcing the pilot to have to stay out of the loop. While other pilots commented on this coupling, none felt it was problematic other than being a ride quality annoyance. This is, however, a consideration that needs to be taken into account if designing these types of control systems—that is, potential large pitching moments may be generated when using longitudinal cyclic for velocity control.

Level 3 Level 2 HQR 4.9 4.1 Level 1 2.8 Baseline 2.5 s rise Augmented Configuration Figure 79. HQRs for baseline 2.5 s rise time and rotor cyclic augmented configurations (3 rad/s actuator).

2.0 Baseline 2.5 s eq. rise time 1.6 Cyclic-augmented 1.2 phase delay (s) 0.8 lon δ X/ 0.4 0 1 2 3 4 Longitudinal stick RMS (in) Τ Figure 80. ࢾ ࢄ phase delay for varying frequency sweep amplitude (3 rad/s ࢔࢕࢒ actuator).

Analysis of Pilot Input Control Activity Figure 81 shows the computed pilot control input cutoff frequencies and root mean square (RMS) for a large proportion of the cases discussed in the sections above. These were computed from time histories of the longitudinal control stick displacements over the entire Hover MTE maneuver. As previously stated, the pilot cutoff frequency, determined from the spectral analysis of the inceptor position time histories, is used as an approximate measure of pilot operating frequency and considered a good estimate of the pilot crossover frequency for pilot-in-the-loop tasks [27]. Additionally, the RMS of the piloted inputs is a statistical measure of the magnitude of control input during the maneuver.

The results suggest that low phase delay control cases (higher nacelle actuator bandwidth) (Figure 81(a) and (b)) generally allowed pilots to operate in a more closely clustered frequency range, roughly between 0.2 and 0.6 rad/s, but possibly lower. High phase delay control cases often resulted in high RMS control input at frequencies closer to 0.8 through 1 rad/s. The later cases would have clearly had the pilots operating at, or near, the í 180 deg phase crossover point (Figure 58), which is entirely consistent with the reported PIO tendencies.

Because of the series of events it could trigger if not executed correctly, the critical sub- phase of the overall maneuver was consistently indicated by the evaluation pilots to be the deceleration from a steady velocity translation into a stable hover within the desired time and position performance criteria. It was reported that a poorly executed deceleration would force the pilot to get into the loop to correct for excursions outside of the desired performance criteria.

This is an important consideration because, with TRC, position regulatory tasks such as the steady speed ingress and hover hold sub-elements of the Hover MTE may not require high installed control bandwidth. The deceleration sub-element, however, could easily require control bandwidths over 1 rad/s.

A clear correlation between control sensitivity and equivalent rise time (or phase bandwidth), and the cutoff frequency and RMS data can be seen in Figure 81(c). The data show that low control sensitivity (indicated by the circle symbols) elicited larger amplitude but lower frequency control inputs. High, and in a few instances, medium sensitivities led to higher operating frequencies and consequently resulted in a tendency to over-control as documented above (e.g., gain set 15/5, which refers to a 15 ft/s/in control sensitivity and a 5 s equivalent first-order rise time).

The effect of a lower (quicker) equivalent rise time generally resulted in lower overall cutoff frequencies. The exceptions were where it led to a tendency to over-control when combined with the medium- and high-control sensitivities. This can be explained in conjunction with the result, above, that lower rise times typically allowed for easier transitions into a stable hover without the need to over-drive the controller.

Extending this discussion into the frequency-domain, the implication is that higher ܺ ߜȀ ௟௢௡ phase bandwidth generally allowed the pilots to operate with lower natural control “gains” (as reflected by the cutoff and RMS data) in order to meet the desired deceleration performance requirements. This seems to imply a fundamental inverse relationship between installed phase bandwidth and required pilot operating frequency, suggesting the lower bandwidth cases were over-driven by the pilots to achieve desired performance.

Pilot longitudinal stick input frequency and magnitude data computed for the overall MTE maneuver may obscure specific events happening at distinct moments in time. When computed for the 30 s the pilot is required to hold the hover position following the enunciation that a stable hover had been reached, the pilot cutoff frequencies and RMS shown in Figure 82 confirm there can be significant residual pilot control activity in the 0.8 to 1.2 rad/s frequency range. Also very minimal pilot control activity, as characterized by an RMS below the neighborhood of 0.4 in is observed, which is a consequence of an improved ability to reject the “moderate” turbulence disturbances and hold position with the TRC. High cutoff frequency values are meaningless in this context, as these are the result of the mathematical characterization of a signal with Actuator bandwidth 3 rad/s (a) TRC Configuration Baseline Cyclic-augmented (b) Sensitivity/Rise time 15/5 10/5 5/5 15/2.5 10/2.5 5/2.5 (c) Figure 81. Longitudinal pilot control activity for entire maneuver: (a) baseline, varying actuator bandwidth; (b) cyclic-augmented (3 rad/s actuator); and (c) varying equivalent rise times and control response sensitivities (8 rad/s actuator).

minimal energy (flat auto spectra). However, seen in conjunction with the RMS, they indicate that pilots were effectively staying out of the loop.

Figure 82 shows that the pilot control activity strongly correlates with the HQRs, where the Cooper-Harper ratings are seen on average to increase dramatically with the amplitude of pilot control inputs. These events consistently corresponded to the TRC configurations possessing high phase delay values. Results in Figure 83 further demonstrate this relationship, where several cases—all essentially with ADS-33 Level 1 rise-time characteristics (or bandwidth)— showed a monotonic increase in the average HQR resulted as a consequence of the increasing phase delay.

Figure 82. Longitudinal pilot control activity for the 30 s hover hold sub-task (all configurations).

Level 3 Level 2 HQR Level 1 0 0.2 0.4 0.6 0.8 1 Phase delay (s) Figure 83. Effect of short-term position response phase delay on handling qualities.

Longitudinal axis time histories and auto-spectra analysis shown in Figure 84 highlight the different nature of the control inputs in these two distinct regions in Figure 82. These correspond to two different runs by the same pilot flying the same sensitivity and rise-time configuration, with the 3 rad/s actuator. Assigned an HQR 6 by the pilot, this configuration exhibited widely different performance in each run. Run A demonstrates a situation where the pilot executed everything perfectly, remaining within desired parameters, and therefore did not need to get in the loop after arresting the initial translational rate. The control compensation employed by the pilot after stabilizing is characterized by infrequent pulse type corrections. This type of time history displays very little energy in its auto-spectrum (Figure 84(c)). Deficiencies with this configuration are illustrated by Run B where, in this case, the same pilot remains in the loop nearly 11 s after indicating a stable hover had been achieved. Examination of the control input and aircraft position time histories during this initial time period suggests significant compensation occurred around 1 rad/s, and the spectral analysis confirms this. Importantly, it is noted that the position response is nearly 180 deg out of phase with the input, clearly indicative of a PIO. This result confirmed the analysis of the ܺ ߜȀ frequency response (Figure 58).

௟௢௡ As phase delay for other configurations was reduced (to less than 200 ms), this propensity to get out of phase during the stabilization was also diminished, a characteristic that was corroborated by the pilot evaluations, as discussed previously. In terms of the pilot input frequency and magnitude characterization, configurations with lower phase delay show consistently low control RMS values in Figure 82, which is strongly indicative of pilots employing minimal compensation.

A final observation from these results is they support the piloted evaluations that indicated that very little compensation was generally required to hold position after stabilizing the aircraft, particularly for phase delays lower than 450 ms. These results highlight one of the most significant benefits of TRC, that the higher augmentation it confers translates into very low workload for position maintenance tasks.

2 full cycles Run A Run B (a) Run A Adequate Desired Run B (b) Run B Pilot in the loop Run A (c) Figure 84. Comparison of different compensation levels in hover hold sub-task (3 rad/s actuator, same pilot): (a) longitudinal input time history, (b) longitudinal position error time history, and (c) longitudinal input spectral analysis (red lines indicate proposed levels where pilot can be considered to be actively in the control loop).

Summary and Discussion

Handling Qualities of Large Rotorcraft With ACAH The analysis above showed that implications of the large vehicle size are notable and have two key aspects. First, the large size of the vehicle confers high mass and moments of inertia that introduce increased delay to the response of the vehicle to both pilot inputs and external disturbances alike—an aspect that factors into the pilot workload required to stabilize the aircraft and reject disturbances in hover and low-speed maneuvering. The trade-offs between disturbance rejection bandwidth (DRB) and closed-loop stability (characterized by the phase margin) were examined. The balance shifted to a preference for increased DRB and reduced phase margin as the vehicle size increased—this was attributed to the aforementioned workload issues, where for the larger vehicles, pilots preferred the increased automatic rejection disturbances—allowing them to “keep out of loop” and not have to work as hard or make as many corrective inputs to stabilize the aircraft attitude or position.

Underlying all these outcomes was the second key factor—that part of the reason pilots wanted to minimize their control inputs was to keep attitude disturbances, particularly in pitch, to a minimum. The reason was that the conventionally located cockpit at the front of the aircraft, some 40 ft from the center of rotation at the center of gravity, led to a number of motion-related ride and handling qualities issues. Pitching the aircraft created heave motion at the cockpit, and yaw created sideward accelerations. Such responses would not be conducive to passenger acceptance. These factors were investigated further through a comprehensive analysis of the short-term attitude response requirements in hover and low-speed maneuvering for a selection of rotorcraft of different sizes. The analysis also included a specific study on the effect of the pilot offset in isolation, and showed that by simply changing the offset location, and thus modifying the motion and visual cues presented to the pilot, a vehicle with the same dynamics would get progressively better HQRs with decreasing longitudinal offset location. The levels of attitude bandwidth in particular, were “too hot” at the 30 to 40 ft offset location and above.

Following the ADS-33 recommendations for Level 1 HQs for cargo/utility class helicopters caused pilots difficulties when trying to perform hovering tasks using attitude control. Reducing the bandwidth of the attitude response ameliorated the problem somewhat, but ultimately the handling qualities for the modified Hover MTE remained Level 2 at best.

There is an open question about the direct applicability of the ADS-33 Hover MTE to the civilian role envisaged for an LCTR2 type rotorcraft. The experimental assessments in this report made some allowance for this by increasing the size of the desired and adequate hover performance box; however the standard ADS-33 time-to-stabilize requirements were maintained. These could possibly still be overly demanding and require unnecessary maneuvering urgency, but certainly the established ADS-33 values were a natural place to start, and leaving them unchanged provided opportunity for comparison to previous experimentation.

If the stabilize time was relaxed, perhaps in conjunction with further precision relaxations, then Level 1 hover and low-speed handling qualities may be achievable with an attitude command response type. Safety is paramount to the civilian role, and handling qualities play an important part. For an LCTR2 type aircraft to be viable it must be able to operate in a cluttered terminal area environment, and be responsive to ATC requirements and commands as well as be operational in all weather conditions. This later point highlights the reasoning for testing in “moderate” levels of turbulence. An argument can be made that the perhaps artificially high MTE demands somewhat push the aircraft limits that would be required in scenarios of high stress or emergency.

Other solutions to the attitude-linked problems could also be proposed, for example, locating the pilot closer to the center of rotation. This would certainly alleviate the motion-related issues but brings a host of other issues such as locating the pilot in a position with adequate field of view without resorting to cameras and/or other sensors, not to mention that the unsatisfactory motion issues still remain for any passengers substantially offset from the center of gravity. One might also argue that a vehicle such as LCTR2 should feature significant automation, thus piloted HQs might be somewhat outmoded. This is likely to be true but not entirely; the handling qualities for redundant/failsafe modes still need to be satisfactory, and the fundamental work to establish minimum-level requirements for good handling qualities also needs to be carried out to prevent overdesigning and adding unnecessary complexity and cost to the design.

Design Feasibility of Nacelle Tilt and TRC Handling Qualities Design Criteria Considering the various challenges and issues connected with the ACAH approach, the use of the nacelles in the TRC scheme is an attractive solution from a handling qualities and flight control perspective. The results presented previously have shown that, whereas rigid body dynamics of the aircraft have been considered, a control law can be devised to confer Level 1 handling qualities using such a scheme. The process of designing and assessing the control law led to a reappraisal of the current state of the art of ADS-33 TRC specifications. Meeting the current criteria did not necessarily confer Level 1 handling qualities, and this outcome led to investigation into finding additional techniques to characterize the TRC response. Frequency- domain parameters such as bandwidth and phase delay were applied to the translational response. The analysis showed that the existing equivalent rise-time criteria range from 2.5 to 5 s was equivalent to a ܺ ߜȀ (or ܻ ߜȀ ) bandwidth of approximately 0.2 to 0.4 rad/s. It was ௟௢௡ ௟௔௧ found, however, that meeting this criterion alone was insufficient, but as is typical in a number of short-term attitude response HQ criteria, combining it with a phase delay criterion led to a much better prediction of the handling qualities. Figure 83 (repeated here for convenience) demonstrates a monotonic increase in average HQR was achieved with increasing phase delay, while essentially all cases met the ADS-33 Level 1 rise-time (or bandwidth) characteristics.

The fact that this is not in the existing criteria is somewhat a consequence of the difference in the implementation of TRC in the configurations used to define ADS-33. These were predominately based on inner/outer loop TRC control laws where the translational motion was created by attitude changes of the aircraft. Ultimately, this form of TRC is driven by the rotor, whose control actuator bandwidths and rate limits are typically much higher than those of the nacelle actuator in the TRC used for LCTR2, and so large phase delay issues were not likely to be encountered. This is exemplified by the lateral short-term response characterization, which Level 3 Level 2 HQR Level 1 0 0.2 0.4 0.6 0.8 1 Phase delay (s) Figure 83. Effect of short-term position response phase delay on handling qualities.

exhibited a phase delay of approximately 0.3 s. As such, the incorporation of the phase delay criteria would be an augmentation of the existing equivalent rise time rather than replacement— albeit that parameter would be converted to its frequency-domain counterpart, bandwidth.

Figure 85 shows how proposed TRC handling qualities criteria boundaries using ܺ ߜȀ ௟௢௡ bandwidth and phase delay would look with some tentative values included based on the research presented previously.

There are a number of aspects of Figure 85 to be described: first, the low bandwidth boundary is directly retained from ADS-33 where the upper rise-time limit of 5 s is converted to its equivalent frequency-domain value. There is no evidence to demand a change in this value, and it sets the minimum bandwidth to protect against slow or sluggish response characteristics.

The top part of the boundary box is more tentative, but it establishes the boundary based on the phase delay results in this report. The bold part of the line represents a small segment where the confidence is somewhat higher, but whether the boundary would be a constant value or perhaps more relaxed with increasing bandwidth capability cannot be determined; the precedent of the ADS-33 attitude command response criteria show such a trend. The final boundary is an upper limit to the bandwidth requirement; this boundary was not explored in the analysis in this report but is extrapolated from the results in reference [61] and others discussed previously.

This boundary exceeds the current ADS-33 levels but, as was discussed in the rationale of investigation, this upper boundary was somewhat overly restrictive as it was based on a particular implementation of TRC that was reliant on the use of attitude changes to generate the translational motion. In attitude-based TRC, beyond a certain TRC bandwidth (or below a certain rise time) the attitude changes required to confer the required response become very large and abrupt, and objectionable to the pilot. However, not all forms of TRC need adhere to this, as demonstrated in the form of the nacelle-tilt-based TRC. Therefore, increased bandwidth can be acceptable if not actually advantageous. However, research in the literature shows there does appear to be a point where the translational response itself can become too abrupt and objectionable—accordingly a boundary as is anticipated in reference [61] is shown.

0.8 Extrapolation of phase delay results Level 2 0.6 (s) p τ 0.4 0.2 rad/s is Possible Level 1 bandwidth for maximum Phase delay, ADS-33 bandwidth equivalent rise 0.2 limit [61] time of 5 s 0 0.1 0.2 0.3 0.4 0.5 Bandwidth, ω (rad/s) BW Figure 85. Proposed short-term position response handling qualities criteria for TRC.

Metrics Used—Applicability to Other TRC Implementations The proposed boundaries should be applicable to any hovering aircraft using TRC; the combined bandwidth and phase delay criteria are generic response characterizations independent of any implementation architecture. Similar issues could be conceived for a compound type rotorcraft with a fixed main rotor(s). Using some form of auxiliary propulsive force to provide the translational motion, sufficient bandwidth of response in the propulsive system (i.e., an engine, propeller, jet, or fan) needs to be provided to ensure phase delay issues are avoided.

A supplementary, supporting, criterion regarding the motion induced at the pilot station and/or other cabin locations (more of a cabin ride quality issue) is also required. This issue was partially accounted for implicitly in the current ADS-33 TRC specifications by virtue of the lower rise time (high bandwidth) guiding against abrupt attitude changes in attitude-based TRC, but what is actually needed is a criterion that directly addresses the issue of motion at the cockpit, such as heave due to pitching, and/or side force due to yaw rates/accelerations.

Modeling Limitations and Requirements The analysis in this report has shown the fundamental feasibility of a nacelle-based TRC in achieving Level 1 handling qualities in hover and low-speed maneuvering using low-to- moderate fidelity flight dynamics models featuring rigid body dynamics, rigid blade flapping dynamics, and basic cross-couplings. These models cannot consider the structural dynamics that might be a significant issue for a vehicle like LCTR2, especially considering that the two large nacelles will be actuated at relatively high frequency at the end of the slender flexible wings. In references [62,63] a detailed analysis of various control aspects of structural flexibility using a high-fidelity LCTR2 comprehensive model is presented. Moreover, structural strength issues might not be the only factor. Aeroelastic couplings may also impact the handling qualities, especially as the large scale of the LCTR2 confers structural natural frequencies closer to those important for pilot and flight control systems. Increased fidelity modeling is required to determine the structural modes and to decide whether further investigations are necessary to investigate the aeroelastic consequences (if any) on the handling qualities and flight control. The models also had limited aerodynamic modeling, with no dynamic inflow or wake modeling or ground effects. It can only be speculated what impact these effects have on the TRC handling qualities without further research.

Conclusions

Rotorcraft configurations of increasing size and gross weight exhibited a preferable trade-off between disturbance rejection bandwidth (DRB) and stability margin allowing for relaxed attitude feedback phase margins in hover and low speed. Relaxation of the design phase margins must be tempered by an acceptable allowance for margin degradation due to airframe wear and uncertainty.

• For all aircraft configurations evaluated, the low phase margin cases (20–23 deg) were unanimously rated as oscillatory, PIO-prone, and objectionable with a handling quality cliff potentially present. This is in spite of the fact that the Cooper-Harper Handling Qualities Ratings (HQRs) for the range of cases were remarkably the same, being either Level 1 or barely into the Level 2 region.

• For the representative medium-lift helicopter, the H-60, the current recommended stability margins in SAE 94900 (i.e., 45 deg and 6 dB), were preferred by the pilots over the lower stability margin/higher DRB cases. Maintaining these margins may allow for acceptable degradation due to uncertainty and wear and would be consistent with SAE 94900 requirements.

• For the representative heavy-lift helicopter, the H-53, the pilots preferred a higher DRB/lower stability margin configuration (roughly 38 deg of phase margin). Extra care must be taken to assess the influence of variability when nominal flight control gains start with reduced margins.

• For the generic ultra-heavy tiltrotor configuration, the LCTR, the pilot preference included not only a 36 deg phase margin case but also an even higher DRB/lower stability margin configuration (roughly 31 deg). Degradations due to uncertainty and wear become even more critical because of the reduced margin starting point.

• The ADS-33 mid-term response-to-control damping ratio requirement of 0.35 can be applied to the disturbance-response damping ratio. Disturbance-response damping ratios less than 0.35, associated with the low phase margin cases, resulted in highly objectionable oscillations for all three aircraft configurations evaluated.

• The pilot comments on the disturbance response of the aircraft correlated well to the DRB guidelines provided in the ADS-33 Test Guide. The comments indicate that the pitch DRB guidelines should be increased slightly from 0.5 to 0.65 rad/s, which correlates well with recent UH-60 flight tests. The roll DRB guidelines should be increased slightly from 0.9 to 1 rad/s.

• The comments also indicate good agreement with the DRP guidelines proposed in reference [47]. The pitch DRP maximum 5 dB value is consistent. The roll DRP guidelines should be increased slightly from 5 dB to 5.4 dB.

The long lever arm of the cockpit, ahead of the center of gravity, in the very large tiltrotor configurations examined created significant heave coupling with pitch. Similarly, yaw axis accelerations can produce substantial side-force at the cockpit, mandating a reduction in the Level 1 yaw bandwidth requirements. In addition, a revision of a subset of ADS-33 MTE maneuvers resulted in modifications of their performance requirements. The lateral and longitudinal position tolerances for the ADS-33 Hover MTE needed to be increased to better fit the vehicle size, and the Hovering Turn MTE was adjusted to be consistent with the Limited Agility MTE category. The Lateral Reposition MTE standards remained unchanged and were satisfactory for this large vehicle.

• An ACAH response type for the precise hover control of an aircraft with a large (i.e., greater than 30 ft) pilot offset from the center of gravity achieved Level 2 handling qualities, at best, when operating in “moderate turbulence” environmental conditions.

• At such large pilot offsets from the center of gravity, aircraft dynamics exhibiting a high bandwidth attitude response in all axes—over 1.2 rad/s pitch and roll commanded response natural frequencies and under 0.5 s yaw rate commanded response time constants—displayed objectionable impulsive load factors at the pilot station (a ride qualities issue) and unpredictable aircraft response (a handling qualities issue).

• Configurations with low bandwidth attitude response generally exhibited a lack of control authority in all axes, with sluggish aircraft response lending itself to excessive workload, and PIO tendencies in the face of large amplitude aggressive control techniques.

• Natural frequency of the response appears to have a fundamental impact on the aircraft HQRs for this size of aircraft, probably because it relates to the cockpit accelerations directly. Proposed boundaries therefore tend to follow the constant natural frequency lines.

• A broad range of acceptable yaw bandwidths was identified based on the proposed heading capture evaluation maneuver. Relaxation of the Level 1 yaw bandwidth requirement from 2 rad/s to 0.25 rad/s helped account for the large pilot offset from the center of gravity.

TRC response types with minimal attitude response were unanimously preferred over the attitude-based ACAH, enabling Level 1 handling qualities for large tiltrotor aircraft in hover, even in turbulent ambient conditions. However, the enforcement of ADS-33 TRC requirements, while necessary, was not sufficient to ensure the Level 1 handling qualities were conferred. The various actuator dynamics, control crossfeeds, and feedback aspects of the design have varying effects on the longitudinal short-term position response phase delay. If excessive, this delay results in objectionable oscillatory characteristics in the longitudinal translational axis, with tendencies to PIO, and a handling quality cliff potentially present.

• TRC using a form of longitudinal and lateral thrust vectoring, by using nacelle tilt and parallel lateral cyclic, was a viable method of providing precise position control in hover and low speed, as evaluated in revised Hover and Lateral Reposition MTEs.

• A frequency-domain characterization of the closed-loop TRC short-term position response measured ܺ ߜȀ . In the context of this minimal-attitude TRC implementation, ௟௢௡ this response is a strong candidate handling qualities design metric, correlating well with the ratings. For all the configurations evaluated, the Level 1 handling qualities boundary is around 0.4–0.5 s of phase delay.

• For the controller force gradients evaluated, an optimal 10 ft/s/in control/response gradient was found to confer Level 1 handling qualities consistently. Higher (15 ft/s/in) and lower (5 ft/s/in) gradients conferred a broader handling qualities range, including Level 2. While based on piloted simulation, these results agree qualitatively with ADS-33 but suggest slightly higher gradients are needed.

• Equivalent rise times of 2.5 and 5 s conferred Level 1 handling qualities.

• Nacelle actuator bandwidths greater than 4 rad/s were required to consistently ensure Level 1 handling qualities for the baseline nacelle-only TRC implementation.

• Although a nonlinear phenomenon, nacelle rate limits have a similar effect on the TRC response phase delay equivalent and are interrelated to that of the actuator bandwidth.

Actuator rate limits above ά 5 deg/s were required for the Level 1 handling qualities to be attainable.

• A simple nacelle rate to longitudinal cyclic crossfeed in the control conferred significant improvements in the handling qualities of this TRC implementation. This crossfeed reduced non-minimum phase pitch responses to almost zero and improved the longitudinal TRC velocity system bandwidth. This was also seen as a reduction in the position response phase delay.

• Augmentation of the nacelle-only TRC through the use of longitudinal cyclic actuation was a viable solution for reducing nacelle actuator bandwidth requirements by providing: (1) a reduction in longitudinal response phase delay, and (2) nacelle rate-limiting prevention.

Appendix A—Aircraft Model Parameters

Table A–1. H-60 aircraft model parameters.

Flight Condition Speed Hover ft/s Altitude 100.0 ft Rotor Parameters Tail rotor radius 5.5 ft Main rotor radius 26.8 ft Main rotor chord 1.7 ft Solidity 0.082 -- Number of blades 4 -- Main rotor speed 27 rad/s Tip speed 724 ft/s Aircraft Weight 16,000 lb Fuselage station (pilots) 229 in Configuration Butt line (pilots) ά 24 in Water line (pilots) 257 in Fuselage station (CG) 359.4 in Butt line (CG) 0 in Water line (CG) 243.8 in x (CG to pilot) 10.87 ft p y (CG to pilot) 2.00 ft p z (CG to pilot) –1.10 ft p I 5,451 slug·ft xx I 1,882 slug·ft xz I 41,323 slug·ft yy I 29,437 slug·ft zz Hover Trim Values ࢥ –4 (–0.07) deg (rad) ș 4 (0.07) deg (rad) Lateral cyclic ( ά 5) –0.5 in Longitudinal cyclic ( ά 5) 0.5 in Pedals ( ά 2.69) –0.3 in Collective (0–10) 5 in Table A–2. H-53 aircraft model parameters.

Flight Condition Speed Hover ft/s Altitude 100.0 ft Rotor Parameters Tail rotor radius 9.4 ft Main rotor radius 39.5 ft Main rotor chord 2.57 ft Solidity 0.145 -- Number of blades 7 -- Main rotor speed 18.53 rad/s Tip speed 732 ft/s Aircraft Weight 46,000 lb Configuration Fuselage station (pilots) 131 in Butt line (pilots) ά 30 in Water line (pilots) 168 in Fuselage station (CG) 355.0 in Butt line (CG) 0 in Water line (CG) 162.3 in x (CG to pilot) 18.67 ft p y (CG to pilot) 2.50 ft p z (CG to pilot) –0.47 ft p I 60,539 slug·ft xx I 296,694 slug·ft yy I 275,834 slug·ft zz I 23,343 slug·ft xz Hover Trim Values ࢥ –2.7 (–0.05) deg (rad) ș 4.9 (0.09) deg (rad) Lateral cyclic ( ά 5) 0.3 in Longitudinal cyclic ( ά 5) 0.25 in Pedals ( ά 2.69) –0.2 in Collective (0–10) 6.7 in Table A–3. LCTR aircraft model parameters.

Flight Condition Speed Hover ft/s Altitude 100.0 ft Rotor Parameters Main rotor radius 37.5 ft Main rotor chord 3.57 ft Solidity 0.12 -- Number of blades 4 -- Main rotor speed 20 rad/s Tip speed 750 ft/s Aircraft Weight 142,708 lb Fuselage station (pilots) 305 in Configuration Butt line (pilots) ά 28 in Water line (pilots) 360 in Fuselage station (CG) 771.2 in Butt line (CG) 0.0 in Water line (CG) 333.9 in x (CG to pilot) 38.85 ft p y (CG to pilot) 2.33 ft p z (CG to pilot) –2.18 ft p I 2,981,688 slug·ft xx I 28,930 slug·ft xz I 1,265,420 slug·ft yy I 3,553,061 slug·ft zz Hover Trim Values ࢥ 0 (0) deg (rad) ș –4.28 (–0.0747) deg (rad) Lateral cyclic ( ά 5) 0 in Longitudinal cyclic ( ά 5) 0 in Pedals ( ά 2.69) 0 in Collective (0–10) 7 in Table A–4. LCTR2 aircraft model parameters.

Flight Condition Speed 0–236.3 ft/s Altitude 100.0 ft Rotor Parameters Main rotor radius 32.5 ft Main rotor chord 3.395 ft Solidity 0.133 -- Number of blades 4 -- Main rotor speed 20 rad/s Tip speed 650 ft/s Aircraft Weight 103,695 lb Fuselage station (pilots) 111 in Configuration Butt line (pilots) ά 24 in Water line (pilots) 136.1 in Fuselage station (CG) 495 in Butt line (CG) 0 in Water line (CG) 182.1 in x (CG to pilot) 32.0 ft p y (CG to pilot) 2.0 ft p z (CG to pilot) 3.83 ft p I 1,540,000 slug·ft xx I 30,500 slug·ft xz I 975,000 slug·ft yy I 2,280,000 slug·ft zz Hover Trim Values ࢥ 0 (0) deg (rad) (86 deg nacelle) ș 0.79 (0.0138) deg (rad) Lateral cyclic ( ά 5) 1.3832 in Longitudinal cyclic ( ά 5) 0 in Pedals ( ά 2.69) 0 in Collective (0–10) 6.2520 in

Appendix B—Flight Dynamics Aspects of the Nacelle Rate to

Longitudinal Cyclic Crossfeed

Use of a one-degree-of-freedom linear perturbation model of the longitudinal motion in TRC

provides insight into the flight dynamics mechanisms behind how the crossfeed improved the

longitudinal TRC handling qualities [64]. There are a number of simplifying assumptions to the model, including that rotor flapping and airframe pitching is primarily only disturbed by nacelle inputs and that because of the primary attitude control loop, other pitch disturbances can be considered negligible when considering the longitudinal motion. As such, the equation of the motion, expressed in Laplace form is: ᇱ ᇱ ᇱ

ܺൌ ݑݏ ܺ൅ ݑ ߚ ܺ൅ ߚ ߠ ݃െ

(39)

௨ ௠ ଵ௖ ఉ ఉ ೘ భ೎ Here, the main influencing factors on the longitudinal body-axis acceleration are the change in body-axis forward speed, nacelle angle, rotor flap angle, and aircraft pitch attitude.

The equation of motion for the rotor flap is dependent on nacelle angular rate, aircraft pitch rate, and the crossfeed gain, ܭ , which inputs an amount of longitudinal cyclic proportional to the nacelle rate: ᇱ ᇱ ᇱ

ߚݏ ܯ ൌ ߚݏ ܯ ൅ ܯ ൅ ݍ ߠ

ଵ௖ ௙ഁ ௠ ௙ ௙ ଵ௦ (40)

ሶ ೜ ഇభೞ ೘ where ߠ ߚݏܭ ൌ . Therefore: ଵ௦ ௠ ᇱ ᇱ ᇱ

ߚݏ ܯ ൌ ߚݏ ܯ ൅ ܯ ൅ ݍ ߚݏܭ

ଵ௖ ௙ഁ ௠ ௙ ௙ ௠ (41)

ሶ ೜ ഇభೞ ೘ Dividing by ݏ and rearranging: ᇱ ᇱ ᇱ

ߚ ܯܭቀ ൌ ܯ ൅ ߚ ቁ ܯ ൅ ߠ (42)

ଵ௖ ௙ ௙ഁ ௠ ௙ ഇభೞ ሶ ೜ ೘ where ߠݏ ൎ ݍ . Substituting Eq. (42) into Eq. (39): ᇱ ᇱ ᇱ ᇱ ᇱ ᇱ ᇱ

ܺൌ ݑݏ ܺ൅ ݑ ߚ ܺ൅ ܯܭቀ ܯ ൅ ߚ ቁ ܺ൅ ܯ ߠ ݃െ ߠ  (43)

௨ ௠ ௠ ఉ ఉ ௙ ௙ഁ ఉ ௙ ሶ ೜ ೘ భ೎ ഇభೞ భ೎ ೘ The simplified pitch equation for hover assumes the dominant effect is rotor flapping: ଶ ᇱ

ݏ ൎ ݍݏ ܯ ൎ ߠ ߚ

(44)

ఉ ଵ௖ భ೎ Also substituting for ߚ from Eq. (42) here gives: ଵ௖ ᇱ ᇱ ᇱ ᇱ ᇱ ଶ

ݏ ܯ ൌ ߠ ܯܭቀ ܯ ൅ ߚ ቁ ܯ ൅ ܯ ߠ (45)

௙ ௙ഁ ௠ ௙ ఉ ఉ భ೎ ഇభೞ ሶ భ೎ ೜ ೘ Solving Eq. (45) for the pitch attitude: ᇱ ᇱ ᇱ

ܯ ܯܭቀ ܯ ൅ ߚ ቁ

ఉ ௙ ௙ഁ ௠ ሶ భ೎ ഇభೞ ೘

(46)

ൌ ߠ

ᇱ ᇱ ଶ

ݏ ܯ െ ܯ

ఉ ௙ భ೎ ೜ Then substituting Eq. (46) into Eq. (43) gives: ᇱ ᇱ ᇱ ᇱ ᇱ

ܺൌ ݑݏ ܺ൅ ݑ ߚ ܺ൅ ܯܭቀ ܯ ൅ ߚ ቁ

௨ ௠ ௙ ௙ഁ ௠ ఉ ఉ ೘ భ೎ ഇభೞ ሶ ೘ ᇱ ᇱ ᇱ

(47)

ܯ ܯܭቀ ܯ ൅ ߚ ቁ

ఉ ௙ ௙ഁ ௠ ሶ భ೎ ഇభೞ ೘ ᇱ ᇱ

ܺቀ ൅ ܯ ቁ ݃െ 

ఉ ௙ ᇱ ᇱ భ೎ ೜ ଶ

ݏ ܯ െ ܯ

ఉ ௙ భ೎ ೜

Equation (47) shows the influence that the crossfeed gain, ܭ , has on the longitudinal

dynamics. The convention is that the nacelle tilt angle, ߚ , is negative for a forward rotation, so ௠ ᇱ ᇱ ᇱ

that the product of ܺ ܯܭቀ ܯ ൅ ߚ ቁ produces a negative longitudinal acceleration when

ఉ ௙ ௙ഁ ௠ ሶ భ೎ ഇభೞ ೘ ᇱ ܭ is zero and the nacelles are rotated forward. This shows the retarding influence of ܺ , which ఉ భ೎ is the longitudinal acceleration due to rotor flapping. This effect is linked directly to the flapping response to nacelle motion—when the rotors flap back against the nacelle tilt rate, the rotor thrust tilts accordingly. This means that the nacelle tilt responding to pilot commands has to work harder against the flap-back-induced thrust tilt. Selecting crossfeed gain ܭ such that ᇱ ᇱ ܯܭ ܯ ൅ ൌ Ͳ eliminates this opposing acceleration effect.

௙ ௙ഁ ሶ ഇభೞ ೘

The same effect is seen for the final term of Eq. (47), which represents the longitudinal

acceleration due to pitch attitude in terms of the rotor flapping and nacelle dynamics derivatives.

The mechanism is that the opposite sense pitching moment induced by the moving nacelles

causes the aircraft to tilt in the ܼܺ -plane. In the body fixed frame, a gravitational component in the aircraft longitudinal axis manifests, whereas in the Earth frame it is equivalent to the trim ܼ -axis force being tilted aft. In either frame of reference this action “robs” the aircraft of some of the ܺ -axis acceleration that it is trying to generate by tilting the nacelle—resulting in the nacelle having to rotate further/faster in order to achieve the commanded acceleration. Cancelling this term using the crossfeed gain eliminates this lagging effect, resulting in a simplified longitudinal ᇱ ᇱ set of dynamics,

ܺൌ ݑݏ ܺ൅ ݑ ߚ . In summary, the crossfeed is able to minimize the lagging

௨ ఉ ௠ ೘ effects on the longitudinal velocity of both rotor flap back to nacelle rate and the subsequent pitching motions by effectively keeping the rotor disc plane perpendicular to the nacelle/shaft axis (Figure 86).

Nacelle rotates and rotor tip- Crossfeed inputs longitudinal Tip-path plane maintained

path plane lags behind hub cyclic proportional to nacelle close to perpendicular to

plane rate shaft axis; flap does not lag

behind nacelle or induce

pitching

Figure 86. Crossfeed mechanism minimizing nacelle-rate-induced flap and pitch.

Appendix C—Pilot Questionnaire

Task Performance 1. Describe ability to meet DESIRED / ADEQUATE performance standards.

2. Describe aggressiveness / precision with which task is performed.

a) Assess level of aggressiveness employed: Limited Unlimited 1 2 3 4 5 6 7 8 9 b) Assess level of precision obtainable: Low High 1 2 3 4 5 6 7 8 9 3. If trying for DESIRED performance resulted in unacceptable oscillations, did decreasing your goal to ADEQUATE performance alleviate the problem?

Aircraft Characteristics 4. Describe any objectionable controller force characteristics.

5. Describe predictability of initial aircraft response.

6. Describe any mid- to long-term response problems.

7. Describe any objectionable oscillations or tendency to overshoot.

8. Describe any nonlinearity of response.

9. Describe any problems with harmony of pitch and roll, speed control, with height control, and with heading hold/turn coordination. For TRC response types, describe any problems with harmony of pitch and longitudinal translation.

Demands on the Pilot 10. Describe overall control strategy in performing the task (cues used, scan, etc.).

11. Describe any control compensation you had to make to account for deficiencies in the aircraft.

12. Describe any modifications you had to make to what you would consider “normal” control technique in order to make the aircraft behave the way you wanted.

MISC.

13. Please comment on anything else that may have influenced you.

Assign HANDLING QUALITIES RATING for overall task.

14. Using the Cooper-Harper rating scale, please highlight your decision-making process and adjectives that are best suited in the context of the task. If assigned HQR is Level 2, briefly summarize any deficiencies that make this configuration unsuitable for normal accomplishment of this task.

15. What was the critical sub-phase of the task (e.g., entry, steady-state, exit) or major determining factor in the overall Handling Quality Rating (HQR).

16. Please comment on the appropriateness of the MTE maneuvers, test course, and performance standards to check for the ability to perform task in context of rotorcraft’s mission.

Figure 87. Cooper-Harper Handling Qualities Rating scale.

References

[1] Federal Aviation Administration: The Economic Impact of Civil Aviation on the U.S.

Economy, Aug. 2011.

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