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Unified Theory for Aircraft Handl!ng Qualities
and AdverseAircraft-Pilot Coupling
R. A. Hess
_ii , • g i L Reprinted from
/(? i iii _, Journal of Guidance, Control, and Dynamics
Volume20, Number6, Pages 1141-1148 !:i•, %¸ : A publication of the American Institute of Aeronautics and Astronautics, Inc.
1801 Alexander Bell Drive, Suite 500 Reston, VA 20191-4344
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JOURNAL OF GUIDANCE, CONTROL, AND DYNAMICS Vol. 20, No. 6, November-December 1997
Unified Theory for Aircraft Handling Qualities
i/_ _ _'i '_,
and Adverse Aircraft-Pilot Coupling
_! LI:-_ !II:,,L',I _
R. A. Hess* University of California, Davis, Davis, California 95616 A unified theory for aircraft handling qualities and adverse aircraft-pilot coupling or pilot-induced oscillations is introduced. The theory is based on a structural model of the human pilot. A methodology is presented for the prediction of 1) handling qualities levels, 2) pilot-induced oscillation rating levels, and 3) a frequency range in which pilot-induced oscillations are likely to occur. Although the dynamics of the force-feel system of the cockpit inceptor is included, the methodology will not account for effects attributable to control sensitivity and is limited to single-axis tasks and, at present, to linear vehicle models. The theory is derived from the feedback topology of the structural model and an examination of flight test results for 32 aircraft configurations simulated by the U.S.
Air Force/CALSPAN NT-33A and Total In-Flight Simulator variable stability aircraft. An extension to nonlinear vehicle dynamics such as that encountered with actuator saturation is discussed.
Starting from the left, one sees the system error e(t) following one Introduction of two possible paths. One path is intended to model the human's visual rate-sensing dynamics, here modeled by a differentiator (s), N adverse aircraft-pilot coupling (APC) or pilot-induced os- cillation (PIO) can be defined as an unwanted, inadvertent, and an •injected noise signal, and a gain K_. The remaining path de- atypical closed-loop coupling between a pilot and the response vari- scribes normal error sensing and gain compensation Ke, including ables of an aircraft. 1 APC or PIO problems are not new phenomena; the possibility of the human's accomplishing low-frequency trim indeed, they have been around since the Wright Brothers and have (or integral) compensation via E/s. In the study herein, E -- 0.
been referred to as the senior handling qualities problem. 2 McRuer 2 The switch labeled $1 allows switching between error and error- gives a concise historical perspective of the PIO problem, including rate tracking. This switching will be hypothesized to play a critical a review and discussion of germane pilot behavior patterns.
role in the initiation and sustenance of APC/PIOs. A central pro- Because of a strong correlation between APC/PIO susceptibility cessing time delay z0 is also included. An inner, proprioceptive and modem, full-authority control systems employing fly-by-wire feedback loop is encountered next. Proprioceptive feedback implies (FBW) technology, interest in studying the APC/PIO phenomenon the use of sensory information about limb position. In the forward has been increasing. For example, NATO's AGARD convened a portion of this loop, the elements YNM and YFS are intended to rep- special workshop on PIO, 3 and NASA has sponsored a National resent, respectively, the open-loop dynamics of the neuromuscular Research Council committee to study the problem of APC/PIO. 4 system driving the cockpit inceptor and the dynamics of the in- U.S. Air Force interest in the APC/PIO problem has led to the pub- ceptor force-feel system itself. The feedback portion of this loop lication of four reports under the general rubric of a Unified PIO contains the element YPF, which receives as its input the propri- Study. 5-8 oceptively sensed inceptor output _,_ (t). The element YPF and its Despite the amount of research that has been directed toward so- position in the model are central to the philosophy of the struc- lution of the APC/PIO problem, there appears to be little consensus tural model, i.e., that the primary equalization capabilities of the about the phenomenon itself in terms of the pilot behavior that initi- human pilot are assumed to occur through operation upon a pro- ates and sustains the APC/PIO. There is general agreement that the prioceptively sensed, as opposed to a visually sensed, variable.
contributing factors are 1) a demanding flight task, 2) a vehicle with As will be discussed, switches S1 and $2 are assumed to oper- unsatisfactory dynamics, and 3) a triggering event. 2 The main thrust ate in unison, i.e., when S1 is in the "up" position, so is $2. Un- of the research to be described is to suggest one possible human- less stated otherwise, it is assumed in what follows that switches centered theory concerning the APC/PIO phenomenon. The theory $1 and $2 _ire in the nominal, "down" position. The switch $3 al- to be proposed will attempt to unify the topics of vehicle handling lows either displacement-sensing or force-sensing inceptors to be qualities and APC/PIO, which have been somewhat disparate in the modeled.
past. Finally, although pertinent to the handling qualities of high- Time derivatives of the vehicle output in (t) are assumed to be in- performance aircraft, the phenomenon of roll ratchet 9 will not be dividually sensed, as indicated in Fig. 1. Switch $4 allows either rate discussed here.
or acceleration cues or neither to be used in vehicular control. Note that feeding back output rate is predicated on that signal creating Revised Structural Model an acceleration that can be sensed by the middle ear. In this study, Figure 1 shows what will be referred to here as the revised struc- K,h = K,h = 0. A visual feedback of vehicle output completes the tural model of the human pilot. The model has its genesis in a model.
previously described structural model 1° and in a later modifica- The particular form of the error-rate loop deserves some com- tion of that model. H As shown in Fig. 1, the model is describ- ment. It is the author's contention that the visual sensing of rate ing compensatory pilot behavior, i.e., behavior involving closed- '. iii ¸_•¸¸ "¸'•:i_i¸¸ information of a quality suitable for precise closed-loop tracking is loop tracking in which the visual input is system error. The ele- compromised by the limitations of the human visual system. The in- ' i_ i!••i, ii¸i_'•: ments within the dashed box represent the dynamics of the human jected noise has been included as a somewhat crude model of these ('i•:i_i _ i(i _?; pilot.
limitations. The noise itself is not pertinent to the discussion and / ' ,_ :i'_ i•'_/_ will not be treated further.
•_;. :.• _, ;_i, ¸ Received Oct. 11, 1996; presented as Paper 97-0454 at the AIAA 35th Aerospace Sciences Meeting, Reno, NV, Jan. 6-9, 1997; revision received March 20, 1997; accepted for publication March 21, 1997. Copyright © Pilot-Vehicle Analysis with the Structural Model 1997 by R. A. Hess. Published by the American Institute of Aeronautics and Model Parameterization Astronautics, Inc., with permission.
As can be seen from Fig. 1, only the elements YNM and YPF need to *Professor, Department of Mechanical and Aeronautical Engineering. As- i:11 ••:: _,, be parameterized because the remaining elements are simply gains, sociate Fellow AIAA.
- 1142 HESS
PILOT r"_ .............
"1 I I I I i
'1 1 vehiCLe
el
---_M I I > .....
_[--7-]. I Proprioceptive
G<
--_ feedback- '_:" '. _ .',4 • _'-'-_ vestibula_ feedback visual feedback :i Fig. 1 Revised structural model of the human pilot.
e.g., K_, Ke, etc., differentiating elements (s, s2), and time delays i.e., YpYc(jw) follows the dictates of the crossover model of the , ,_ 7, _.!i'iL human pilotJ 2 The implementation of Eq. (4) is critical to the suc- 0:0). Here, _ i_'_ =i cess of the handling qualities and APC/PIO analyses to follow, so o_M it is important to specify in a precise manner just how this is done.
YNM = $2 ..1_ 2_nMwmas + wzM (1) Limiting discussion to the last two forms of YPF (those most likely to be encountered in pilot-vehicle analyses), the right-hand side of Eqs. (2) is selected so that YpF=K(s+a) or K or K/(s+a) (2) Yc(jw) Kl for / w _ wc with the particular equalization of Eqs. (2) dependent on the form YpF(jW) _" j---£ [ KI arbitrary (5) of the vehicle dynamics around the crossover frequency.
The forms of Eqs. (2) can be interpreted as the pilot's "internal The gain K appearing in Eqs. (2) is chosen so that, with all other model" of the vehicle dynamics. That is, in the range of crossover, loops open, the minimum damping ratio of any quadratic closed- YPF (X s. Yc(s). There will be reason to return to this internal model loop poles of(3M/EM)(s) is _'min= 0.15. Finally, K_ is selected so concept in discussing pilot behavior in APC/PIO events later.
that the desired crossover frequency of 2.0 rad/s is obtained.
The use of fixed parameters in the pilot model is obviously an an- Crossover Frequency Selection alytical simplification. However, it has been the author's experience In the analyses to follow, a constant crossover frequency wc = that the model so derived is of sufficient accuracy to justify its use in 2.0 rad/s is chosen. Of course, the human pilot can, in a limited the pilot-vehicle analyses that are the subject of the research to be manner, vary crossover frequency, n However, for the purposes of described. As described, the model will reflect the important, experi- analysis, the assumption of a constant crossover frequency is very mentally verified human pilot dynamics, 12i.e., faithful reproduction useful. Selecting wc = 2.0 rad/s is not an arbitrary decision. Using of crossover model characteristics across different vehicles and the the crossover model of the human pilot, 12 Ref. 13 examined the important dynamics of the closed-loop neuromuscular system, in- sensitivity of the closed-loop system bandwidth w8 to changes in cluding high-frequency amplitude peaking and phase roll-off.
the open-loop crossover frequency. It was shown that, for wc < 0.34/re (where re is the crossover model's effective time delay), ws Analysis of Handling Qualities becomes very sensitive to reductions in we. Selecting a value for re Previous Results representative of the lower limit found in the literature (re = 0.2 s) A theory for handling qualities based on the original structural leads to a "critical" value of we = 1.7 rad/s. This value was rounded model has been proposed and discussed elsewhere. 12,14 The the- up to 2.0 rad/s for the purposes of this study.
ory postulates that the power in the proprioceptive feedback signal Um(t) of Fig. 1 is the determining factor in a pilot's perception of Parameter Value Selection a vehicle's handling qualities when Eq. (4) is satisfied. The signal As in applications of the original structural model, a number of Urn(t) can be shown to be proportional to the output rate rh(t) due model parameters will be considered invariant across different ve- to control activity _m (t). Because the power in u,, (t) is dependent hicles and tasks. The particular values chosen are considered rep- on I(UM/C)(jw)I, it was found that this function itself could be resentative of values associated with the dynamic subsystem being used to predict handling qualities levels and was referred 1o as the modeled. Choosing the undamped natural frequency of the open- ! ' • • J" LI handling qualities sensitivity function (HQSF)J TM The similarity loop neuromuscular system as corm = 10 rad/s is one such example.
between the previous structural model and its revised incarnation in Nominal values for these "fixed" parameters can be given as Fig. 1 allows the HQSF definition to remain unchanged: r0 = 0.2 s, WNM = 10rad/s, _'rqM = 0.7 (3) HQSF = I(UM/C)(jo_)I (6) The relatively simple relations of Eqs. (1-3), the crossover rela- In calculating the HQSF, it is necessary to remove the effects tion w,. = 2.0 rad/s, and the selection of one of the three forms on of control sensitivity. By this it is meant that the model results are the right-hand side of Eqs. (2) allow implementation of the model forced to be independent of control and force-feel system sensitivity.
of Fig. 1. The appropriate form in Eqs. (2) is chosen so that the This sensitivity includes command path gains between the inceptor resulting open-loop transfer function and the actuators and the static gain of the pertinent vehicle trans- fer function, i.e., the gain appearing in the vehicle transfer function YpY_.(jw) = (3M/E)(jw). Y_.(jog) ,-_ (wc/jw)e -r: when written in "time-constant" form. Removing the effects of un- for w ,_ coc (4) certainty in the HQSF is accomplished as follows: HESS 1143 all configurations by selecting the control sensitivity that produced Displacement-sensing inceptor the same maximum pitch rate for a step inceptor input. One can- not guarantee that these procedures eliminated control sensitivity effects from the handling qualities and APC/PIO susceptibility, but M 1 1 YpF(jw) HQSF = (jco)'K'--_'y_.(jco)" their impact was minimized.
Given the necessary information on vehicle and force-feel system Force-sensing inceptor dynamics, pilot-vehicle analyses were undertaken as just described for the 32 configurations identified in Table 1. The average Cooper- I Harper Pilot Opinion Ratings (PORs) that these configurations re- 1 1 • YFsYpF(jw)I (7) HQSF = "K--'_'Yc(jw---_
I ceived in flight tests are also given. In cases in which separate overall
and approach/flare/landing ratings were elicited, just the averaged overall ratings were used.
For level 1 handling qualities, i.e., 1 < Cooper-Harper ratings < In undertaking the pilot-vehicle analyses, two exceptions to the 3.5, the previous structural model required HQSF<I.0. However, 2.0-rad/s crossover frequency rule were necessary. These exceptions because the previous model differed in detail, especially in the pro- occurred with configuration 5-3 (Ref. 15) and configuration H2-8 prioceptive feedback loop, the criteria for level 1 handling qualities (Ref. 16). In each case, an attempt to apply Eq. (5) resulted in the will probably change when the model of Fig. 1 is used. In addi- open-loop pilot-vehicle transfer function exhibiting a flat amplitude tion, there were no bounds suggested for level 2 and 3 handling region about crossover. Thus, small changes in pilot gain resulted in quality levels in previous handling quality studies with the original structural model. This restriction will be removed in what follows. large changes in stability margins that the author did not consider to be realistic pilot-vehicle characteristics. The following procedure was implemented to handle these cases. First, an attempt was made New Results to increase the crossover frequency until the offending fiat portion Flight-test handling quality results from Refs. 15-18 were of the amplitude plot was at least 2.0 dB above the 0-dB line. If this used to obtain new bounds for the HQSFs. The data concen- change could not be accomplished with positive stability margins, trated on the longitudinal approach and landing tasks for the U.S.
the crossover frequency was reduced to 1 rad/s for that configuration.
Air Force/CALSPAN NT-33A 15A6 and Total In-Flight Simulator ] i :5 _ ; The latter approach was necessary for configuration 5-3, whereas (TIFS) 17'18 vehicles. The configurations shown in Table 1 were the former sufficed for configuration H2-8.
selected to give as wide a distribution in handling qualities and Figure 2 shows the HQSFs resulting from the pilot-vehicle anal- APC/PIO susceptibility as possible. Because the pilot-vehicle anal- /( yses of the configurations that received level 1 PORs in flight tests.
ysis technique does not consider the effects of control sensitivity, The dashed line approximates a least upper bound for these HQSFs.
the question of how the flight-test control sensitivities were deter- Figure 3 shows a similar plot for the configurations that received mined naturally arises. The "back seat" NT-33A pilot selected what level 2 PORs. The upper dashed line again provides an approximate he determined to be the optimum sensitivity for each configuration upper bound. Finally, Fig. 4 does the same for configurations that in Ref. 15. This value remained unchanged for the other evaluation received level 3 PORs. (For the purposes of this research, level 3 pilots. In Ref. 16, each evaluation pilot determined what he believed was considered to include all PORs > 6.5.) The only "failure" in to be the optimum sensitivity for each configuration. In Refs. 17 and this categorization of 32 HQSFs is that for configuration 4 in the 18, an attempt was made to achieve comparable sensitivities across Table I Configurations for handling qualities and APC/PIO investigation Ref. 18 Ref. 15 Ref. 16 Ref. 17 PIOR Configuration POR PIOR Configuration POR PIOR Configuration POR PIOR Configuration POR 5-2-2 2.5 1.0 1-3 9.5 3.25 H2-1 2.33 1.0 B 2.7 1.0 6-1-1 5.0 2.5 1-C 4.0 1.0 H2-5 9.0 4.33 1 2.9 1.0 2-C 2.5 1.0 H2-8 8.67 4.0 4 3.75 1.25 3-C 5.0 1.25 H3-1 4.0 2.33 11 5.7 3.33 4-4 6.5 2.67 H3-3 2.5 a 1.66 17 2.6 1.0 4-7 3.0 1.0 H3-6 4.5 2.0 17L+L 3.5 1.0 4-10 9.0 4.0 H3-D 2.0 1.0 20 3.5 1.0 5-3 6.1 2.1 H3-12 8.0 4.5 21 4.5 2.25 6-1 10.0 4.0 H4-1 2.67 1.0 22 6.75 4.0 6-2 2.0 1.0 H5-10 10.0 5.0 H5-11 6.33 3.0 aThree ratings of 7/2/3 were given. Reference 16 lists this as level 1. The author does the same and assumes that the pilot rating of 7.0 was treated as anomalous.
- _qo)
- Level 1 _ boundary _- 4 6 8 £0
r_/s
Fig. 2 HQSFs for flight-test configurations receiving level 1 POI_.
1144 HESS V---- Level 2
_
- oun ar
- !//11/%kklt/ V ""h% \ \_-..
failure _
:!!(:i i¸_i'_,!/_':, ¸
2 4 6 8 18 g
(o rad/s
Fig. 3 HQSFs for flight-test configurations receiving level 2 PORs.
I _ I f I f O 4 6 8 10 O 2 CO ro_s Fig. 4 HQSFs for flight-test configurations receiving level 3 PORs.
?: Level 3
- __q_)
/*" \ i Level 2 \ \ // ,/,/ Level 1 1 _ ¢¢.
f I i I i [ ; Q r I 0 2 4 6 8 IO o_ rad/s Fig. 5 Handling quality boundaries for HQSFs.
Analysis of APC/PIO Events
TIFS data of Ref. 17. Figure 3 would place this configuration in level 1, whereas the average POR reported in flight tests was 3.75, PIO Ratings An analysis of the vehicle configurations of Table 1 using the which would place this configuration just within level 2.
:, i
pilot-vehicle analysis procedure described in the preceding was Figure 5 summarizes all of the handling quality boundaries. Fig- conducted with the goal of developing a theory for APC/PIO. Again, ure 5 implies that, if the HQSF resulting from application of the the characteristics of the proprioceptive feedback signal u,_ (t) were pilot-vehicle analysis described in the preceding is below the level 1 i : investigated in this context. It was found that a sensitive metric for boundary, the configuration should be expected to receive level 1 APC/PIO susceptibility was the power spectral density (PSD) of the PORs. If the HQSF exceeds the level 1 boundary but remains below signal Um (t) when a filtered white noise command c(t) was applied.
the level 2 boundary, the configuration should be expected to receive The PSD of c(t) was selected as level 2 PORs. Finally, if the HQSF exceeds the level 2 boundary, it should be expected to receive level 3 PORs. The theoretical basis for this categorization derives from the hypothesized importance of
• cc(_O) = _ (8)
the signal Um (t) in the pilot model.
' ii HESS Table 2 PIOR scale description Description Numerical rating No tendency for pilot to induce undesirable motions. 1 Undesirable motions tend to occur when pilot initiates abrupt maneuvers or attempts 2 tight control. These motions can be prevented or eliminated by pilot technique.
Undesirable motions easily induced when pilot initiates abrupt maneuvers or attempts tight 3 control. These motions can be prevented or eliminated but only at sacrifice to task performance or through considerable pilot attention and effort.
Oscillations tend to develop when pilot initiates abrupt maneuvers or attempts tight control• 4 Pilot must reduce gain or abandon task to recover.
Divergent oscillations tend to develop when pilot initiates abrupt maneuvers or attempts 5 tight control. Pilot must open loop by releasing or freezing the stick.
Disturbance or normal pilot control may cause divergent oscillation. Pilot must open control 6 loop by releasing or freezing the stick.
dp_..... (co). Figure 9 implies that, if the dpu,n_,_ (co) resulting from application of the pilot-vehicle analysis described in the preceding No is below the lowest bound, the configurations should be expected to receive a 1 < PIOR < 2. If the _, ..... (co) exceeds the lowest bound in Fig. 9 but remains below the next bound, the configura- Yes tion should be expected to receive a 2 < PIOR < 4. Finally, if the dp_ ..... (co) exceeds the upper bound in Fig. 9, the configuration should be expected to receive a PIOR > 4. The theoretical basis for this categorization is again based on the hypothesized importance of the signal urn(t).
No Yes Development of an APC/PIO Event As mentioned in a preceding section, conditions almost invariably accompanying an APC/PIO event are 1) a demanding flight task, 2) a vehicle with unsatisfactory dynamics, and 3) a triggering event. In terms of the pilot-vehicle analysis technique that has been described, the first two conditions are respectively realized by 1) the existence / of a relatively high crossover frequency in a compensatory tracking Abrupt Maneuvers or PilOt IrVt_ated I pilot model and 2) the evidence of • ...... (co) exceeding the boundary "ngat Cor_ associated with PIOR >_ 4. The triggering event itself is not part of the pilot-vehicle model. Triggers can originate in the external environment, e.g., a sudden patch of turbulence, the vehicle, e.g., a stability augmentation transient, or the pilot him/herself, e.g., a Yes change in the vehicle response variable being actively controlled.
However, the effect of this event is hypothesized to cause switches Sl and $2 in Fig. 1 to move to the position in which the pilot tracks error rate instead of error and does so without proprioceptive feedback.
It is hypothesized that this altered feedback structure represents the pilot's temporary regression to a type of tracking behavior that can to Erter Ccr_rd occur in initial exposure to a new dynamic system. In the latter case, I PilotArtemis Loop no internal model has been formed through training (no YPF to permit proprioceptive feedback and adequate compensation of the plant), Fig. 6 PIOR scale.
and the task becomes one of simply keeping the error bounded by attempting to control error rate with no compensation. Obviously, _,.(co) was chosen with a break frequency at 2.0 rad/s, identical to in an operational setting, this behavior is unwanted, inadvertent, and the crossover frequency enforced in the pilot-vehicle analysis. It was atypical.
found that, similar to the HQSF, plots of dp ...... (o_) could be used to delineate "levels" of pilot-induced oscillation ratings (PIORs) using APCfPIO Frequency the scale of Fig. 6 and Table 2. The levels were defined herein as The legitimacy of any analytical pilot-vehicle model that is used to study APC/PIO events is often judged by the ability of that model 1 < PIOR < 2, 2 < PIOR < 4, PIOR > 4 (9) to predict APC/PIO frequencies that have been measured in exper- iment. Because the model of Fig. 1 is linear, conditions of neutral Table 1 lists the averaged PIORs that each of the configurations received in flight test. Figure 7 shows • ...... (co) [defined as dPcc(co) • stability (with switches S] and $2 in the up position indicating rate [HQSF] 2] for theconfigurationsthatreceived 1 < PIOR < 2.Figure tracking with no proprioceptive feedback) can be easily obtained.
This includes the unstable frequency (frequency of oscillation). De- 8 shows _u,_,n (co) for configurations that received 2 < PIOR < 4, and finally, Fig. 9 shows _,,,"m (co) for configurations that received fine the loop transmission with rate tracking as Lr, where from PIOR > 4. In each of these figures, the dashed lines approximate a Fig. 1, least upper bound for the PSDs in question. The nature of the PSDs Lr = s • K_ • (M/Ec)lsl.s2upposition (10) and their relation to the PIORs has allowed simpler bounds to be drawn than those of Fig. 5. Also note that, as opposed to Figs. 2-5, ,_ , i: I .•. , Neutral stability will occur when the ordinates in Figs. 7-9 have different scales. There is one failure in this categorization of the PIORs. In Fig. 8, configuration H3-1 /Lr(jco) = -180deg (11) (Ref. 16) lies in the area indicating 1 < PIOR < 2, whereas Table 1 indicates that it received an average PIOR of 2.33 from flight tests.
Configuration 22 from Ref. 17 can be selected as an exam- As in the case of the HQSF boundaries of Fig. 5, Figs. 7-9 sug- ple. As Table 1 indicates, the configuration received an average gest that one can delineate between the PIOR levels of Eq. (9) using HESS
_... (to) ,,'
< PIOR < 4 'x'x // / 2k \\ "-.
L
,,f" 1 < PIOR < 2-_"_... x.,.
failure _ , I I T 8 lk 2 3 4 co rad/s Fig. 8 C_UmUm (tO) for flight-test configurations receiving 2 < PIOR < 4.
1.0 _L_ -- _llmltm (fdO) ?
--" _ PIOR >_ 4 - 1N _ _ //j je \\ 72 < PIOR < 4 ""..
. .,. %/ .... "....
I - _-'- _.--_tl <- PIOR < 2 __--7-- _ 1 2 3 4 (0 ra_ Fig. 9 _UmUm (w) for flight-test configurations receiving PIOR > 4.
PIOR = 4, and flight-test-time histories from Ref. 17 clearly indi- addition, and in terms of the model of Fig. 1, it is possible for the cate APC/PIOs. A root locus analysis indicated that the frequency pilot to switch back to position tracking (with proprioceptive feed- of oscillation will be 3.26 rad/s; an APC/PIO of 3.3 rad/s occurred back) in an APC/PIO event. The fact that an APC/PIO was initiated, in flight tests. 17 The closeness of this agreement is probably fortu- however, suggests that even position tracking may be oscillatory in itous. Although APC/PIO events are oscillatory, a precise frequency nature. This means that the actual APC/PIO frequency(s) may also , / , , definition is often difficult. Indeed, in examining the time histories reflect the dominant frequency in qb...... (co). Consider configura- of single APC/PIO events, different frequencies can be detected. In tion H3-12 (Ref. 16). There a relatively low-frequency APC/PIO research flight tests in which APC/PIO events occur with a single of 2.2 rad/s was recorded. With switches $1 and $2 in the up po- configuration, it is possible to see different frequencies for different sition, a root locus analysis with the model of Fig. 1 indicated an "i pilots. For this reason, no detailed comparison of APC/PIO fre- APC/PIO frequency of 3.1 rad/s, a considerably higher value than quencies between model and experiment will be attempted here. In that recorded in flight tests. However, ep...... (co) for this case, shown HESS IO ? i ¸ ,'(.: , center frequency 7, H.
3 4 03 rad/s Fig. 10 _UmUm(W) for configuration H3-12 from Ref. 16.
O 18B 0 dB line - minimum gain for -4
,e ormance
N_\\\\\\'x_x\\xx\x\x !
-2B gain range -t [_"_-0 dB line- maximum gain for _.
-4fl _r(J03 )L_B _'"x, / Lr(flo) deg -'t-- \ - - -laa ix \ -6O magnitude \ -270 phase x I f _ I _ I _f [ ! I J s _ s J s --360 -8_ _ _ I I I f I _ I 101 10 2 1Q -1 10 ° 03 rad]s Loop transmission Lr (jw) for a pilot-vehicle analysis of configuration 1-12-5 from Ref. 16.
Fig. 11 occurring in the flight test. The APC/PIO frequency resulting from in Fig. 10, indicates a narrow band U m (t) [and, by inference, rh (t)].
the model-based root locus analysis was 3.1 6 rad/s. The flight-test This frequency band is centered at 2.3 tad/s, much closer to the oscillations appeared to be gradually increasing in frequency. At the value obtained from flight tests. In this light, a range of possible end of the event, the frequency was approximately 3.1 rad/s.
APC/PIO frequencies may be a better prediction than a single fre- quency resulting from the rate-tracking model. The low frequency in this range would be that for ¢P'm u,. (o)) Imax, and the high frequency Application to Nonlinear Vehicle Dynamics would be that obtained from the root locus analysis.
A convenient categorization of APC/PIO encounters has been Note that the range of K_ that the pilot can adopt during rate track- suggested that includes three categories. 2 Category I describes ing is quite limited. This is demonstrated in Fig. 11, which shows events with essentially linear vehicle dynamics and pi10t behavior.
Lr(jw) as defined in Eq. (10) for the model of Fig. 1. The vehi- Category II describes events in which fundamental nonlinearities cle configuration is H2-5 (Ref. 16). Shown on the magnitude plot come into play, chiefly, those associated with the actuators. Cate- is the probable range of gains that the pilot could adopt, with the gory III describes events that fundamentally depend on nonlinear minimum gain corresponding to some minimum level of acceptable transitions in either the effective vehicle dynamics or the pilot's be- rate-tracking performance and the maximum gain corresponding havioral dynamics. The model-based theory that has been described to neutral stability. This diagram suggests why, once initiated, an herein addresses only Category I events. Many of the APC/PIO en- APC/PIO event is not easily arrested.
counters of modern FBW aircraft involve rate limiting in the actu- ators, a factor that has not been included in the analysis described here. Thus, exonerating a vehicle from APC/PIO using the tech- Inceptor Applied Force-Output Rate Phasing niques described here may be premature, unless one can ensure that Another measure of model validity in describing APC/PIO events actuator saturation, particularly rate saturation, will not produce an is the phasing between the vehicle response variable (or its rate) APC/PIO.
being controlled and the inceptor force being applied by the pilot Extending the theory that has been described here to the case during the APC/PIO event. Again returning to configuration H2- of actuator saturation should be straightforward. This is because 5 (Ref. 16), Fig. 12a shows an APC/PIO event that occurred in a the fundamental metric that has been used in determining APC/PIO flight test. Note the phasing between stick force and response rate susceptibility is simply the PSD of a signal that is easily accessible in (pitch rate). When the pitch rate is experiencing an axis crossing, the a non-real-time simulation of the pilot-vehicle system. In addition, control force has just passed its maximum value and is beginning calculation of the HQSF with nonlinear vehicle dynamics can also be to decrease in magnitude. Figure 12b shows the corresponding pair accomplished using existing techniques for determining the Laplace of time histories from the model of Fig. 1. Note the similar phasing transforms of the input-output pairs of nonlinear systems, e.g., the between pitch rate and control force. The variables in Fig. 12b have technique used in nonlinear quantitative feedback theory.19 Research been scaled so as to produce nearly equal amplitudes. Of course, in this area is underway.
the linear, noise-free model results are much smoother than those 1148 HESS 20 in which no proprioceptive feedback (and appropriate plant com- pensation) is used. This behavior is considered to be unwanted, inadvertent, and atypical.
stick force 0 lb.
4) The theory and pilot-vehicle analysis technique appear to be I I I extendable to the study of APC/PIO events involving nonlinear ve-
4. pull i • *
-20 hicle dynamics such as actuator saturation.
I I I I Acknowledgments This research was supported by NASA Langley Research Center pitch rate 0 under Grant NAG 1-1744. Barton Bacon was the Contract Technical deg/s Manager.
zero -5 References crossings 1Smith, R. H., "A Theory for Longitudinal Short-Period Pilot Induced I I F t Oscillations," U.S. Air Force Flight Dynamics Lab., AFFDL-TR-77-57, 15 20 25 30' Wright-Patterson AFB, OH, June 1977.
time, s 2McRuer, D. T., "Pilot-Induced Oscillations and Human Dynamic Be- a) Flight test havior," NASA CR 4683, July 1995.
3"Flight Vehicle Integration Panel Workshop on Pilot Induced Oscilla- _t_ tions," AGARD Advisory Rept. 335, Feb. 1995.
4Aviation Safety and Pilot Control--Understanding and Preventing Un- stick force - push\ /_ /f _ /_ /f _ /_ /_ favorable Pilot-Vehicle Interactions, Rept. of the NRC Committee on the Effects of Aircraft Pilot Coupling on Flight Safety, National Academy Press, i /, i!!, Washington, DC, !997.
5Klyde, D. H., McRuer, D. T., and Myers, T. T., "Unified Pilot-Induced : i , ' '_ //_ Oscillation Theory, Volume I: PIO Analysis with Linear and Nonlinear Effec- tive Vehicle Characteristics, Including Rate Limiting," U.S. Air Force Flight (no scale) . s Dynamics Directorate, WL-TR-96-3028, Wright-Patterson AFB, OH, Dec.
1995.
15 20 25 30 6preston, J. D., Citurs, K., Hodgkinson, J., Mitchell, D. C., Buckley, time, s J., and Hoh, R. H., "Unified Pilot-Induced Oscillation Theory, Volume II: b) Pilot-vehicle analysis Pilot-lnduced Oscillation Criteria Applied to Several McDonnell Douglas Aircraft," U.S. Air Force Flight Dynamics Directorate, WL-TR-96-3029, Fig. 12 Comparison of phasing of applied control forces and vehicle Wright-Patterson AFB, OH, Dec. 1995.
output rate for configuration 1t2-5 from Ref. 16.
7Anderson, M. R., and Page, A. B., "Unified Pilot-Induced Oscillation Theory, Volume III: PIO Analysis Using Multivariable Methods," U.S.
Air Force Flight Dynamics Directorate, WL-TR-96-3030, Wright-Patterson Limitation and Caveat [ , i AFB, OH, Dec. 1995.
The primary limitation of the pilot-vehicle analysis that has 8Bailey, R. E., and Bidlack, T. J., "Unified Pilot-Induced Oscillation The- been discussed is its inability to reproduce the changes in handling ory, Volume IV: Time-Domain Neal-Smith Criterion," U.S. Air Force Flight qualities and APC/PIO susceptibility that accompany changes in Dynamics Directorate, WL-TR-96-3031, Wright-Patterson AFB, OH, Dec.
1995.
control sensitivity. Of course, this limitation is common to most, 9Chalk, C. R., "Excessive Roll Damping Can Cause Roll Ratchet," Jour- if not all, pilot-model-based analysis procedures. One must sim- [! ] : nal of Guidance, Control, and Dynamics, Vol. 6, No. 3, 1983, pp. 218, 219.
ply rely on experimental results to provide guidance regarding this 1°Hess, R. A., "A Model for the Human's Use of Motion Cues in Vehicular important parameter.
Control," Journal of Guidance, Control, and Dynamics, Vol. 13, No. 3, 1990, The handling qualities and APC/PIO boundaries that have been pp. 476-482.
derived resulted from the application of a very specific model of the 11Hess, R. A., "Analyzing Manipulator and Feel System Effects in Aircraft human pilot, with very specific fixed parameter values and formal Flight Control," IEEE Transactions on Systems, Man, and Cybernetics, Vol.
procedures for obtaining pilot compensation elements, e.g., YPF in 20, No. 4, 1990, pp. 923-931.
Fig. 1. Changes in any part of this analysis will affect the boundaries 12Hess, R. A., "Feedback Control Models--Manual Control and Track- that have been derived and should be avoided if one wishes to use ing," Handbook of Human Factors and Ergonomics, 2nd ed., edited by G.
Salvendy, Wiley, New York, 1997, pp. 1249-1294.
the proposed methodology in predictive fashion.
13Hess, R. A., "Analysis of Aircraft Attitude Control Systems Prone to Conclusions Pilot-Induced Oscillations," Journal of Guidance, Control, and Dynamics, Vol. 7, No. 1, 1984, pp. 106-112.
Based on the research that has been described, the following con- 14Hess, R. A., Malsbury, T., and Atencio, A., Jr., "Flight Simulator Fi- clusions can be drawn.
delity Assessment in a Rotorcraft Lateral Translation Maneuver," Journal of 1) A unified theory for aircraft handling qualities and APC/PIOs Guidance, Control, and Dynamics, Vol. 18, No. 1, 1993, pp. 79-85.
is possible. The theory is based on a revised structural model of 15 Smith, R. E., "Effects of Control System Dynamics on Fighter Approach the human pilot and the central importance of a proprioceptively and Landing Handling Qualities, Vol. I," U.S. Air Force Flight Dynamics Lab., AFFDL-TR-78-122, Wright-Patterson AFB, OH, March 1978.
derived signal in that model.
16Bjorkman, E. A., "Flight Test Evaluation of Techniques To Predict Lon- 2) Using a well-defined pilot-vehicle analysis technique and gitudinal Pilot Induced Oscillations," M.S. Thesis, U.S. Air Force Inst. of flight-test results, it was possible to categorize the following: i) han- Technology, AFIT/GAE/AA/86J- l, Wright-Patterson AFB, OH, Dec. 1986.
dling quality levels using a handling qualities sensitivity function, 17Berthe, C. J., Chalk, C. R., and Sarrafian, S. K., "Pitch Rate Flight Con- easily derived from the pilot model; and ii) PIOR levels using the
!
trol Systems in the Flared Landing Task and Design Criteria Development," PSD of a signal easily derived from the pilot model.
NASA CR-172491, Oct. 1984.
3) A theory for describing pilot behavior in initiating and sus- 18Weingarten, N. C., Berthe, C. J., Jr., Rynaski, E. G., and Sarrafian, taining an APC/PIO event can be hypothesized, consistent with the S. K., "Flared Landing Approach Flying Qualities," Vols. 1 and 2, NASA feedback topology of the structural model. The theory postulates CR-178188, Dec. 1986.
19Horowitz, I., Quantitative Feedback Design Theory (QFT), QFT Pub- that, in initiating and sustaining an APC/PIO, the pilot regresses lications, Boulder, CO, 1993, Chap. l 1.
to a type of tracking behavior in which error rate is controlled and !i ¸ [
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