Integrating Flight Dynamics & Control Analysis and Simulation in Rotorcraft Conceptual Design

Integrating Flight Dynamics & Control Analysis and Simulation in Rotorcraft

Conceptual Design

Ben Lawrence Tom Berger San Jose State University Mark B. Tischler NASA Ames Research Center, VMC Technical Area Moffett Field, CA Aviation Development Directorate U.S. Army AMRDEC Colin R. Theodore Moffett Field, CA National Aeronautics and Space Administration NASA Ames Research Center Moffett Field, CA Josh Elmore Andrew Gallaher Eric L. Tobias Concept Design and Assessment Technical Area San Jose State University Aviation Development Directorate Aviation Development Directorate U.S. Army AMRDEC US Army AMRDEC Huntsville, AL / Moffett Field, CA Moffett Field, CA ABSTRACT The development of a toolset, SIMPLI-FLYD ( “ SIMPLIfied FLight dynamics for conceptual Design ” ) is described. SIMPLI- FLYD is a collection of tools that perform flight dynamics and control modeling and analysis of rotorcraft conceptual designs including a capability to evaluate the designs in an X-Plane-based real-time simulation. The establishment of this framework is now facilitating the exploration of this new capability, in terms of modeling fidelity and data requirements, and the investigation of which stability and control and handling qualities requirements are appropriate for conceptual design.

Illustrative design variation studies for single main rotor and tiltrotor vehicle configurations show sensitivity of the stability and control characteristics and an approach to highlight potential weight savings by identifying over-design.

 NOTATION Cost function for frequency response Δ 𝑊 Change in Weight (lbs) J error Multi-blade coordinate rotor longitudinal 𝛽 1 𝑐 Aircraft body axis roll rate 𝑝 flap angle (subscript for rotor number) Multi-blade coordinate rotor lateral flap 𝑞 Aircraft body axis pitch rate 𝛽 1 𝑠 angle 𝑟 Aircraft body axis yaw rate Elevator control deflection 𝛿 𝑒 𝑢 Aircraft body X - axis velocity 𝜃 Rotor lateral cyclic angle 𝑐 𝑣 Aircraft body Y - axis velocity 𝜃 Rotor longitudinal cyclic angle 𝑠 𝑤 Aircraft body Z - axis velocity 𝜃 Rotor collective angle Stability Derivatives (semi - normalized) 𝑋 , 𝑋 , 𝑢 𝑤 𝜃 , 𝜃 Tail rotor collective angle 𝑇𝑅 0 𝑇 1 𝜕𝑋 1 𝜕𝐿 𝑍 , 𝑀 , 𝑁 i.e. 𝑋 = 𝐿 = 𝑤 𝛿 𝜃 𝑢 𝑃 𝑒 0 𝑇 𝑀 𝜕𝑢 𝐼 𝜕𝑝 𝑥𝑥 𝜃 Aircraft pitch angle Change in roll moment of inertia Δ 𝐼 𝑥𝑥 𝜓 Aircraft yaw angle Δ 𝐼 Change in pitch moment of inertia 𝑦𝑦 𝜙 Aircraft roll angle Δ 𝐼 Change in yaw moment of inertia 𝑧𝑧 Presented at the AHS 72nd Annual Forum, West Palm Beach, Florida, USA, May 17-19, 2016. This is a work of the U.S.

Government and is not subject to copyright protection.

Distribution A. Approved for public release; distribution is unlimited INTRODUCTION TECHNICAL APPROACH Thorough studies of flight dynamics and control have been Figure 1 shows the architecture of the SIMPLI-FLYD toolset.

historically neglected in conceptual design processes (Ref. 1 ), The schematic identifies the primary components within the primarily because the view has been that there is insufficient SIMPLI-FLYD process as well as the key interfaces to knowledge of the aircraft properties to create and include external components and processes. The dashed blue box reasonable and useful mathematical models. This lack of indicates the tools and activities encompassed in an overall flight dynamics modeling at the earliest stages of design conceptual design process when considering the FD&C disregards a potentially significant contributor to size, weight, aspects. Stage (1) is the primary conceptual design activity and performance estimates for some design activities. It also using NDARC, in a future context this process might well be defers flight dynamics, rotor response lags, and control represented by a variety of other analyses encompassed in a authority considerations to later in the design process, which Multi-disciplinary Design and Optimization (MDAO) have led to problems during flight test (Ref. 2 ). The flight environment to iterate on a design. In the context of this paper, dynamics and control of an air vehicle are fundamentally a stage (1) is the input for the current version of SIMPLI-FLYD function of its inherent control power and damping that encompasses stages (2) through (6).

characteristics and are typically augmented by the feed- forward and feed-back loops programmed into a flight control system. Predicting these characteristics of a yet-to-be-built air vehicle is a challenge at the conceptual design phase where limited data is available.

The work presented in this paper draws on lessons learned from Ref. 3 where a preliminary framework was developed for conducting flight dynamics and control (FD&C) analyses in conceptual design. The key conclusions were that there was a technical feasibility in defining FD&C models using conceptual design data and that the inclusion of a stabilizing control system is important, not only to make the very likely unstable bare-airframe rotorcraft stable, making subsequent analyses more tractable and meaningful, but its inclusion in terms of gains and actuator performance requirements are themselves very useful indicators for design.

This paper describes the evolution of the preliminary Figure 1 SIMPLI-FLYD Architecture for including framework of Ref. 3 to a more comprehensive toolset stability and control analysis into conceptual design SIMPLI- FLYD (“ SIMPLIfied FLight dynamics for The process generates two key outputs: set(s) of stability conceptual Design”) to enable flight dynamics and control and control and handling qualities parameters, and an X-Plane assessments early in the design and assessment cycle.

compatible real-time simulation model vehicle for use in an SIMPLI-FLYD is a joint NASA and Army development and X-Plane simulation station.

uses a suite of tools including NDARC (Ref. 4 ), ® ® ® MATLAB/Simulink , CONDUIT (Ref. 5 ), and X-Plane Flight Dynamics Modeling ( www.xplane.com ) to automatically model and analyze rotorcraft configurations, configure stability and control A key requirement for the toolset was that it would ultimately augmentation systems, and to integrate the combined flight be capable of modeling arbitrary rotorcraft configurations dynamic and control models in an X-Plane-based simulation.

with various combinations of rotors, wings and other surfaces This feature allows pilot-in-the-loop, real-time simulation of and auxiliary propulsion. Figure 3 shows a schematic of how conceptual designs.

the flight dynamic models are built up. The imported data consists of geometric, aerodynamic, and configuration data The output of these analyses, in terms of which are most about the vehicle and pre-calculated data from a sweep of trim important, their form, and how they are used to influence a flight conditions from NDARC. Along with user input conceptual design evolution continues to be a key research options, these data are processed to establish the number and question. Through a description of the development of type of components (rotors, wings etc.), and the number of SIMPLI-FLYD and its subsequent application to illustrative model states and controls, amongst other parameters. The designs, the paper investigates these issues, highlights the flight dynamic calculations then proceed to loop over the capabilities of the methodology implemented, and explores flight conditions and components calculating linear stability the lessons learned.

and control derivatives for each. For the rotors, this process uses a non-linear blade element model which is initialized at the NDARC calculated trim state from which the stability derivatives are calculated using numerical perturbation. For the other components: wings, aerodynamic surfaces and for use in the real-time model). This was important to make fuselage, a simplified direct calculation of the linear the control system requirements and optimization problem derivatives is used. The philosophy behind this approach was more tractable and to reduce the overall complexity for the twofold: Firstly, the models are intended to be relatively initial implementation. The actuator characteristics are simple for reasons of computational efficiency and also to be configurable for each analysis point model to allow for congruent with the level of modeling in NDARC. Secondly, representation of different actuator classes (i.e. swashplate vs.

the derivative calculation approach is intended to only add aerodynamic surfaces) required for particular flight information that is not already available (i.e. flight dynamic conditions/configurations. These are represented separately in characteristics) and repetition of calculations has been the stitched model used for the X-Plane-based real-time avoided as much as possible to minimize use of secondary simulations.

parameters that may already exist in the main design Model Verification database/model.

To verify that the flight dynamics models generated were The total vehicle linear models are computed through the representative, comparisons were made to higher fidelity summation of the state- space ‘A’ and ‘B’ matrix terms from legacy models. Figures 3 and 4 compare the hover roll, pitch, the various components. The linear models can be optionally heave and yaw response of a UH-60A single main rotor 6-degree-of-freedom (6-DoF) rigid body states only or can configuration generated by SIMPLI-FLYD using input from include first order flapping equations, with one longitudinal an NDARC model to that extracted from the Army and one lateral per “main” rotor, following the “ hybrid ” “ FORECAST ” code, as described in Ref. 7 . To add a model formulation in Tischler (Ref. 5 ). As such, a single main quantitative measure of the closeness of fit, a LOES (Lower rotor configuration would have 11 states, 9 rigid body states Order Equivalent System) cost, J, is computed. This considers the cost of the fit of both the magnitude and phase of the (𝑢, 𝑣, 𝑤, 𝑝, 𝑞, 𝑟, 𝜑, 𝜃, 𝜓) and 2 rotor states (𝛽 , 𝛽 ) as the 1𝑐 1𝑠 1 1 frequency response over the 1-20 rad/s range, the critical tail rotor derivatives are always reduced to their 6-DoF frequency range of interest for handling qualities and flight contribution. Other configurations that feature two main control design. Ref. 5 states that J ≤ 50 “can be expected to rotors such as a tiltrotor or a tandem would contain 13-states, produce a model that is nearly indistinguishable from the with 4 rotor states, and so on.

flight data in the frequency domain and the time domain” , while costs of J ≤ 100 “generally reflects an acceptable level of accuracy for flight- dynamics modeling”. The costs for the four UH-60A primary axis responses are all acceptable ( ≤ 100). Some differences become apparent at lower frequencies, however these are considered less significant as per the increasing MUAD (Minimum Unnoticeable Added Dynamics, Ref. 8 ) boundaries represented by the dashed lines.

The boundaries are derived from piloted experiments and reflect that large differences in low frequency modes with long time periods are indiscernible by pilots.

p/  1c Cost J = 93.4 -20 Magnitude [dB] -40 FORECAST SIMPLI-FLYD v1.01 Figure 2 Schematic of the flight dynamics model 0 build up process and output -90 -180 For the control derivatives, an important simplification -270 Phase [deg] imposed for the analysis point models was that any vehicle -360 -450 had a fixed set of “controls” for the four primary roll, pitch, -1 0 1 10 10 10 thrust and yaw response axes. The effects of multiple or Frequency [rad/sec] redundant control effectors such as combinations of rotor Figure 3 Roll rate frequency response comparison of controls and wing or aerodynamic surface controls are UH-60A hover linear models extracted from SIMPLI- combined in advance of analysis at stages (3) and (4) using FLYD and FORECAST (MUAD boundaries dashed) mixing matrices (the separate control derivatives are retained q/  Figures 5 and 6 show frequency response comparisons 1s for a 32,000lb class Tiltrotor model compared to a linear Cost model of the same vehicle extracted from the high fidelity J = 5.1 HeliUM multi-body dynamics code described in Ref. 9 . The flight condition is for the tiltrotor in airplane mode (nacelle tilt = 0 degrees), at a speed of 160kts. In this configuration, Magnitude [dB] the aircraft is flying wing-borne and the control effectors are -50 the aileron, elevator and rudder aerodynamic control surfaces.

The comparisons are generally good for the tiltrotor both qualitatively and quantitatively. The LOES cost is somewhat FORECAST high for the lateral velocity response to rudder where the main SIMPLI-FLYD v1.01 difference is in the magnitude. This brief snapshot of model comparisons are reflective of a wider set that have been made -90 as part of this work which have also shown similar levels of Phase [deg] -180 comparison and provides confidence that the tool is able to capture the primary flight dynamic features of a range of -270 -1 0 1 10 10 10 rotorcraft types, sizes and flight conditions.

Frequency [rad/sec] p/aileron w/  Cost Cost J = 80.2 J = 33.0 -20 -40 20 Magnitude [dB] Magnitude [dB] -60 HeliUM FORECAST SIMPLI-FLYD v1.01 270 SIMPLI-FLYD v1.01 Phase [deg] Phase [deg] -90 -180 -1 0 1 -1 0 1 10 10 10 10 10 10 Frequency [rad/sec] Frequency [rad/sec] q/elevator r/  TR Cost J = 14.3 -20 Cost Magnitude [dB] Magnitude [dB] J = 55.6 -40 -50 HeliUM FORECAST SIMPLI-FLYD v1.01 270 SIMPLI-FLYD v1.01 Phase [deg] Phase [deg] -1 0 1 -1 0 1 10 10 10 10 10 10 Frequency [rad/sec] Frequency [rad/sec] Figure 4 Pitch rate, vertical velocity and yaw rate Figure 5 Roll and pitch rate frequency response frequency response comparison of UH-60A hover linear comparison of 32,000lb tiltrotor at 160kts linear models models extracted from SIMPLI-FLYD and FORECAST. extracted from SIMPLI-FLYD and HeliUM. (MUAD (MUAD boundaries dashed) boundaries dashed) u/col Table 1 shows the response types used in each axis and flight regime.

Table 1. Control system response types for various axis and flight modes Cost Magnitude [dB] J = 104.7 Rotor - Borne Wing - Borne -50 Hover Forward - Flight Forward - Flight a HeliUM Roll RCAH RCAH RCAH SIMPLI-FLYD v1.01 Angle - of - Attack - Pitch RCAH RCAH Command Sideslip - b Yaw RCDH Sideslip - Command Phase [deg] Command -90 c -180 Thrust RCHH Open - loop Open - loop -1 0 1 10 10 10 a Frequency [rad/sec] RCAH = Rate-Command/Attitude-Hold b v/rudder RCDH = Rate-Command/Direction-Hold Cost c RCHH = Rate-Command/Height-Hold J = 284.6 The command model in each axis sets the desired dynamics of the closed-loop system. This is achieved using lower-order command-model responses. The order of the Magnitude [dB] command model (either first-order or second-order) is chosen -50 based on the inherent order of the aircraft response. For example, for a rate command response type in the roll axis, a first-order command model is used: 360 HeliUM 𝑝 𝐾 SIMPLI-FLYD v1.01 lat = 𝛿 𝜏 𝑠 + 1 stk lat Phase [deg] Whereas for example, sideslip command is used in the -90 yaw axis at forward flight, and a second-order command -180 -1 0 1 10 10 10 model is used: Frequency [rad/sec] Figure 6 Longitudinal and lateral velocity frequency 𝐾 𝛽 ped response comparison of 32K tiltrotor at 160kts linear = 2 2 𝛿 𝑠 + 2𝜁 𝜔 𝑠 + 𝜔 models extracted from SIMPLI-FLYD and HeliUM. ped ped ped ped (MUAD boundaries dashed) The parameters of the command model are the gain K, CONTROL SYSTEM ARCHITECTURE, time constant (first- order only) τ, natural frequency (second - OPTIMIZATION AND S&C ANALYSIS order only) ω, and damping (second - order only) ζ. These parameters are tuned to meet the piloted response criteria, The control system applied to the vehicle model at stage 3 in such as piloted bandwidth, damping, quickness, and stick Figure 1 is based on an explicit model following architecture sensitivity requirements of ADS-33E or MIL-STD-1797B shown in Figure 7 , which consists of independent feed- (Refs. 10 and 11 ). A good model following cost ensures that forward and feedback paths.

the actual closed-loop response of the aircraft tracks the commanded response.

The feed-forward path also includes a lower-order inverse of the on-axis bare-airframe response used to generate the actuator commands needed to follow the command model.

The inverse plant dynamics are based on an accurate lower- order equivalent system (LOES) representation of the bare- airframe response in the frequency range around crossover (typically around 1-10 rad/sec). The order of the inverse Figure 7 Explicit Model Following Architecture model (either first-order or second-order) is chosen based on the inherent order of the aircraft response, with first-order The feed-forward path includes the command model being used for roll rate, pitch rate, yaw rate, and vertical which sets the response type of the aircraft.

velocity, and second-order being used for sideslip and angle- for Moderate Agility / All Other MTEs. Specifications from of-attack. MIL-STD-1797B were chosen for Category B flight (nonterminal flight phases that are normally accomplished using gradual maneuvers) and Air Vehicle Classes I (small, The feedback path of the control laws is optimized independently to meet the stability, damping, gust rejection, light), II (medium weight, low-to-medium maneuverability), or III (large, heavy, low-to-medium maneuverability).

and performance robustness requirements. The feedback path in each axis is comprised of proportional, integral, and derivative (PID) gains. Once the control system optimization is complete, the block diagram parameters (feedback gains, feed-forward gains, inverse model parameters, etc.) are saved. Also the HQ Additional elements of the block diagram include the specification results of the control system optimization, given actuator and sensor blocks. Four primary actuators are including in the block diagram for the four primary control individually for each axis, including the amount of over- or under-design are saved. First, the “ Phase ” (Ref. 5 ) at which axes (roll, pitch, yaw, and collective/thrust). Actuators are modeled as second-order systems with position and rate the optimization finished is recorded, which gives an limits: indication of whether or not all of the specifications were met.

The optimization process is broken into three phases. During 𝛿 𝜔 act 𝑛 Phase 1, CONDUIT tunes the gains to meet all of the Hard = 2 2 𝛿 𝑠 + 2𝜁𝜔 𝑠 + 𝜔 cmd 𝑛 𝑛 Constraints (stability specifications). If the optimization ends while still in Phase 1, then one or more of the stability Sensor models are included on each signal fed back to the specifications could not be met. The specifications that limit control system. Sensors are modeled as second-order systems the optimization from continuing to achieve a higher level of with default values of natural frequency and damping of ω n = over-design is identified at this stage.

31 rad/sec and ζ = 0.7, as well as a sampling time delay of 0.02 sec.

If all the Hard Constraints are met, CONDUIT will move to a second phase. During Phase 2, CONDUIT will tune the Setup and optimization of the control laws is fully gains to meet all of the Soft Constraints (handling qualities ® automated within CONDUIT . First, the bare-airframe model specifications). Again, if the optimization ends while in is decoupled to maintain separate results for each axis. It is a Phase 2 this means one or more of the handling qualities safe assumption that a well-designed input mixer and control specifications could not be met and the specification that is system will decouple the aircraft responses. Next, the control limiting the optimization is identified for review.

system is optimized for each axis, starting with the feedback path to stabilize the system, and then with the feed-forward Finally, after all of the specifications are met CONDUIT path to meet the handling qualities requirements. In each axis, moves to Phase 3, and tunes the gains to reduce the Summed key metrics are used to assess the level of over- or under- Objective (“cost of feedback” or performanc e specifications), design in the control system. In the case of feedback, the thus ensuring the design meets the requirements with the metrics used are the control system's ability to reject minimum amount of overdesign. If the optimization ends in disturbances (disturbance rejection bandwidth) and the Phase 3, then CONDUIT was able to tune the gains to meet control system's performance robustness (crossover all of the specifications.

frequency). These are the two metrics that provide a measure of the key benefit of the feedback path of the control system.

Starting with a baseline required value for each of those two specification (defining 0% over-design), the requirements are progressively increased (more over-design) until a feasible design can no longer be achieved. If the baseline design cannot be met, the requirements are decreased (under-design) until a feasible solution is achieved. After the feedback path is optimized, the feed-forward path is optimized using the same approach. In the case of the feed-forward path, the specifications used to assess over-design are piloted bandwidth, quickness, and control power. These three metrics are the key requirements that cover the speed of response to piloted input, and provide a measure of the benefits of the feed-forward path of the control system.

The handling qualities specifications used to drive the control system optimization are divided by aircraft type, flight regime, control axis, and feedback or feed-forward. Table 7 through Table 12 in the Appendix list all of the specifications used. Specifications boundaries were chosen from ADS-33E The variations in geometry, mass and inertia were EXAMPLE RESULTS USING SIMPLI-FLYD applied to the NDARC models and the output passed to the This section will present two example case studies using SIMPLI-FLYD toolset. The response in the trim behavior is NDARC models of a UH-60A and a 32,000lb tiltrotor to shown in Figure 9 . This is an important first check as ability demonstrate the SIMPLI-FLYD toolset.

to trim within reasonable limits is an important design criterion. In this case, it can be seen that the 50% reduced tail UH-60A Tail Rotor Size Variation Study rotor has a particularly large collective setting to achieve trim (the missing points for this case above 100kts are because no The first example is for a ±20% and ±50% variation in the tail trim solution was achieved). Here, the NDARC rotor model rotor blade area (proportional radius and chord, tip velocity thrust does not limit due to stall (stall effects power in maintained via rpm adjustment) for the NDARC UH-60A NDARC but is considered in the HQ analysis) and thus inputs model as depicted in the schematics in Figure 8 . Also note the can be continually increased until a trim solution is reached.

fuselage length and empennage location were adjusted Closer inspection of the NDARC output for this case had accordingly to maintain separation between rotors and shown that this rotor had exceeded thrust limits. The other surfaces and to ensure surfaces remain in their correct variation cases were less extreme in the trim requirements attachment point.

although the 20% reduced case has a relatively large 5-6 degree increase in collective at hover. Despite these issues, all the variation cases are retained for the purposes of this example study.

-10 -20 -30 -40 pedal [deg] Baseline -50 +20% Tail Rotor +50% Tail Rotor -60 -20% Tail Rotor -50% Tail Rotor -70 0 20 40 60 80 100 120 140 V [kts] Figure 9 Tail rotor collective pitch required for trim for NDARC UH-60A with variations in tail rotor size Figure 8 Illustration of NDARC UH-60A tail rotor Figure 10 shows the effect of the tail rotor size variation radius/chord variation for SIMPLI-FLYD analysis on the bare-airframe flight dynamic and control The impact of the variations in the configuration on the characteristics. As the focus for this example are the primary resulting aircraft weight, c.g. and moments of inertia were yaw axis characteristics in the hover, the two key influential also predicted. These effects were captured jointly by a stability and control derivatives, 𝑁 and 𝑁 (yaw rate 𝑟 𝜃 0𝑇 combination of NDARCs built-in weight equations and a damping and yaw moment due tail rotor collective) are separate weight and balance analysis of the configurations presented (the forward flight derivatives are retained for after their layout had been finalized as per Figure 8 . The comparison). The trends in the derivatives are as expected, resulting weight and inertia changes are presented in Table 2 .

with control power and damping varying almost The resulting weight changes for this case are fairly minimal proportionately with the change in tail rotor size (the moment (less than 50lbs) but variations of up to nearly ±10% are arm is also changing).

observed for the yaw and pitch inertias.

Table 2 Effect of tail rotor size variation on UH-60A moments of inertia and weight Tail rotor - 50% - 20% +20% +50% size : - 0.074 - 0.009 - 0.007 - 0.143 Δ 𝐼 (%) 𝑥𝑥 - 9.78 - 4.17 +4.63 +11.46 Δ 𝐼 (%) 𝑦𝑦 - 9.64 - 4.11 +4.59 +11.3 Δ 𝐼 (%) 𝑧𝑧 - 0.226 - 0.081 +0.106 +0.246 Δ 𝑊 (%) amplitude control power. The trends for bandwidth with the tail rotor size variation are similar, with the bandwidth -0.5 reducing/increasing accordingly with size.

It is worth noting that even the +50% tail rotor case -1 cannot achieve Level 1 yaw bandwidth and attitude N r Configuration quickness. This observation aligns with a widely held opinion Baseline -1.5 in the HQ community that the current yaw axis bandwidth and +20% Tail Rotor attitude quickness requirements are too demanding. As such, +50% Tail Rotor -2 Ref. 12 shows data that support this position along with -20% Tail Rotor proposed relaxations of the yaw axis bandwidth and attitude -50% Tail Rotor -2.5 quickness boundaries for an upcoming update to the HQ 0 20 40 60 80 100 120 140 requirements in ADS-33F. The tool yaw bandwidth and Airspeed [kts] quickness boundaries will be updated accordingly when ADS-33F is published.

The other key output of the CONDUIT analysis is manifested in the HQ requirements “design margins” (DM ), 15 these are equivalent to the percent over/under design and are N  T computed for each control axis analyzed and for both the feedback and feed-forward control paths. Table 3 shows the yaw axis design margins for the NDARC UH-60A tail rotor size variations for the hover flight condition. For the FB specifications the baseline and larger tail rotors have significant design margin which reduces as the tail rotor size 0 20 40 60 80 100 120 140 is reduced.

Airspeed [kts] Table 3 CONDUIT Yaw axis Design Margins (DMs) for NDARC UH-60A tail rotor size variation at hover Figure 10 SIMPLI-FLYD yaw axis stability & control derivatives for NDARC UH-60A tail rotor size T ail Rotor changes - 50% - 20% BL +20% +50% size: The results of the CONDUIT optimization and analysis F eed - of the models at the hover flight condition with tail rotor size - 90% - 70% - 60% - 40% - 20% forward variations are shown in Figure 11 for feedback and Figure 12 for feed-forward. The results show that for a similar level of Feedback - 30% + 20% + 50% + 70% + 100% actuator usage (as seen on the "OLOP" PIO criteria and Actuator RMS specification), as tail rotor size increases, For the baseline and even the increased tail rotor size higher disturbance rejection bandwidth and crossover configurations, it can be seen there is a significant under frequency values are achievable. This comes at the cost of design for the feed-forward path. The limiting specification lower stability margins for the larger tail rotor configurations, being the Level 2 yaw bandwidth and quickness requirements.

but still within Level 1. This is also shown in Table 3 by the Decreasing tail rotor size leads to a further reduction in the increased level of feedback over-design for increased tail under-design (negative) design margin. There is +50% rotor size. In fact, the 50% reduced tail rotor case cannot even margin in the feedback design margin for the baseline which, meet the minimum requirement and therefore has 30% under- as already highlighted, becomes an (-)30% under design design.

margin for the smallest tail rotor and doubles to an 100% over Sensitivity is also observed for piloted bandwidth, design for the largest tail rotor.

Quickness, and control power specifications in the feed- forward specifications in Figure 12 . Here it can be seen that all the configurations are not able to achieve Level 1 bandwidth as per the ADS-33E-PRF hover/low speed utility class rotorcraft specifications in Ref. 10 . All the tail rotor size cases are unable to achieve better than Level 2 yaw quickness whereas all the cases are able to achieve Level 1 control power in yaw (the -50% tail rotor is borderline Level 1/2).

This result is consistent with the application of the larger tail rotor, where the greater thrust of the larger tail rotor is able to impart greater yawing moments, augmenting the medium amplitude response quickness characteristics and large EigLcG1: StbMgG1: Gain/Phase Margins Eigenvalues (All) (rigid-body freq. range) NicMgG1:Robust Stability Baseline +20% Tail Rotor 60 2 +50% Tail Rotor 40 -20% Tail Rotor -2 PM [deg] Gain [dB] -50% Tail Rotor -4 Ames Research Center 0 MIL-DTL-9490E -6 GARTEUR -1 0 1 0 10 20 -150 -100 -50 0 Real Axis GM [dB] Phase [deg] DrbYaH1:Dist. Rej. Bandwidth DrpAvH1:Dst. Rej. Peak EigDpG1:Damping Ratio Yaw; Attitude Hold Attitude, Velocity; AH/VH Generic OlpOpG1: PIO Criteria -5 Amplitude [dB] -10 ADS-33E Test Guide AFDD-UH60 -15 DLR Ames Research Center 0 1 2 0 5 10 -180 -160 -140 -120 -100 -1 0 1 DRB [rad/sec] Max. Magnitude [dB] Phase [deg] Damping Ratio (Zeta) EigDpG1:Damping Ratio CrsMnG2:Min. Cross. Freq. CrsLnG1:Crossover Freq.

Generic (linear scale) (linear scale) RmsAcG1:Actuator RMS Ames Research Center Ames Research Center Ames Research Center Ames Research Center -1 0 1 0 2 4 0 10 20 0 1 2 Damping Ratio (Zeta) Crossover Frequency [rad/sec] Crossover Frequency [rad/sec] Actuator RMS Figure 11 CONDUIT yaw axis feedback (FB) HQ window for NDARC UH-60A tail rotor size variation at hover BnwYaH2:BW & T.D. MaxYaH2:Min. Ach. Yaw Rate QikYaH2:Quickness Other MTEs (Yaw) Moderate Agility Other MTEs (Yaw) OlpOpG1: PIO Criteria 0.4 30 2.5 15 0.3 [1/sec] 20 5 1.5 0.2 0 10 -5 0.1 Amplitude [dB] 0.5 -10 Phase delay [sec] Yaw Rate [deg/sec] r-pk / (d-psi)pk 0 ADS-33E 0 ADS-33E 0 ADS-33E -15 DLR 0 2 4 0 20 40 60 -180 -160 -140 -120 -100 Bandwidth [rad/sec] (d-psi)min [deg] Phase [deg] RmsAcG1:Actuator RMS Baseline +20% Tail Rotor +50% Tail Rotor -20% Tail Rotor -50% Tail Rotor Ames Research Center 0 1 2 Actuator RMS Figure 12 CONDUIT yaw axis feed-forward (FF) HQ window for NDARC UH-60A tail rotor size variation at hover Tiltrotor Tail Surface Size Variation Study and inertia characteristics than were seen for the tail rotor changes on the UH-60 example. The changes in weight were A second example of SIMPLI-FLYD usage is via a variation of the order of hundreds of pounds as opposed to tens (albeit in the tail area (proportional span and chord) for a NDARC for a vehicle twice the weight), this led to weight deltas in the 32,000lb (32K) tiltrotor model as depicted in Figure 13 . This order of 1-2%. The yaw and pitch inertia differences were also variation was somewhat simpler than the UH-60A example as larger, with deltas in the range of 10-20% of the baseline the tail was simply scaled with no other adjustments to the design. As for the UH-60A example, it is first informative to airframe. The variations examined were a +20% increase and consider the trim plot in Figure 14 , in this case elevator angle -20% and -50% area reductions. Although this example study for an airplane mode speed range. The results are as expected, case was primarily aimed at a pitch axis evaluation, the tail with the smaller tail requiring greater elevator angle for trim size variation also affected the lateral-directional flight and vice versa. At the 160kts flight condition, the differences dynamics and control (not shown) due to the “V - tail” in trim between the configurations are not particularly large configuration. The results shown are for elevator actuators (2-3 degrees) but grow as the stall speed is approached.

(30% flap chord ratio) where the baseline position saturation and rate limits were ±20deg and ±20 deg/s.

-5 -10 -15 -20 elevator [deg] Baseline -25 +20% Tail Area -20% Tail Area -30 -50% Tail Area -35 Figure 13 Illustration of NDARC 32K tiltrotor tail size 120 140 160 180 200 220 240 260 280 300 V [kts] variation for SIMPLI-FLYD analysis Figure 14 Elevator angle required for trim for Table 4 Effect of tail rotor size variation on 32K NDARC 32K tiltrotor with variations in tail rotor size tiltrotor moments of inertia and weight The impact on the bare-airframe flight dynamic and Pitch - 50% - 20% Baseline +20% control characteristics is illustrated in Figure 15 . Here the key Δ 𝐼 (%) - 1.23% - 0.61% - +0.74% 𝑥𝑥 primary longitudinal stability and control derivatives are Δ 𝐼 (%) - 27.95% - 11.73% - +12.30% 𝑦𝑦 shown for the airplane mode speed range of 140-300kts.

Δ 𝐼 (%) - 10.81% - 4.56% - +4.83% Again there is almost a directly proportional relationship of 𝑧𝑧 the tail size with many of these derivatives governing the Δ 𝑊 (%) - 1.67% - 0.70% - +0.73% vehicle pitch and vertical axis damping, stability, and control The effect of the tail size variation, as summarized in power.

Table 4 , had a more significant impact on the vehicle mass Configuration -0.2 0.4 -0.1 Baseline 0.3 +20% Tail Area -0.25 -0.12 X X Z w -20% Tail Area u u 0.2 -50% Tail Area -0.3 -0.14 0.1 -0.35 0 -0.16 100 150 200 250 300 100 150 200 250 300 100 150 200 250 300 Airspeed [kts] Airspeed [kts] Airspeed [kts] -0.5 0 0.015 -50 Z -1 0.01  Z M e w u -100 -1.5 0.005 -150 -2 -200 0 100 150 200 250 300 100 150 200 250 300 100 150 200 250 300 Airspeed [kts] Airspeed [kts] Airspeed [kts] 0 0 0 -0.05 -2 -20 M M q M w  -0.1 -4 e -40 -0.15 -6 -0.2 -8 -60 100 150 200 250 300 100 150 200 250 300 100 150 200 250 300 Airspeed [kts] Airspeed [kts] Airspeed [kts] Figure 15 SIMPLI-FLYD Longitudinal stability & control derivatives for NDARC 32K tiltrotor tail size changes EigLcG1: StbMgG1: Gain/Phase Margins Eigenvalues (All) (rigid-body freq. range) NicMgG1:Robust Stability 4 Baseline +20% Tail Area 60 2 -20% Tail Area 0 -50% Tail Area Gain [dB] PM [deg] -2 -4 Ames Research Center 0 MIL-DTL-9490E -6 GARTEUR -1 0 1 0 10 20 -150 -100 -50 0 Real Axis GM [dB] Phase [deg] DrbPiH1:Dist. Rej. Bandwidth DrpAvH1:Dst. Rej. Peak EigDpG1:Damping Ratio Pitch; Attitude Hold Attitude, Velocity; AH/VH Generic OlpOpG1: PIO Criteria -5 Amplitude [dB] -10 ADS-33E Test Guide AFDD-UH60 -15 DLR Ames Research Center 0 1 2 0 5 10 -180 -160 -140 -120 -100 -1 0 1 DRB [rad/sec] Max. Magnitude [dB] Phase [deg] Damping Ratio (Zeta) EigDpG1:Damping Ratio CrsMnG2:Min. Cross. Freq. CrsLnG1:Crossover Freq.

Generic (linear scale) (linear scale) RmsAcG1:Actuator RMS Ames Research Center Ames Research Center Ames Research Center Ames Research Center -1 0 1 0 2 4 0 10 20 0 1 2 Damping Ratio (Zeta) Crossover Frequency [rad/sec] Crossover Frequency [rad/sec] Actuator RMS Figure 16 CONDUIT pitch axis feedback (FB) HQ window for NDARC 32K tiltrotor tail size variation at 160kts BnwFpL2:Flight Path vs Atttiude Bandwidth BnwPiL4:BW & T.D. MaxPiF1:Pitch Contror Power Cat B&C Class I, IV Cat B&C Class I, II, III Load Factor Limit (Pull-up) 0.2 [rad/sec]  W 0.15 Baseline B  +20% Tail Area -20% Tail Area 0.1 -50% Tail Area 0.05 Phase delay [sec] 0 MIL-STD-1797B 0 MIL-STD-1797B ADS-33E 0 2 4 6 8 0 2 4 0 1 2 3 Flight Path Bandwidth Pitch Attitude Bandwidth  [rad/sec] Bandwidth [rad/sec] Level B W  TdlPiL1:Equivalent Time Delay CapPiL2:Control Anticipation Parameter (pitch response) Cat B All Classes OlpOpG1: PIO Criteria RmsAcG1:Actuator RMS 0.3 10 15 0.25 10 2) 0 - 0.2 5 1 sec 0.15 - 0 -1 0.1 -5 Amplitude [dB] CAP (g 0.05 -10 -2 0 MIL-STD-1797B 10 MIL-STD-1797B -15 DLR Ames Research Center -1 0 equiv. pitch delay (tau-eq.) , [sec] -180 -160 -140 -120 -100 0 1 2 10 10 Phase [deg] Actuator RMS  sp Figure 17 CONDUIT pitch axis feed-forward HQ window for NDARC 32K tiltrotor tail size variation at 160kts BnwFpL2:Flight Path vs Atttiude Bandwidth BnwPiL4:BW & T.D. MaxPiF1:Pitch Contror Power Cat B&C Class I, IV Cat B&C Class I, II, III Load Factor Limit (Pull-up) 0.2 [rad/sec]  W 0.15 B  Baseline 0.1 Increased Actuator Limits 0.05 Phase delay [sec] 0 MIL-STD-1797B 0 MIL-STD-1797B ADS-33E 0 2 4 6 8 0 2 4 0 1 2 3 Flight Path Bandwidth Pitch Attitude Bandwidth  [rad/sec] Bandwidth [rad/sec] Level B W  TdlPiL1:Equivalent Time Delay CapPiL2:Control Anticipation Parameter (pitch response) Cat B All Classes OlpOpG1: PIO Criteria RmsAcG1:Actuator RMS 0.3 15 0.25 10 2) 0 - 0.2 5 1 sec 0.15 - 0 -1 0.1 10 -5 Amplitude [dB] CAP (g 0.05 -10 -2 0 MIL-STD-1797B 10 MIL-STD-1797B -15 DLR Ames Research Center -1 0 -180 -160 -140 -120 -100 equiv. pitch delay (tau-eq.) , [sec] 0 1 2 10 10 Phase [deg] Actuator RMS  sp Figure 18 CONDUIT pitch axis feed-forward HQ window for NDARC 32K tiltrotor actuator variation at 160kts For the CONDUIT analysis outputs in Figure 16 and Table 5 CONDUIT pitch axis Design Margins (DMs) Figure 17 , large changes do not occur for the pitch axis for NDARC tiltrotor tail size variation at 160kts forward flight feedback specification results in response to the tail size variation. Sensitivities are observed for the feed- - 50% - 20% Baseline +20% forward requirements. For the load factor limit/pull-up Feed - forward - 5 0 % - 1 0% - 10% 0 % requirement, the 20% increased tail case is on the Level 1/2 boundary with the result moving steadily more Level 2 for the Feedback +20 0 % + 20 0% + 20 0% +20 0% baseline, 20% and 50% reduced tail cases.

An example of this sensitivity to actuators is illustrated in Overall, it is notable that apart from the 50% reduced tail, Figure 18 which compares the tiltrotor at 160kts with the most of the configurations remain mostly or close to Level 1.

baseline elevator actuators and ones with increased saturation In this case, it is more useful to evaluate the design margins and rate limits of ±30deg and ±30 deg/s. Only the feed- as these are more likely to highlight the differences between forward specification results are shown, but a strong the configurations. These are shown in Table 5 and show that sensitivity (much larger than seen for the tail geometry at 160kts, the baseline aircraft has plenty of design margin for changes in Figure 17 ) in the load factor limit/pull-up control the feedback specifications ( a maximum limit of +200% was power requirement is observed. This requirement is pushed applied) but has a slight under design margin (10%) for the well into the level 1 region from borderline level 1/2 by feed-forward specifications. Varying the tail size leaves the increasing the allowable elevator control deflection/rate feedback design margins unaltered but it does affect the feed- limits. Again, it is important to compare the design margins forward specifications, increasing the tail size mirrors the for the two cases, shown in Table 6 . As for the tail size result observed for the load factor limit/pull-up requirement variation, there is no variation in the feedback design margin, plot described earlier, in that all the specifications are Level 1 however, a significant boost in the design margin is observed, with minimal margin. Decreasing the tail size reduces the with the added control authority of the increased actuator feed-forward DM. position and rate limits now conferring a +50% design margin.

It is important to highlight the influence of the actuator Table 6 CONDUIT pitch axis Design Margins (DMs) characteristics as an important factor in these results. When for NDARC 32K tiltrotor actuator variation at 160kts using the linear models, the amount of control deflection is the critical factor in limiting the overall control response; and Baseline Increased because of the model-following control laws which effectively “negate” the bare airframe dynamics via the Feed - forward - 10% +50% inverse models it uses, many of the response requirements end up being a function of the vehicles’ control authority to track +20 0% + 20 0% Feedback the desired response being specified by the command model.

The X-Plane simulation capability is intended to augment X-PLANE REAL-TIME SIMULATION the overall conceptual design process by offering an A further feature of the SIMPLI-FLYD toolset is the opportunity to get a “sense” of how different flight dynamic s capability to integrate a number of the elements to facilitate a and control characteristics of the conceptual designs manifest piloted real-time simulation of the vehicle. The X-Plane real- themselves when flown pilot-in-the-loop. The piloted time simulation consists of a MATLAB/Simulink based simulation is not intended for rigorous handling qualities “stitched model” flight d ynamics model combined with analyses but it provides an environment where the flight control system that features a gain scheduled versions of the dynamic characteristics can play a part in examining design control laws optimized at the CONDUIT analysis stage. A tradeoffs when flown in representative operational scenarios.

stitched model (Refs. 13 and 14 are examples used and DISCUSSION developed by the authors previously) is a method by which multiple linear state- space models are “stitched” together via The example results have demonstrated a number of their constituent trim states and stability and control potential use scenarios of the SIMPLI-FLYD toolset and derivatives being lookup table functions of flight condition allows the conceptual designer to see the impact of design and configuration. This forms what is known as a quasi-linear choices on S&C and HQ aspects of rotorcraft conceptual parameter varying model (qLPV) (Ref. 15 ). This type of designs. The UH-60 example showed how potential HQ models offer the ability to represent changing trim and issues might be identified and also provide mechanisms and dynamic characteristics across the flight envelope in a model metrics to effect and evaluate design changes. It is noted that architecture that has a more direct correlation with the the weight results for the UH-60A tail rotor variation showed simplified analysis point models. The approach also has a relatively weak sensitivity. The weight equations used in added advantages in that it avoids some of the overheads in NDARC for this analysis are a weak function of the tail rotor complexity, robustness and computational demand that more radius directly, the more dominant parameters being the main sophisticated non-linear real-time models require – an rotor radius, main rotor tip speed, and main drivetrain torque important consideration in the context of rapidly evaluating limit. The changes to the tail rotor in this scenario are at more lower complexity models of wide variety of configurations in component-level for HQ concerns, and the weight a conceptual design methodology.

dependencies are not fully configured for such a study. In other words, the sizing of the tail rotor itself is assumed to be The stitched model is integrated along with additional mostly a function of the main rotor and drivetrain in the modeling for undercarriage, powerplant and actuators into a weight model. The tiltrotor example showed an “inverse” real-time version of the control laws that feature scheduling scenario where desired HQs were established but any of the command model and feedback gains with flight potential overdesign margins in the HQ and control aspects condition and configuration. The anchor points for the gain can be evaluated in the context of seeking reduced design scheduling are specified by the user and are the result of weight.

CONDUIT optimizations at point models through the desired envelope. The real-time control system also has a number of The example cases shown represent only a small sub-set features to enable gross maneuvering (loops, rolls etc), of the overall design problem that would feature multiple protection against integrator wind up as well as mode inputs and outputs, simultaneously incorporating multiple switching, blending and logic for transition between weight- axes, flight conditions and potentially multiple flight on-wheels, hover/low-speed and forward flight modes. The configurations. With the establishment of the SIMPLI-FLYD simulation runs in real-time from the MATLAB/Simulink framework, future research can now squarely focus on GUI console and communicates data to/from the X-Plane addressing the questions regarding the issue: How are the HQ simulation environment using a shared memory interface factors used to feed back to the conceptual design process?

developed with the support of Continuum Dynamics Inc. and The challenge begins with selection of the HQ specifications.

a number of NASA Ames Research Center Aeromechanics The current version of the SIMPLI-FLYD tool has a set of office interns. X-Plane provides the interface to the pilot specifications intended as a first attempt at a “generic” set inceptor hardware and provides the graphical scene as requirements. Of course, a framework exists for the definition depicted in Figure 19 , or can be run on a desktop computer of more tailored sets of HQ requirements in that the criteria with off-the-shelf gaming pilot control sticks.

used by SIMPLI-FLYD are mainly drawn from ADS-33E and MIL-STD-1797B both of which already feature categorization of requirements and multiple boundaries for different aircraft types and mission roles. However, it is not yet clear what is most appropriate at conceptual design: is it a more generic set that can be applied for a variety of designs and roles to drive an initial “conceptual design level” of handling qualities requirements; or perhaps the ability to set optional specification sets for differing design requirements is a more valid approach?

Figure 19 Typical X-Plane fixed-based simulator station Another key aspect relates to the setting of the HQ assigned actuator performance with a weight/cost/tech factor requirements boundaries themselves. A great deal of research in the overall conceptual design so that the “cost” of actuators underpins the metrics and the boundaries between Level 1, 2 are properly accounted for.

and 3 boundaries, however the models themselves are simplified and are based on a relatively low level of data and CONCLUDING REMARKS design “clarity”. This all introduces uncertainty, via the This paper has demonstrated the development and capability accuracy of the models and of the data they are based on, an of the SIMPLI-FLYD toolset for performing flight dynamics issue that only becomes greater when trying to predict the and control and handling qualities analysis of rotorcraft characteristics of unfamiliar new vehicle configurations.

conceptual designs. The toolset possesses the following Many of the emerging designs are featuring multiple rotors, main features: wings, control surfaces and other auxiliary propulsion devices which are likely to exhibit a degree of aerodynamic  Ability to automatically model the flight dynamics and interactions between them, something that is notoriously difficult to predict even with high fidelity simulation codes. control characteristics of multiple rotorcraft Getting a better answer through the use of such modeling is configurations and flight conditions.

also still not a practicable approach for conceptual design.

 Automatically integrates the flight dynamics models into Although the verification results in this paper have shown that a model following control system architecture for the modeling used in this toolset is able to reasonably predict analysis in CONDUIT.

the flight dynamics characteristics of a variety (albeit well-  Output of handling qualities and stability and control known) of rotorcraft configurations, it seems that building in a certain amount conservativeness into the requirements will parameters, charts, and control system design margins for be necessary.

multiple axes and flight conditions/configurations.

 Ability to automatically generate a model that can be The application of the CONDUIT concept of design operated in pilot-in-the-loop real time simulation in X- margin (DM) may well be an important factor in addressing Plane.

this. Indeed, the original concept for the design margin in CONDUIT is to compensate for uncertainty in the vehicle The test cases using the UH-60A and tiltrotor dynamics and account for off-nominal conditions when demonstrated sensitivity of the handling qualities parameter designing control laws (Ref. 16 ) – this is conceptually akin to output to simple design parameter variations. The the uncertainty in the predicted dynamics in the simplified establishment of the SIMPLI-FLYD toolset now permits modeling and data of SIMPLI-FLYD. Establishing those exploration of the broader research questions pertaining to the margins will likely require design test cases that are carried incorporation of HQ analysis such as type of criteria to be forward to higher fidelity detailed analyses.

applied, their HQ “ L evel” boundaries, and how the outcomes are used in the vehicle conceptual design process.

As was concluded in the study preceding this work in Ref. 1 , incorporating a control system produces overall flight dynamic and control models that are more realistic, and make analysis of the often unstable designs more tractable.

However, the incorporation of CONDUIT is a significantly more sophisticated approach over the aforementioned work and this comes at the cost that direct correlations between the HQ outcomes and design changes are increasingly obfuscated by the optimized control system compensation. As was highlighted in the results section, the influence of the actuator characteristics is a critical factor. Their specification not only limit the overall maximum control response but their application in conjunction with a model-following control law architecture mean that the ability to meet many of the response requirements end up being a function of the vehicle ’ s control authority/bandwidth required to track the desired response specified by the command model.

Of course, the underlying bare-airframe characteristics are still playing an important part in the HQ outcomes but the actuator characteristics play almost an equally prominent role in the overall outcome. As such, care should be applied in defining their characteristics. Furthermore, an important factor for conceptual design will be the correlation of the Appendix Table 7 Rotor-borne Hover Feedback Specifications Spec Name Description (Motivation) Source Axis Design Margin Hard Constraints EigLcG1 Eignevalues in L.H.P. (Stability) Generic All StbMgG1 Gain Phase Margin broken at actuator (Stability) MIL - DLT - 9490E All NicMgG1 Nichols Margins broken at actuator (Stability) GARTEUR All Soft Constraints ModFoG2 Command model following cost (HQ) Generic All DrbRoH1 Disturbance Rejection Bandwidth (HQ, Ride Quality) ADS - 33E Roll ✔ DrbPiH1 Disturbance Rejection Bandwidth (HQ, Ride Quality) ADS - 33E Pitch ✔ DrbYaH1 Disturbance Rejection Bandwidth (HQ, Ride Quality) ADS - 33E Yaw ✔ DstBwG1 Disturbance Rejection Bandwidth (HQ, Ride Quality) ADS - 33E Heave ✔ DrpAvH1 Disturbance Rejection Peak (HQ, Ride Quality) ADS - 33E All OlpOpG1 Open Loop Onset Point (PIO) DLR All EigDpG1 Eigenvalue Damping, 0.5 - 4 rad/sec (HQ, Loads) ADS - 33E All EigDpG1 Eigenvalue Damping, 4 - 20 rad/sec (HQ, Loads) ADS - 33E All CrsMnG1 Minimum crossover frequency (Robustness) Generic All ✔ Summed Objectives CrsLnG1 Crossover Frequency (Actuator Activity) Generic All RmsAcG1 Actuator RMS (Actuator Activity) Generic All Table 8 Rotor-borne Hover Feed-Forward Specifications Spec Name Description (Motivation) Source Axis Design Margin Soft Constraints BnwAtH1 Attitude bandwidth, phase delay (HQ) ADS - 33E Roll, ✔ Pitch BnwYaH2 Heading bandwidth, phase delay (HQ) ADS - 33E Yaw ✔ FrqHeH2 Heave mode time constant (HQ) ADS - 33E Heave ✔ MaxRoH2 Minimum achievable roll rate (HQ) ADS - 33E Roll ✔ MaxPiH2 Minimum achievable pitch rate (HQ) ADS - 33E Pitch ✔ MaxYaH2 Minimum achievable yaw rate (HQ) ADS - 33E Yaw ✔ MaxHeH1 Minimum achievable vertical rate (HQ) ADS - 33E Heave ✔ QikRoH2 Roll attitude quickness (HQ) ADS - 33E Roll ✔ QikPiH2 Pitch attitude quickness (HQ) ADS - 33E Pitch ✔ QikYaH2 Heading quickness (HQ) ADS - 33E Yaw ✔ OlpOpG1 Open Loop Onset Point (PIO) DLR All Summed Objectives RmsAcG1 Actuator RMS (Actuator Activity) Generic All Table 9 Rotor-borne Forward-Flight Feedback Specifications Design Margin Spec Name Description (Motivation) Source Axis Hard Constraints EigLcG1 Eignevalues in L.H.P. (Stability) Generic All StbMgG1 Gain Phase Margin broken at actuator (Stability) MIL - DLT - All 9490E NicMgG1 Nichols Margins broken at actuator (Stability) GARTEUR All Soft Constraints ModFoG2 Command model following cost (HQ) Generic All DrbRoH1 Disturbance Rejection Bandwidth (HQ, Ride Quality) ADS - 33E Roll ✔ DrbPiH1 Disturbance Rejection Bandwidth (HQ, Ride Quality) ADS - 33E Pitch ✔ DrbYaH1 Disturbance Rejection Bandwidth (HQ, Ride Quality) ADS - 33E Yaw ✔ DstBwG1 Disturbance Rejection Bandwidth (HQ, Ride Quality) ADS - 33E Heave ✔ DrpAvH1 Disturbance Rejection Peak (HQ, Ride Quality) ADS - 33E All OlpOpG1 Open Loop Onset Point (PIO) DLR All EigDpG1 Eigenvalue Damping, 0.5 - 4 rad/sec (HQ, Loads) ADS - 33E All EigDpG1 Eigenvalue Damping, 4 - 20 rad/sec (HQ, Loads) ADS - 33E All CrsMnG1 Minimum crossover frequency (Robustness) Generic All ✔ Summed Objectives CrsLnG1 Crossover Frequency (Actuator Activity) Generic All RmsAcG1 Actuator RMS (Actuator Activity) Generic All Table 10 Rotor-borne Hover Feed-Forward Specifications Spec Name Description (Motivation) Source Axis Design Margin Soft Constraints BnwRoF3 Roll attitude bandwidth, phase delay (HQ) ADS - 33E Roll ✔ BnwPiF3 Pitch attitude bandwidth, phase delay (HQ) ADS - 33E Pitch ✔ BnwYaH2 Heading bandwidth, phase delay (HQ) ADS - 33E Yaw ✔ FrqHeF1 Heave mode time constant (HQ) ADS - 33E Heave ✔ MaxRoF1 Minimum achievable roll rate (HQ) ADS - 33E Roll ✔ MaxPiF1 Minimum achievable pitch rate (HQ) ADS - 33E Pitch ✔ MaxYaF1 Minimum achievable yaw rate (HQ) ADS - 33E Yaw ✔ MaxHeH1 Minimum achievable vertical rate (HQ) ADS - 33E Heave ✔ QikRoF2 Roll attitude quickness (HQ) ADS - 33E Roll ✔ OlpOpG1 Open Loop Onset Point (PIO) DLR All Summed Objectives RmsAcG1 Actuator RMS (Actuator Activity) Generic All Table 11 Wing-borne Forward-Flight Feedback Specifications Design Margin Spec Name Description (Motivation) Source Axis Hard Constraints EigLcG1 Eignevalues in L.H.P. (Stability) Generic All StbMgG1 Gain Phase Margin broken at actuator (Stability) MIL - DLT - 9490E All NicMgG1 Nichols Margins broken at actuator (Stability) GARTEUR All Soft Constraints ModFoG2 Command model following cost (HQ) Generic All DrbRoH1 Disturbance Rejection Bandwidth (HQ, Ride Quality) ADS - 33E Roll ✔ DrbPiH1 Disturbance Rejection Bandwidth (HQ, Ride Quality) ADS - 33E Pitch ✔ DrbYaH1 Disturbance Rejection Bandwidth (HQ, Ride Quality) ADS - 33E Yaw ✔ DstBwG1 Disturbance Rejection Bandwidth (HQ, Ride Quality) ADS - 33E Heave ✔ DrpAvH1 Disturbance Rejection Peak (HQ, Ride Quality) ADS - 33E All OlpOpG1 Open Loop Onset Point (PIO) DLR All EigDpG1 Eigenvalue Damping, 0.5 - 4 rad/sec (HQ, Loads) ADS - 33E All EigDpG1 Eigenvalue Damping, 4 - 20 rad/sec (HQ, Loads) ADS - 33E All CrsMnG1 Minimum crossover frequency (Robustness) Generic All ✔ Summed Objectives CrsLnG1 Crossover Frequency (Actuator Activity) Generic All RmsAcG1 Actuator RMS (Actuator Activity) Generic All Table 12 Wing-borne Hover Feed-Forward Specifications Spec Name Description (Motivation) Source Axis Design Margin Soft Constraints BnwRoD1 Roll attitude bandwidth, phase delay (HQ) MIL - STD - 1797B Roll ✔ RolPfD1 Time to bank (HQ) MIL - STD - 1797B Roll ✔ MaxYaD1 Minimum achievable yaw rate (HQ) MIL - STD - 1797B Yaw ✔ DmpDrD2 Dutch roll damping ratio (HQ) MIL - STD - 1797B Yaw FrqDrD3 Dutch roll frequency (HQ) MIL - STD - 1797B Yaw FrqRoD4 Roll mode time constant (HQ) MIL - STD - 1797B Roll TdlRoD1 Equivalent roll axis time delay (HQ, PIO) MIL - STD - 1797B Roll TdlYaD1 Equivalent yaw axis time delay (HQ, PIO) MIL - STD - 1797B Yaw BnwFpL2 Flight path bandwidth, phase delay (HQ) MIL - STD - 1797B Pitch ✔ BnwPiL4 Pitch attitude bandwidth, phase delay (HQ) MIL - STD - 1797B Pitch ✔ MaxPiF1 Minimum achievable pitch rate (HQ) ADS - 33E Pitch ✔ DrpPiL1 Pitch attitude dropback MIL - STD - 1797B Pitch TdlPiL1 Equivalent pitch axis time delay (HQ, PIO) MIL - STD - 1797B Pitch CapPiL2 Control anticipation parameter (HQ) MIL - STD - 1797B Pitch OlpOpG1 Open Loop Onset Point (PIO) DLR All Summed Objectives RmsAcG1 Actuator RMS (Actuator Activity) Generic All added dynamics." AIAA Atmospheric Flight Mechanics ACKNOWLEDGMENTS Conf. and Exhibit Proceedings, Keystone , CO, pp. 21-24.

A number of individuals are acknowledged for their input and 2006.

advice in this work. At NASA Ames Research Center, Dr.

Juhasz, Ondrej, Roberto Celi, Christina M. Ivler, Mark B.

Wayne Johnson is thanked for his NDARC expertise and Tischler, and Tom Berger. " Flight dynamic simulation technical consultation on conceptual design. Also at NASA Ames, Dr. Carlos Malpica is thanked for many technical modeling of large flexible tiltrotor aircraft." Proc. American discussions and for his consultation on rotor modeling. Jeff Helicopter Society 68th Annual Forum, Fort Worth , TX, Keller of Continuum Dynamics Inc. is thanked for his support 2012.

with the X-Plane shared memory interface development. A Anon., "Handling Qualities Requirements for Military former NASA Ames Research Center Aeromechanics office Rotorcraft" , Aeronautical Design Standard-33 (ADS-33E- intern, Nando Van Arnhem, is also acknowledged for laying PRF), US Army Aviation and Missile Command, March 21, the foundations of the SIMPLI-FLYD/X-Plane interface code. John Davis, of Daviation Technologies is 2000.

acknowledged for technical consultation and for Anon., “Flying Qualities of Piloted Aircraft,” MIL -STD- documentation. Finally, Bruce Tenney, US Army retired, is 1797B, Department of Defense Interface Standard, February, acknowledged for his leadership in initiating the project that 2006.

encompassed this work.

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