A flight control design methodology for reducing pilot workload during shipboard ... aircraft when compared to a basic model following controller without the ...
A Model Following Controller Optimized for Gust Rejection during Shipboard Operations Joseph F. Horn Derek O. Bridges Associate Professor Graduate Research Assistant Department of Aerospace Engineering The Pennsylvania State University University Park, PA A flight control design methodology for reducing pilot workload during shipboard operation of helicopters is presented. The objective of the control synthesis is to improve the gust rejection properties of the aircraft when operating in an unsteady ship airwake. An airwake compensator is designed to integrate with a standard model following control scheme. The spectral properties of the ship airwake are used in the design of the airwake compensator. The model following controller and airwake compensator are implemented in a simulation model of a UH-60A Black Hawk operating near an LHA-class ship. Simulations were performed for approaches and hovering over the deck. The results show that the airwake compensator results in significantly lower angular motion of the aircraft when compared to a basic model following controller without the airwake compensator.
Introduction1 High pilot workload during launch and recovery of ship-based rotorcraft presents a major safety issue for both military and civilian operators. One of the major factors contributing to the high workload is the unsteady flowfield, or ship airwake, that can exist over the landing deck. The unsteady flowfield results in disturbances on the aircraft not unlike the effect of atmospheric turbulence, but in many cases the turbulence levels in the ship airwake are much higher than those found in natural wind.1 There can also be spatial gradients in the time-averaged flow resulting in changes in trim as the aircraft approaches the landing spot.2 These disturbances must be compensated for by the pilot and the automatic flight control system (AFCS), during the high precision tasks of approach, stationkeeping, and landing. The current approach is to establish Wind-over-Deck (WOD) envelopes, also known as Ship Helicopter Operating Limits (SHOL) in the U.K., Canada, and Australia. Using rigorous flight testing, constraints on the allowable relative wind speed and azimuth are established to ensure safe operation for a specific combination of helicopter, ship, and landing spot. Much research effort has gone into developing advanced simulations that couple measured or calculated ship airwake data with real-time flight dynamics models to help predict and understand pilot workload during shipboard operations3-10, but ultimately flight tests need to be conducted in order to establish Presented at the American Helicopter Society 63rd Annual Forum, Virginia Beach, VA, May 1-3, 2007. Copyright© 2007 by the American Helicopter Society International, Inc. All rights reserved.
safe operating envelopes. In some cases, the WOD envelope is restricted due to high pilot workload when operating in the unsteady flowfield. Clearly, if flight control systems could be designed so that the AFCS carried more of the burden of compensating for the unsteady airloads in the shipboard environment, pilot workload would be reduced, and safe operating envelopes could potentially be expanded. Recently, there have been a number of papers that have proposed methods for designing and optimizing flight controllers specifically for shipboard operations. This includes using higher levels of augmentation in the flight controller to hold position over the landing deck11, and optimization of feedback loops to better reject gust disturbances in the ship airwake.12,13 This paper seeks to extend previous research on flight control optimizations to improve disturbance rejection properties in the airwake. Specifically, whereas previous research focused on design of a limited authority stability augmentation system (SAS), the current effort will extend the method using a modern model following control law architecture.
Modified SAS for Airwake Gust Rejection In previous work,13 a method was developed for characterizing the spectral properties of the equivalent disturbances of the unsteady flow in the airwake, and deriving stochastic models that accurately represent the spectral properties of these disturbances. The stochastic models are similar to classical atmospheric turbulence models, and the method for extracting the airwake properties was based on the method developed by Lusardi et al.14 The airwake disturbances are modeled using spectral filters that replicate the power spectral
LHA-class ship. Simulations were performed using a pilot model for the aircraft hovering over a spot on the landing deck in 30 knots, 30° WOD conditions. This WOD condition was found to have unacceptably high workload in flight tests of the baseline aircraft. Results were analyzed in both the time domain and frequency domain, and showed significant reduction in control activity and angular rate over the aircraft with the baseline SAS (see Figure 3). However, the closed loop response to pilot control inputs as also modified (see Figure 4).
density of the airwake disturbances when driven by white noise (a sample filter is illustrated in Figure 1). The spectral filters were then incorporated into an augmented plant model (see Figure 2), and an AFCS was optimized for gust rejection using modern multiinput multi-output (MIMO) design methods. The controller was simplified using model order reduction to develop a “Modified SAS” design to reject airwake disturbances while maintaining similar levels of SAS actuator activity compared to a baseline SAS. The controller was demonstrated using a non-linear simulation model of the UH-6015 operating off of an
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Model Following Controller with Airwake Compensation One drawback of the modified SAS described in the previous section is that, although the controller reduces the gust response of the vehicle, it also alters the response to the pilot control input. This is observed in Figure 4 shown above, which shows the pitch attitude closed-loop frequency response to a pilot input. The spectral properties of the airwake disturbances typically exhibited a magnitude peak in the range of 1 to 4 rad/sec, as shown in Figure 1. The modified SAS partly compensates for this by adding gain and phase lead in this frequency range, and thus it also tends to alter the closed loop response to pilot controls around the crossover frequency, which could lead to other handling problems. The modified SAS controller did not include any feed-forward compensation. By using a combination of feed forward compensation (designed to track pilot commands) and feedback compensation (designed to reject disturbances) one could potentially decouple the command tracking and disturbance rejection problems.
A model following / model inversion control architecture is proposed that would allow similar gust compensation, while maintaining a more desirable closed-loop response to pilot commands. The augmented plant model used for this architecture is shown in Figure 5 below. The main advantage of the model-following scheme is that in the absence of disturbances or inversion error, the controller achieves a desired response without the need for feedback compensation. Feedback is only used to correct for errors in the simplified inversion model and to account for external disturbances. In this approach, an airwake compensator is added as an additional feedback loop to a standard model following controller. The airwake compensator is optimized in a similar manner as the modified SAS discussed above, but in this case the feedback signal and the controller performance are based on angular rate tracking error as opposed to angular rate itself. Thus, if the controller is already tracking the pilot commands, the airwake compensator has no effect. This architecture also has the advantage that the airwake compensation can be readily engaged or disengaged, and compensators designed for different types of airwake can be readily added to an existing model following controller.
Fig. 5 Augmented Plant Used for Model Following Control (MFC) Design
Fig. 6 Model Following Control with Airwake Compensation (Expanded Pitch Axis) Baseline Model Following Controller The baseline controller used in this study a simple model following controller (MFC) design with nonlinear inversion. The controller is designed only for the roll, pitch, and yaw axes (the collective axis is left open loop) specifically for the hover and low speed flight regime of the UH-60A. Details of the pitch axis controller are shown in Figure 6. In the case of the roll and pitch axes, the controller is designed to achieve attitude command / attitude hold (ACAH) response, and a second order ideal response model is used to meet ADS-33 specifications for small amplitude response (in this case a natural frequency of 2.0, and a damping ratio of 0.9 were used). In the yaw axis, a rate command response is achieved, and a first order ideal response model (with time constant 0.4) is used. The ideal response model (or command filter) generates the desired attitudes, rates, and angular accelerations. In the case of the roll and pitch axes, a proportional-derivative (PD) compensator operates on the error in the attitude and attitude rates. In the yaw axis, a proportionalintegral (PI) compensator operates on the error in yaw rate. The output of the PI and PD compensators are then added to the desired accelerations, which results in the so-called pseudo-commands. The pseudocommands are passed through an inverse model to get the actuator commands. The inverse model is non-linear in that the pseudocommands for roll and pitch represent the desired 2nd derivative of the roll and pitch Euler angles. A nonlinear transformation can convert these to the desired first derivative of the body axis angular rates. This conversion was derived using the method of Rysdyk et al.16 and are shown below:
tan θ tan φ tan θ p& D = U φ − U θ tan φ tan θ − φ&θ& − θ& 2 −U r cos 2 φ cos 2 θ cos φ tan φ tan θ 1 − rφ& − rθ& cos φ cos φ cos 2 θ
1 tan φ 1 + φ&θ& + U r tan φ + rφ& cos φ cos φ cos 2 φ After this transformation a simplified linear model is used for inversion. A linearized model of the aircraft in hover was reduced to a simple square system: ⎡ δ lat ⎤ ⎡ p⎤ ⎡ p& ⎤ ⎢ q& ⎥ = [A ]⎢ q ⎥ + [B ]⎢δ ⎥ ⎢ long ⎥ ⎢ ⎥ ⎢ ⎥ ⎢δ ped ⎥ ⎢⎣ r ⎥⎦ ⎢⎣ r& ⎥⎦ ⎦ ⎣ This can be inverted as: ⎡ δ lat ⎤ ⎛ ⎡ p& d ⎤ ⎡ p⎤ ⎞ ⎜ ⎢ ⎥ −1 ⎢ ⎥ ⎢ ⎥⎟ ⎢δ long ⎥ = [B ] ⎜ ⎢ q& d ⎥ − [A ]⎢ q ⎥ ⎟ ⎜ ⎢ r& ⎥ ⎢δ ped ⎥ ⎢⎣ r ⎥⎦ ⎟⎠ ⎝⎣ d ⎦ ⎣ ⎦ q& D = U θ
In practice the inverse model can be scheduled with flight condition (airspeed, altitude, etc …). In this study, the controller was designed for hover but was found to operate effectively over a range of low speed flight conditions that were sufficient for the simulation analysis. If the inversion was exact then the tracking errors for the attitudes and rates would be driven to zero, and the error dynamics would be governed solely by the PID compensators. For example, in the pitch axis one can show the error dynamics would be governed by: ~& ~ &~& θ + K Dθ + K P θ = 0 ~ where θ = θ cmd − θ In practice, external disturbances and inversion error cause persistent perturbations on the tracking error, but
the controller is still effective, even when using a simplified linear model for inversion. Typically the PID gains are chosen so that the error dynamics have similar characteristics as the ideal response model. So for example, in the roll and pitch axes the PD gains are based on the natural frequency and damping ratio of the ideal response model: K D = 2ζω n and K P = ω n2 This choice in the gains causes the bandwidth associated with disturbances to be identical to the bandwidth associated with pilot commands. Airwake Compensator The airwake compensator is designed as another feedback loop around this closed-loop system. The same approach used in Ref. 13 is applied here, but the plant model now represents the closed-loop system of aircraft and model following controller as opposed to the open-loop aircraft. An augmented linear plant model, as shown in Figure 5, is used in the control synthesis and can be derived using the following procedure. First the MFC is implemented in the Simulink environment along with a 28th order linearized model of the UH-60 dynamics in hover (derived from GENHEL). This model includes the rigid blade flapping and lagging dynamics of the main rotor. In addition, the gust filters derived for the LHA airwake over Landing Spot 8 in 30 knot / 30 degree WOD conditions are incorporated into the model. Performance weighting functions are also included in the linear model. Tracking performance is based on the error in the attitude rates, and in this case the error in each axis was given equal weight with uniform weighting over all frequencies. For the actuator performance the following weighing functions were used:
s+2 ⎡ ⎢20 s + 20 ⎢ Wa = ⎢ ⎢ ⎢ ⎢⎣
⎤ ⎥ ⎥ s+2 ⎥ 20 s + 20 ⎥ s+2 ⎥ 37 s + 20 ⎥⎦
The frequency weighting penalizes high frequency actuator activity from the compensator. The scale factors are chosen to put equal percentage weighting on
each control input (which are tracked in units of inches of equivalent stick position). Once the augmented linear plant model is extracted, the compensator can be optimized to minimize the H2 norm for the closed-loop MIMO system that describes the response of performance due to the disturbances. See Reference 13 for more details of the method. In this case, the Riccati equations derived by Haddad and Bernstein17 are used to synthesize the compensator. The compensator derived from this process is a MIMO system with three inputs (the three attitude rate errors) and three outputs (the roll, pitch, and yaw actuator commands), and it is typically very high order (as many as 50 states). This is because all of the states of the aircraft model, weighting functions, and gust filters are effectively embedded in the compensator. In addition, some channels of the compensator exhibit a high gain at very low frequencies (effectively an integrator). There is already integral action on the angular rates, since the baseline model following controller uses attitude feedback. As a result the low frequency gain in the compensator can cause wind up issues when implemented in the non-linear simulation. Thus, some modification of the compensator is required. First, any very-low frequency poles are removed from the compensator along with an equal number of low frequency zeros. This process can be repeated for all nine channels (one for each input / output pair) in the compensator. The modified compensators match the original design in the middle frequency range, but do not exhibit a large gain at low frequency. Next, model order reduction is performed using balanced realization of the compensators, reducing the number of states on the final compensator to 30. This is still a relatively high order controller, but it is likely the order could be reduced further. This is a matter of ongoing research. Figure 7 shows the closed-loop frequency response from pitch attitude command to pitch attitude response of the model following controller, model following controller with airwake compensation, and the ideal response model. The results show that this new architecture follows the ideal response relatively well, and the closed loop frequency response is well behaved when compared to the results seen in Figure 4. In fact, the controller with airwake compensation tracks the ideal response at least as well as the baseline MFC.
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Figure 8 shows the Bode magnitude plot for the linearized on-axis rate feedback compensation in roll, pitch, and yaw for both the baseline MFC and the MFC with airwake compensation. The baseline MFC clearly provides simple PI compensation on the angular rates (equivalent to PD compensation on the attitudes). It should be noted that the baseline MFC also has some cross axis coupling channels due to the model inversion. The airwake compensator plots in Figure 8 include the effect of both the baseline MFC as well as the airwake compensation. The airwake compensator clearly has a large effect on the gain for frequencies between 1 and 10 rad/sec. There are also significant changes in the phase in this frequency range. There is a noticeable peak in the gain at around 3 rad/sec, which corresponds to same frequency where peaks are observed in the PSD of the airwake disturbances. For higher and lower frequencies the gain and phase approach those of the baseline MFC. Note that a high order linear model, including rigid blade flapping and lagging dynamics is used in the control synthesis of the airwake compensator. So the increased gain in the high frequencies should theoretically not cause instability due to rotor-body coupling. In practice, some air resonance oscillations were occasionally observed in the non-linear simulations, but could be mitigated by adding filters to the compensators. The airwake compensator also results in significant modification to gains in the crossaxis channels. It is postulated that the gain in roll-topitch and pitch-to-roll channels help alleviate rotor-body coupling.
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Simulation Results The model following controller and airwake compensator were implemented in the flight simulation facility at Penn State University.18 This simulator, shown in Figure 9, uses a rotorcraft flight dynamics model based on the GENHEL15 model of the UH-60A Black Hawk from the U.S. Army / NASA Ames. Outthe-window displays and interfaces with flight controls are provided by an open-source flight simulation program called FlightGear.19 In addition, the simulation facility includes another program that communicates with the flight dynamics model to provide airwake data in real time for multiple points on the rotorcraft, including the main rotor blade segments, the tail rotor, the fuselage, and the horizontal and vertical tails. The airwake data was calculated by Sezer-Uzol et al. using the computational fluid dynamics solver PUMA220. In this study, the airwake used was for an LHA-class amphibious assault ship with a 30 knot / 30 degree wind over deck (WOD) condition; the ship is stationary, so the steady wind is 30 knots coming from 30 degrees off of the starboard bow. The airwake disturbances are then superimposed on this steady wind.
Fig. 9 Penn State’s Low-Cost Multi-Disciplinary Rotorcraft Flight Simulation Facility (MDRSF) Initial testing of the controllers was performed in our low-cost simulator without the use of qualified pilots. Thus, a simple outer loop controller is implemented to provide translational rate command (TRC) control of the helicopter. This outer loop controller, shown in Figure 10, relates longitudinal stick input to forward speed, lateral stick input to lateral speed, collective to vertical speed, and pedal input to yaw rate. The speed commands are then related to roll attitude, pitch attitude, and collective commands through the use of PI controllers. The output of the outer loop provides the roll and pitch attitude commands and the yaw rate command to the MFC. The TRC mode
allows the helicopter to be maneuvered in low speed by an untrained pilot, and the helicopter can hold station without any pilot compensation. One of the buttons on the control stick was reassigned so that a pilot can switch the airwake compensator on or off at the press of a button. It should be noted, that although the TRC controller allows the helicopter to be operated by untrained pilot for the difficult task of shipboard operations, it may not be a practical control system to implement on fleet aircraft. It would at least require a full authority AFCS and would also require special sensors to measure aircraft motion relative to the ship deck. The TRC was implemented in this study primarily to help evaluate the inner loop controllers by removing the need for pilot compensation. It plays a similar role as the pilot models used in previous studies.10, 11, 13 Two sets of simulation time history results are presented below. In the first set, the helicopter was flown to a point over Landing Spot 8 on the LHA and transitioned into hover. Hover was then maintained by the combination of the outer loop and model following controllers; no pilot stick input was used during hover. This was done once with the airwake compensator off and once with the airwake compensator on. Figures 11 and 12 show the time history results for the hover portion of this maneuver. Clearly, the figure shows that the airwake compensator reduces the effect of the time-varying airwake disturbances on the attitude response of the aircraft. Figure 12, which shows the time history of the airwake velocities at the helicopter fuselage for each case, illustrates that the disturbances were similar between the two runs. The same airwake data was used both runs; the reason for the small difference in the airwake disturbances is due to small differences in the helicopter position between the two runs. For the second set of simulation results, the helicopter was flown approaching the LHA at a 45 degree angle and transitioning to hover above Landing Spot 8. The approach portion (the first 40 seconds) was flown with the airwake compensator off, then the airwake compensator was turned on after hovering for approximately 40 seconds. The compensator was then alternately turned on and off for periods of approximately 30 seconds (times when the compensator was switched on or off are shown by dashed black lines in Figures 13 and 14). In the approach portion, the helicopter starts outside of the grid where airwake data was available (only steady wind is included); in Figures 13 and 14, the time when the helicopter enters the airwake is shown by a dotted blue line. As in the previous case, the effect of the airwake disturbances on the aircraft attitude is noticeably decreased when the airwake compensator is on and noticeably increased when the compensator is disengaged.
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Fig. 10 Outer Loop Controller for Translational Rate Control
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Fig. 15 Autospectra of Angular Rates, Airwake Compensator Comparisons Finally, the helicopter was hovered over Landing Spot 8 with no pilot compensation for approximately 60 seconds both with and without the airwake compensation. The angular rate response of the aircraft was analyzed in the frequency domain using CIFER®.21 The square root of the autospectra of the aircraft rate responses are shown in Figure 15. The plots represent the RMS fluctuations in each of the angular rates as a function of frequency. The results show that the compensator results in a significant reduction in the motion of the aircraft, with the most dramatic improvements in roll.
Conclusions The objective of this study was to develop a model following control architecture that features special compensation to help reject disturbances from a ship airwake. The ultimate goal is to reduce pilot workload for shipboard operations. The control design methodology was applied towards a UH-60A Black Hawk helicopter operating off an LHA-class ship in a
30 knot / 30 degree wind over deck condition. This WOD condition results in relatively large disturbances and high pilot workload on the baseline aircraft, and thus presents a challenging case study. The airwake compensation controller was designed to be seamlessly integrated with a typical MFC architecture, such that the airwake compensator can be readily engaged or disengaged. An outer loop controller that achieves TRC response type was also implemented to help evaluate the performance of the inner loop controllers. Simulations were performed to analyze the benefit of the airwake compensation as compared to a baseline MFC without airwake compensation. In these simulations, the UH-60A was maneuvered to hover over Landing Spot 8 on the LHA in the 30 knot / 30 degree condition. Time history results seem to indicate a qualitative improvement in the aircraft handling qualities, as the fluctuations in aircraft angular rates and attitudes are significantly reduced. Frequency domain analysis was performed on the aircraft rate response and verified that rate response was significantly reduced with airwake compensation, especially in roll.
Future Work Piloted simulation evaluations of this flight control architecture are currently planned for April 2007 at the simulation facilities at Sikorsky Aircraft Corporation. These evaluations will be carried out by trained pilots in a high fidelity simulation facility allowing for more detailed handling qualities analysis.
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