GENERIC PILOT AND FLIGHT CONTROL MODEL FOR USE IN SIMULATION STUDIES

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1 AIAA Modeling and Simulation Technologies Conference and Exhibit 5-8 August 22, Monterey, California AIAA GENERIC PILOT AND FLIGHT CONTROL MODEL FOR USE IN SIMULATION STUDIES Eric N. Johnson * and Amy R. Pritchett School of Aerosace Engineering, Georgia Institute of Technology, Atlanta, GA ABSTRACT In develoing an aircraft simulation, a number of aircraft dynamic models are available with a range of fidelity. However, many alications of simulation also require a model of the flight control or of the ilot to realize their goals. These models can be difficult to imlement using classical control methods and, in the case of flight control systems, may not be ublicly available. This aer describes a generic ilot and flight control model suitable for many alications of simulation in research and design. This model may be easily imlemented in simulation by using a architecture adated from adative control for innerloo attitude control, which caitalizes uon the dynamic information known within a simulation to create a stable control behavior. This architecture allows secification of the closed-loo behavior of the aircraft and controller (ilot or autoilot). Secific imlementations of inner- and outer-loo control behavior are detailed. Simulation runs with this controller, acting as both a ilot and as a flight control system, are documented. INTRODUCTION In develoing an aircraft simulation, a number of aircraft dynamic models are available with a range of fidelity. 1,2,3 However, many alications of simulation including flight deck rototying and testing, avionics integratio n, reliminary aircraft design, air traffic control research, and education also require a model of the autoilot or of the ilot to realize their goals. Historically, these models of autoilot and ilot behavior are not commonly available in a form that can be easily imlemented in a flight simulator. While ilot control behavior has been widely studied and documented, 4,5 the closed-loo invariant behavior associated with iloted control is difficult to imlement in a simulation without inverting the aircraft dynamics. *?Lockheed Martin Assistant Professor of Avionics Integration, Member AIAA. Eric.Johnson@aerosace.gatech.edu Assistant Professor, Member AIAA. Amy.Pritchett@isye.gatech.edu Similar difficulties are also faced in imlementing models of flight control system behavior into simulations. Although the general form of the flight control systems resulting closed -loo behavior may be known, re-creating this behavior with the aircraft dynamics can be difficult, traditionally requiring a significant amount of reverse-engineering to develo an aroximate model. Comrehensive, exact models of the flight control system s internal behavior are rare and usually rorietary. Recent advances in adative control allow the desired closed -loo inner-loo dynamics of a combined control system and aircraft to be secified as a reference model. 6 These control architectures use dynamic inversion (created or trained by adative elements such as neural nets) to infer the aircraft controls required to follow the closed-loo reference model dynamics. This aer demonstrates a modification of an adative control architecture that allows ilot or flight control system closed-loo inner-loo dynamics to be secified in the control of detailed, non-linear aircraft dynamic models. This modified architecture takes advantage of the exact knowledge about the aircraft available in simulation to eliminate the adative elements of the control architecture, roviding a simle, generic imlementation suitable for many simulations. While outer-loo control by ilots and flight control systems is not as consistent between aircraft and tasks and inner-loo control, this aer also discusses the general forms of their outer-loo behavior and rovides reresentative outer-loo models of both ilots and flight control systems. This aer first reviews general models of autoflight systems and of ilot control behavior, including the distinction between inner- and outer-loo control behavior. A control architecture that can be modified from adative control to rovide a generic model of ilot or flight control is then outlined, and a secific imlementation is detailed. Results from several simulation tests are documented. The aer ends with a summary and notation of how these generic models may be imroved uon with further develoment. Coyright 22 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc., with ermission.

2 MODELS OF PILOT AND FLIGHT CONTROL CLOSED-LOOP BEHAVIOR As shown in Figure 1, a common and useful reresentation of aircraft control identifies an innerloo element that tracks attitude through commands to aircraft control surfaces, and an outer-loo element that generates the attitude commands to the inner-loo element to achieve a secified velocity and altitude. The following sections will review the current state of knowledge of inner- and outer-loo control behavior. Models of Pilot Control Behavior The secific linkages between aircraft, inner-loo control element and outer-loo control element shown in Figure 1 mimic ilot control behavior in many tasks. Pilot outer-loo control behavior is modeled as three outer-loo controllers. Each controller was develoed as a model of ilot guidance behavior in each dimension, roll, itch, and airseed. The set of four inner-loo controllers takes in the commanded φ c, θ c and T c from the outer-loo as well as the requirement that β c for coordinated flight. These four inuts are used by the roll, itch, thrust and yaw controllers to define the the commands δ a, δ e, δ T and δ r resectively. This division of inner-loo and outer-loo control is substantiated and reinforced by ilot training and cockit instrumentation. For examle, during instrument flight training ilots are taught that the focus of their scan should be on their artificial horizon to monitor their attitude, sulemented by frequent glances to indications of heading, seed and altitude to reevaluate whether they are tracking the correct attitude or should readjust their desired attitude and engine settings. This scan is suorted by a standard cockit design which laces the artificial horizon in the center of the instruments, surrounded by the airseed, heading indication or directional gyro, and altimeter. Pilot Inner-Loo Control Behavior Several mathematical ilot models have been develoed based on simulator and flight test data. The main difficulty in modeling ilot inner loo control behavior arises from their ability to adat to changes in the aircraft behavior. A simle but effective reresentation of this closedloo behavior for a manual control task is the crossover model where the combined ilot and aircraft in a single control dimension are described by the following transfer function near the crossover frequency by the following oen loo transfer function 1,2 : G FL ( s) G S ( s) G ( s) c S c s e τ e. s DESIRED ALTITUDE, SPEED AND HEADING OUTER-LOOP V, h, Ψ β c, θ c, φ c, T c INNER-LOOP β, θ, φ, T δ r, δ e, δ a, δ T AIRCRAFT Figure 1 Generic Control Model Comosed of Inner- and Outer-Loo Elements where: S is the ilot gain, S c is the effective gain of the aircraft dynamics in this control axis in the vicinity of the crossover frequency, and τ e is the ilot s effective time delay. The ilot transfer function is modeled as τe. s S ( τ Ls + 1) e G ( s) ( τ I s + 1) and arameters in the model are adjusted to match the crossover model near the crossover frequency. The lant model here deends on the aircraft and on any stability and control augmentation used in the flight control system. The form of the resulting system will vary, but it is tyically desirable to have a first order resonse of roll inut to roll rate and a second order resonse of itch control to itch angle resonse. Pilot Outer-Loo Control Behavior Unlike innerloo control behavior, ilot outer-loo control behavior has not been found to have a consistent form across all ilots and across all iloting tasks. For examle, deending on the hase of flight and immediate situation, a ilot may choose to use throttle to control flight ath angle (in tracking a glide-sloe), vertical seed (in a stee climb or descent), or airseed (in adjusting seed during cruise). However, the selection of these outer-loo behaviors for a trained ilot is usually rationale and therefore redictable if the roer contextual factors are taken into account.

3 Models of Flight Control Closed-Loo Behavior In generating an aroximate model of most flight control systems, the distinction shown in Figure 1 between inner- and outer-loo control elements is again aroriate, as they are often searated functionally within the flight control system into attitude control and velocity control. The secific choice of arameters considered by inner- and outer-loo, and controlled by the outer-loo, may v ary between systems; for examle, one may choose to control attitude, while another may choose to control angle of attack. This differences are largely aircraft secific and tuned to the secific erformance requirements, while the overall form is reasonable consistent. Flight Control System Inner-Loo Control Behavior In designing flight control systems, a common desired closed-loo behavior is a second order resonse for the two attitude commands (roll and itch) and for sidesli. The secific mechanis ms by which this resonse is created within the control system varies with the design aroach for the controller, the sensor information available to the control system, and the aircraft dynamics. Flight Control System Outer-Loo Control Behavior As with ilots, several secific forms of outer-loo control may be rovided by the flight control system. For examle, modern autoilots may have searate modes for altitude hold, flight level change, vertical seed hold (to a commanded altitude) and flight ath angle hold (to a commanded altitude). To first order, the general form of these modes of behavior are redictable; each may have secific idiosyncrasies which a model can be tuned to as data is available. EXTENSIONS FROM ADAPTIVE CONTROL ARCHITECTURES FOR INNER-LOOP CONTROL Adative control architectures now exist that create (within the caabilities of the aircraft dynamics) a consistent closed-loo inner-loo behavior. 6 This consistency is achieved through dynamic inversion of the lant (aircraft) model, which allows the controls to be set directly to values redicted to create the desired behavior. In actual flight, adative elements (such as neural nets) are needed to tune the dynamic inversion. In the control architecture described in this section modified for use in simulation, exact knowledge of aircraft dynamic behavior is available and can be used directly, negating the need for an adative element. Each inner loo controller is comosed of three comonents: a reference model, a lant model, and an actuator model. The reference model defines the desired behavior of aircraft and controller (ilot alone, stability augmentation system and ilot, or autoilot). In this study it is chosen to be the crossover model for a human ilot, and a desired second order resonse to model a roduction autoilot system. Since the reference model and aircraft dynamics are assumed to be of second order,? (seudo -control) is a desired (angular) acceleration of the aircraft. The acceleration desired of the aircraft is: ν ν + K x x ) + K ( x& x& ). rm P ( rm D rm The first term reresents the dynamics of the reference model. The second and third terms are feedback terms for any differences between the state and state derivative values actually attained by the aircraft comared to the desired reference model values. The fourth term, model error, is model error as measured in the simulation, and is described below. The inut-outut relationshi of control effect on dynamics is simlified by a single gain bˆ. Corresondingly, this simle function may be inverted to comute the control command to the aircraft d that will generate the desired dynamic?. 1 δ ( bˆ) ν This estimate bˆ does not need to be accurate; it need only have the correct sign as the true value. Actual controls are not always those commanded: actuator dynamics and saturation can cause differences between the commanded controls (d ) and actual values (d). The difference between actual and commanded controls also causes an estimate of aircraft acceleration ( νˆ bˆ δ ) to be different from the desired dynamics?. The difference between the actual dynamics and the desired dynamics defines the hedge signal: ν h ν νˆ. 6 The hedge signal reresents the increment of the desired dynamics that can not be achieved due to actuator limitations. This hedge dynamics is subtracted from the simulation of the reference model states so that the reference model continues to reresent achievable dynamics: x& rm νrm νh. Model error (?) reresents the difference between the actual acceleration of the aircraft and its estimate: + x& & νˆ. In a controller on an actual vehicle, comutation of this model error is difficult as it requires an accurate noise-free measurement of angular acceleration. However, in the simulator, these values are known exactly; because model error is both an inut to νˆ as well as its outut, the values of acceleration and νˆ from the revious timeste are used in calculating?, a reasonable aroximation when the time-ste is small. The set of equations could also be iterated to converge on the correct values at every udate.

4 Inner-Loo IMPLEMENTATION In imlementing inner-loo controllers in simulation, the modified control architecture described in the revious section may be used; the secific control behavior is determined by the reference model as selected to model ilot or flight control system. In modeling a flight control system, a second order resonse may be secified for the two attitude commands (roll and itch) and for sidesli. A first order resonse is secified for thrust. Roll resonse is tyical; this second order resonse is secified by 2 ν ω ( φ φ ) + 2ςω ( φ & φ & ) rm n rm n with selected natural frequency and daming ratio as indicated. The remainder of the setu is consistant with that introduced above. The structure is illustrated in Figure 2. Command 2 nd Order Reference Model Hedge Actuator Limits Solve for Exact Control Inut rm Vehicle Figure 2 Inner Loo Autoilot Structure for a Single Axis or Channel In the human ilot model (erhas in series with a stability augmentation system), the reference model is based on the crossover model. With an ideal stability augmentation, the lead and lag terms of S G ( s) ( τ L s + 1) e ( τ s + 1) I τ. s (or both) τ L and τ I may be omitted. For roll, the generic stability augmentation system exhibits the desired resonse φ & ( s) u K ( s) ( τ s + 1) with exact cancellation of all but one rigid body mode, where u is the roll inut from the ilot. As a result, the crossover ilot model design (for manual control of roll angle) is comleted based on the lant model φ( s) u K ( s) s( τ s + 1). e The secified itch angle resonse is similar. This structure is illustrated in Figure 3. The comonents that make u the generic stability augmentation system model are deliniated. Command Crossover Pilot Model 1 st /2 nd Order Reference Model Hedge Actuator Limits Solve for Exact Control Inut Stability Augmentation Model Vehicle Figure 3 Inner Loo Stability Augmentation System and Pilot Model Structure for a Single Axis Outer-Loo Less emhasis is laced on an outer loo generic autoilot or ilot model here, since, noted earlier, several different tyes of outer-loo control behaviors are common, selected based on contextual factors beyond the scoe of traditional dynamic analysis. However, one broadly alicable aroach is to rovide attitude and thrust commands to the inner loo to achieve a desired velocity, itself based on a desired osition. Internal limits are used on attitude commands and ossibly velocity commands. This is the aroach taken here. However, to kee the autoilot truly generic, data available only in a simulation is used to adjust these thrust and attitude commands as though an ideal autoilot has been develoed. This is accomlished by continually including the error in exected and achieved acceleration in the next attitude and thrust command generation cycle, effectively solving for the attitude and thrust commands needed at every instant to give the desired resonse within the limitations of the lant inuts. This is reasonable as an autoilot, flight director, or human ilot model for many alications. The itch angle comutation is tyical. The vertical seed command is determined based on altitude error. ( h h) τ h which may then be limited. Next, commanded rate of change of vertical seed is determined & ( ) τ

5 where is model error comuted below. Now commanded itch angle is determined based on estimated scale factor, bˆ, which need not be very accurate; in ractice the sign needs to be correct and the magnitude within an order or magnitude is sufficient. θ & bˆ Pitch angle command is normally limited at this oint, either to an arbitrary value or to one based on maximum erformance climbs and descents (corresonding to maximum and minimum available thrust). Model error is found based on information from the revious udate. Alternatively, these equations could be iterated with the aircraft model to solve for the correct itch angle command, but in ractice this is not necessary. RESULTS The roosed generic autoilot and SAS/ilot model was tested utilizing an F-16 model that is available in the literature. 3 This allowed the system to be demonstrated on an aircraft with a large flight enveloe and that benefits from stability augmentation. For the ilot/sas results, the SAS was a rate command system on itch and roll, both with a frequency of resonse of 1 rad/sec. The directional channel was a sidesli-command system with a natural frequency of 3 rad/sec. The ilot model utilized the crossover model form. 4,5 The autoilot model has a second order resonse on all three inner loos, with 1 rad/sec undamed natural frequency in roll and itch, and 3 rad/sec in yaw. The daming ratio was selected to be critical, one, for all loos. The secified thrust resonse was first order with a time constant of 5 seconds for all cases. The itch angle resonse of both aroaches is shown in Figure 4 from brake release to level off at 2 ft. Pitch angle command is limited to 3 degrees (thrust limitations are not a factor for this time history). The ilot model resonse differs, and has a significantly larger steady state offset to the ram inut of heading during level off. The elevator angle is shown in Figure 5 for the same resonses. Here, the ure time delay in the ilot model is evident when the aircraft rotates for takeoff. The airseed resonse is shown in Figure 6. At 25 KCAS, a ste inut of heading command is given to exercise the lateral channels. The heading resonse is shown in Figure 7. The aileron used is given in Figure 8. The roll angle commanded and the result is given in Figure Pilot Cmd Pilot Resonse Autoilot Cmd Autoilot Resonse itch angle (deg) Figure 4 - Pitch attitude resonse, autoilot model and human ilot model with SAS resonse, commanded and actual shown, for rotation, takeoff, and level-off at 2 ft

6 5-5 elevator angle (deg) Pilot Resonse Autoilot Resonse Figure 5 - Elevator time history, for both ilot model with SAS and autoilot model, ure time delay in ilot model is visible just after rotation 15 1 KCAS Figure 6 - Airseed resonse from brake release, in Knots Calibrated Air Seed (KCAS), resonse with ilot model and autoilot model are similar

7 12 1 heading angle (deg) Pilot Cmd Pilot Resonse Autoilot Cmd Autoilot Resonse Figure 7 - Heading resonse for a 1 degree ste inut of heading command, ilot model resonse is initially slower.6.4 Pilot Resonse Autoilot Resonse aileron (deg) Figure 8 - Aileron time history for 1 degree ste inut of heading command, for both ilot model with SAS and autoilot model

8 Pilot Cmd Pilot Resonse Autoilot Cmd Autoilot Resonse 2 roll angle (deg) Figure 9 - Roll angle resonse, commanded and actual, for a 1 degree ste inut of heading command CONCLUSIONS This aer described a generic model of ilot or flight control system behavior suitable for, and easily imlemented in, flight simulations. The inner-loo element is modified from adative control architectures, and allows a closed-loo behavior to be secified and followed that incororates the dynamics of the aircraft; this allows for the inclusion of closed-loo behaviors established by models of ilots and by common secifications for flight control systems erformance. While outer-loo control behavior is not secified as exactly by models of ilot and flight control system behavior, some general forms were also given here. The generic model was alied to an aircraft dynamic model with a large flight enveloe and requiring stability augmentation. This model was set to enact both ilot and flight control system behavior, and the dynamic resonses of trajectory commands were found to behave in the general form exected when under iloted and automatic control. While not an exact reresentation of one secific autoflight system and within the limitations of ilot models this generic model rovides a reasonable, easy-to-imlement means of incororating ilot and flight control system behavior into flight simulation. The fidelity of this reresentation is suitable for many tyes of research and design activities, including avionics integration, flight deck design and testing, air traffic control research, and education. As a further develoment, the ilot model may be further imroved by automating the tuning of its arameters in resonse to the dynamic characteristics of the aircraft model, as secified in the literature. 4,5 REFERENCES 1 Hanke, C.R., and Nordwall, B.R. The Simulation of a Large Jet Transort Aircraft, Vol. I: Mathematical Model, NASA CR-1756, 1971 N Boeing Doc. D6-3643, with D.R. Nordwall as an additional author. 2 McRuer, D., Askenas, I., and Graham, D., Aircraft Dynamics and Automatic Control, Princeton University Press, Stevens, B. and Lewis, F., Aircraft Control and Simulation, John Wiley & Sons, McRuer, D. and Jex, H. A Review of Quasi- Linear Pilot Models, IEEE Transactions on Human Factors in Electronics, Vol. 8, No. 3, Blakelock, J., Automatic Control of Aircraft and Missiles, John Wiley & Sons, 1991, Johnson, E., Calise, A., Rysdyk, R., and El- Shirbiny, H., Feedback Linearization with Neural Network Augmentation Alied to X-33 Attitude Control, AIAA , AIAA Guidance, Navigation and Control Conference and Exhibit, 2, Denver, CO.

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