Document
Adaptive Control Using Neural Network
Augmentation for a Modified F - 15 Aircraft
J ohn J. Burken, Peggy Williams - Hayes, John T. Kaneshige and Susan J. Stachowiak approach does not require information on the nature or the Abstract — Description of the performance of a simplified extent of the failure, knowledge of the control surface dynamic inversion controller with neural network positions, or information on aerodynamic failures or augmentation follows. Simulation studies focus on the results unmodeled parameters. The Gen 2 tracking controller adds with and without neural network adaptation through the use direct adaptive neural network signals to the control law of an F - 15 aircraft simulator that has been modified to include [2] – [6]. These neural networks are used to generate canards. Simulated control law performance with a surface command augmentation signals to compensate for errors failure, in addition to an aerodynamic failure, is presented.
The aircraft, with ada ptation, attempts to minimize the caused by unmodeled dynamics, including dynamics inertial cross - coupling effect of the failure (a control resulting from damage or failure. Flight de monstration derivative anomaly associated with a jammed control surface).
began in early 2006 on the NASA F - 15 aircraft. An F - 15 The dynamic inversion controller calculates necessary surface six - degree - of - freedom (6 - DOF) simulator was used in the commands to achieve desired rates. The dy namic inversion evaluation test, which compared stabilator and canard controller uses approximate short period and roll axis failure compensation with the neural network algorithm. A dynamics. The yaw axis controller is a sideslip rate command system. Methods are described to reduce the cross - coupling canard failure emulat es a change in pitching moment due to effect and maintain adequate tracking errors for control angle of attack, C and is considered an aerodynamic , m !
surface failures. The aerodynamic failure destabilizes the malfunction caused by modeling errors or damage. The pitching moment due to angle of attack. The results show that control of the aircraft with the neural networks is easier (more specific objectives of Gen 2 are to 1) implement and fly a damped) than without the neural networks. Simulation results direct adaptive neural netw ork – based flight controller, show neural netwo rk augmentation of the controller improves 2) demonstrate the ability of the system to adapt to performance with aerodynamic and control surface failures in simulated system failures by suppressing transients terms of tracking error and cross - coupling reduction .
associated with the failure, 3) reestablish sufficient control and handling of the vehicle for safe recovery, and I. INTRODUCTION 4) provi de flight experience for the development of HE objective of the NASA Intelligent Flight Control verification and validation processes for flight - critical
T
System (IFCS) program is to dev elop and flight - test neural network software.
schemes that enhance control during primary control surface failures or aerodynamic changes resulting from II. DESCRIPTION OF THE GENERATION 2 failures or modeling errors. The first flight phase, known as CONTROLLER generation one (Gen 1), required aerodynamic parameter The general control scheme of the Gen 2 controller is identificat ion and is not discussed in this report (please see based on an adaptive neural cont roller that cancels errors [1] for a discussion on the Gen 1 flight phase). The second associated with the dynamic inversion of the model.
flight phase, known as generation two (Gen 2), evaluates a Initially, constant values of aerodynamic stability and neural flight control system that can provide adaptive control derivatives for a fixed condition in the flight control without explicit param eter identification. The Gen 2 envelope are used for model inversion. In addition, desired handl ing qualities are achieved with low - order reference Manuscript received January 26, 2006.
models, which are based on pilot preferences [7]. The yaw J. J. Burken is with the National Aeronautics and Space Administration axis controller is not a reference - based controller, but rather (NASA) Dryden Flight Research Center, Edwards, CA 93523 USA a classical yaw system. The Gen 2 control structure that (phone: 661 - 276 - 3726; fax: 661 - 276 - 2586; e - mail: john.burken@mail.dfrc.nasa.gov).
uses a direct adaptive co ntrol method is shown in Fig. 1.
P. Williams - Hayes is with NASA Dryden Flight Research Center, The symbol dd in a subscript indicates direct derivative and Edwards, CA 93523 USA (e - mail: peggy.williams@mail.dfrc.nasa.gov).
ad indicates adaptation.
J. T. Kaneshige is with NASA Ames Research Center, Moffett Field, CA 94035 USA (e - mail: j.kaneshige@mail.arc.nasa.gov).
A. Reference Models S. J. Stachowiak is with NASA Johns on Space Center, Houston, TX 77058 USA (e - mail: susan.j.stachowiak@mail.jsc.nasa.gov).
The pilot generates flight commands through Fig. 1. Generation 2 architecture in which the inversion is applied to t he B matrix.
longitudinal and lateral stick deflections { dep , dap } and ! U U p ! $ ! $ ! $ p pad c = ' (3) # & # & rudder pedals { drp }. When these inputs are used, the # & ! U U q q qad c " % " % " % reference model ( ref ) provides pitch ( p ), roll ( q ) and yaw ( r ) rate commands { p , q } and acceleration r e f r e f in which { U , U } are augmentation commands pad qad commands { ! p , ! q } by means of first - order roll rate r e f r e f generated by adaptive neural networks. The symbol U is and second - order pitch rate transfer functions, as shown in controller command and the subscript c represents (1) and (2). The symbol ! is rise time, in sec onds, and s is r command. These augmentation commands compensate for the Laplace operator. The symbol K is for constant gain, the estimated e rrors resulting from the difference between with the subscripts lat for lateral and lon for longitudinal.
reference ( p or q ) and aircraft angular rates (4).
r e f r e f Short period frequency, ! , and short period damping, s p ! , are in rad/sec . The symbol L represents neural p = p ! p e r r r e f s p (4) q = q ! q network error - modification damping in rad/sec.
e r r r e f p K r e f The subscript err is for error. The pseudocontrol l at = (1) acceleration commands { U , U } are computed with the dap ! s + 1 r p q equations q K ! ( s + L ) r e f l on s p " (2) = K 2 2 ! $ i p de p s + 2 # ! s + !
s p s p s p U = K + p + ! p (5) p p p # & e r r r e f s " % These transfer functions are low - order equivalent K ! $ systems designed to achieve level - one handling i q U = K + q + ! q (6) q p q # & e r r r e f qualities [7 ].
s " % B. Simplified Dynamic Inversion in which K and K are proportional ( p ) and integral ( i ) p i The inputs to the dynamic inversion controller are commanded angular accelerations { ! p , ! q }, which are constants, respectively, for each axis. The computation c c process for the pseudocontrol acceleration commands is computed with the equation shown in Fig. 2. The simplified dynamic inversion Fig. 2. Simple sigma pi neural netw ork structure ( ∑ = sum, π = product).
algorithm inverts a B matrix with states for modeling the network operates in conjunction w ith the error of the short period and roll modes. The symbol B indicates control control system. By recognizing patterns in the behavior of and T means transpose in (7). To protect against a poorly the error, the neural networks can learn to remove the error B ranked matrix, the inversion is generated by a biases through control augmentation commands (Fig. 1).
pseudoinverse (7). The adaptation signal attempts to remove errors in the neura l flight control system to improve handling qualities T T in the presence of unknown failures. The neural network B " A dj oi nt ( B " B ) ! 1 B = (7) that provides this online adaptation scheme is known as T D e t e r m i na nt ( B " B ) "sigma pi." A simple single hidden layer sigma pi network is shown in Fig. 2. The name "si gma pi" is derived from the The inversion is used to determine necessary control underlying equations of the network that sum ( ) the !
surface deflections { ! (roll axis), ! (pi tch axis)}. Control a e products ( ! ) of the inputs to the neural network with their ! !
surface commands { , } are obtained with the a e associated weights. The weights of the neural network, W , c c equation are determined by a training algorithm, also known as an adaptation or learning rule. Learning involves adjusting these weights so that the network has a valid relationship !
" % a ! p ( L " % c c 1 ( 1 (8) $ ' = B between the inputs and outputs, and in turn, minimizes the $ ' ! ! q ( M e c 1 # & $ ' c # & err or.
Because a neural network is designed to recognize in which B is the state space system control matrix and the patterns between inputs and errors, the selected inputs must ! !
terms { p ! L , q ! M } are the differences between provide enough coverage for the network to be able to c 1 c 1 capture the behavior of the error. If too many inputs exist, input acceleration commands and actual plant acceleration however, the neural networ k may not be able to adapt contributions { L (rolling moment, ft - lbf ), M (pitching 1 1 quickly enough for practical application. Although the moment, ft - lbf )}. These plant contributions are calculated adaptation gain can be used to increase the rate of from the appropriate states for modeling the short period adaptation, it can cause large transients in the neural and roll mode dynamics.
network outputs when it becomes too big. These transients C. Adaptive Neural Network are caus ed by spikes and sometimes sign changes in the network weights, which are often encountered before the The purpose of the neural network system is to network converges to a learned state.
accommodate large errors that are not anticipated in t he nominal control law design phase. In a failed flight D. Application of the Adaptive Neural Network condition or configuration ( A or B matrix), errors will The adaptive neural network implemented for the flight develop that are larger than expected. The adaptive neural test is divided into three separate networks, one each for the gains can be viewed as specifying the relative rates of pitch, roll, and yaw axes. Inputs to the network consist of adaptation.
control commands, sensor feedback, and bias terms. The III. SIMULATION RESULTS number of inputs to each individual neural network vary; the roll axis uses six, the pitch ax is uses seven, and the yaw The first type of simulated failure ( A matrix failure), axis uses ten. The output of each neural network is an which represents an aerodynamic failure, inserts a angular acceleration command that augments the control multiplier onto the canard surface command (change in signal from the research controller for each axis. To couple C ). The second type of simulated failure ( B matrix m !
the three networks, pitch information is included in the r oll failure), w hich represents a surface failure, inserts a and yaw neural networks, and some roll axis signals are jammed stabilator failure. Simulation results illustrate the included in the pitch and yaw neural networks.
experiment that was flown and highlight the benefits The neural network output, U , is the control ad provided by the Gen 2 control system. The flight condition augmentation command comprised of three components: used in this research is at a Mach num ber of 0.7 and an roll, pitch, and yaw ( U , U , U ). This neural pad qad r ad altitude of 6,096 m. All of the pilot inputs to the simulation time histories are “canned” piloted stick inputs, and no network output is computed with (9) (see Fig. 1).
attempt to correct for the aircraft attitudes is added to the T piloted inputs. This “canned” pilot input method was use d U = W B C (9) ad a only for comparison purposes and is not intended for flight test at this point in time. Because the controller is a rate The vector of basis function, B , is computed from the a command system, attitudes such as bank angle, φ , are used inputs in each signal input category by means of a product.
only for comparison and disturbance rejection trade - off The network weights, W , are computed by an adaptation studies. For instan ce, when a failure is imparted on the law, which includes an adaptation gain, G , and an error - aircraft and the resulting attitudes change minimally, the modification term, L . The error - modification term helps control system is considered to have good robustness contain the parameter growth of the weights and can be properties .
considered a damping term. The final adaptation law is A. A Matrix Failure (Aerodynamic Failure) !
The first case is an A matrix failure imposed on both the
W = ! G U B + L U W ( ) dt (10)
e r r a e r r left and right canards, with a multiplier of – 0.5 on the nominal angle - of - attack schedule. This failure forces the !
in which W is the weight increment for the current time canards to a less stable configuration. A 30 - second time step; W is the weight from the previous time - step; dt is the history with three longitud inal pilot stick inputs and a time - step, which is 0.0125 seconds (80 Hz); G is the failure imposed at 11 seconds is shown in Fig. 3. Neural adaptation gain, which is sometimes called th e learning network is labeled NN and n indicates normal z rate; and U is the error compensation. This weight e r r acceleration. In the first 10 seconds a normal response calculation is currently implemented in the Gen 2 system.
demonstrates how the pitch rate follows th e commanded The squashing function used to normalize inputs to the pitch rate (represented by the solid black line). The blue neural network is a sigmoid function and has the form ( also lines in Fig. 3, which represent the aircraft response when shown in Fig. 2) the neural network is inactive, show that after the failure is inserted the aircraft is stable but it experiences two or thre e ! x ! x f ( x ) = ( 1 ! e ) / ( 1 + e ) . (11) overshoots. When the neural network is active (represented by the red lines in Fig. 3), the response is better damped and the commanded pitch rate is followed more closely The adaptation law is computed as a function of the than when the neural network is inactive. By the third pilot proportional and integral (PI) controller gains and tracking input, the neural net work response is very close to the error ( p , q , and r ) equated to e r r in (12). The z e r r e r r e r r commanded pitch rate (represented by the solid black line).
subscript indicates pitch ( p ), roll ( q ) or yaw ( r ).
The results demonstrate that with this type of failure the neural networks help with tracking and damping .
U = Kz e r r + Kz e r r (12) e r r i p
!
This computation allows the neural networks to work in conjunction with the dynamic inversion PI contr ollers.
Furthermore, because the adaptation gain can be used to specify the overall rate of adaptation, the adaptation law Fig. 4. Time history of longitudinal aircraft stat es of a B matrix Fig. 3. Time history of longitudinal aircraft sta tes of an A matrix right stabilator lock failure (right stabilator = – 4 degrees lock canard failure at 11 seconds (multiplier = – 0.5).
from trim at 11 seconds).
B. B Matrix Failure (Control Surface Failure) The lateral - directional states from the roll inputs are shown The second case is a B matrix failure, involving a in Fig. 5. As previously noted, the inputs are “canned” and – 4 - degree lock from trim, which is impo sed on the right no other pilot commands are injected to level the aircraft stabilator 11 seconds into the simulation run. A 40 - second after the failure. Note that the yaw rate, bank angle, and time history in which lateral pilot stick inputs are sideslip excursions are lower when the neural networks are commanded is shown in Fig. 4. During the first 10 seconds active than when the neural networks are inactive. The roll the pitch rate does not move with the lateral pilot input.
axis is a roll rate command system (represe nted by the This situa tion is preferred; roll inputs should have little or black solid line on the top plot). During the first no impact on longitudinal states. When the stabilator failure commanded doublet no failure occurs and the tracking is is injected at 11 seconds, note that transients occur in angle good for both cases (neural networks inactive and active).
of attack, normal acceleration, and pitch rate. Initially After the failure is activated, the tracking is somewhat cross - coupling reduc es minimally when the neural better when the neur al networks are active than when they networks are active, compared to when the neural networks are inactive. And finally, Fig. 6 shows the neural network are inactive, as shown in Fig. 4 (see angle of attack and contribution commands to the roll, pitch, and yaw axes. An normal acceleration time histories). As the “canned” pilot abundance of cross - coupling occurs with this failure, which input resumes at 16 seconds, the neural networks con tinue in turn causes all three networks to bec ome active. For a to adapt and show improvement over the nonadaptive case.
more detailed description of this research see [10].
The amount of normal acceleration disturbance during a roll command is approximately 40 - percent less when the neural networks are active.
control for the pitch and roll axes and a classical sideslip rate controller for the yaw axis. The neural network is an on - li ne direct adaptive algorithm that attempts to drive the error between the reference model and commanded state to zero. An aerodynamic failure and jammed control surface failure have been demonstrated. In both failure cases the controller with neural networ k augmentation demonstrated improvements compared to the nonadaptive controller without neural network augmentation.
During the aerodynamic failure, the neural networks improved the damping and tracking. During the jammed control surface failure, the neura l networks reduced cross - coupling, enabling the pilot to fly to the desired trajectory with fewer tracking errors. The neural networks also reduced the tracking errors.
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[3] A. J. Calise, S. Lee, and M. Sharma, “Direct Adapt ive matrix right stabilator lock failure (right stabilator = – 4 degrees Reconfigurable Control of a Tailless Fighter Aircraft,” AIAA - 98 - lock from trim at 11 seconds).
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[6] John Kaneshige, John Bull, and Joseph J. Totah, “Generic Ne ural Flight Control and Autopilot System,” AIAA - 2000 - 4281, Aug. 2000.
[7] Flying Qualities of Piloted Vehicles , U.S. Department of Defense, MIL - STD - 1797, March 31, 1987.
[8] John H. Blakelock, Automatic Control of Aircraft and Missiles , 2nd edition, John Wiley & Sons, Inc., New York, 1991.
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Fravolini, “Design and Testing of a Safety Monitor Scheme on the NASA Gen 2 IFCS F - 15 Flight Simulator,” A IAA - 2004 - 6284, Sept.
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Fig. 6. Time history of neural network activity of a B matrix right stabilator lock failure (right stabilator = – 4 degrees lock from trim at 11 seconds).
IV. SUMMARY OF RESULTS Simulation results have been presented of a neural network adaptive controller that compen sates for errors resulting from aerodynamic and control surface failures.
This hybrid controller uses simplified dynamic inversion