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Adaptive/Learning adaptive controller and compare to Desired response
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Aircraft Control
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Mental Model
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Control signal (IFCS F-15, Navy F/A-18C)
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adaptive controller on the GTM in the simulation and
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initial model of a pilot as an adaptive element
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Stability and Performance Implications l
Design requirements on adaptive controller to compliment pilot’s actions Predicted analytical bounds on pilot-in-the-loop task specific performance Analytically calculate stability robustness margins of an those obtained from flight data Compare adaptive pilot model performance to research pilot performance from flight data - - - - dynamics change flight test. flight test in batch simulation adaptive controller while explicitly incorporating the pilot. i in a closed-loop system with changing dynamics interactions leading to potentially conflicting actions (e.g. flight and structural mode control systems or flight and propulsion control systems) well as pilot’s situational awareness of system’s capabilities
athematically define the pilot as an adaptive controller
Adaptive Control with Adaptive Pilot Element: • Use system identification techniques to build a pilot model that changes as system • Pilot in the loop with an • Adaptive pilot model from system identification will fly the maneuvers from GTM Implications • Analytically evaluate stability and performance of a closed-loop system with an • Provide a framework for analytical analysis of interaction of two adaptive elements • Contribute to functional allocation between pilot and adaptive control schemes as Motivation Different adaptive control approaches on different platforms exhibited unpredicted interactions with pilot-in-the-loop Adaptive controller will have full control authority Technical Approach (Trujillo, Morelli, Gregory) M th M For system stability and performance analysis, model the pilot as an adaptive controller; therefore, analyze a system consisting of two adaptive controllers of potentially different architectures. In addition, this analysis will provide: Framework for analyzing interaction between two adaptive elements will facilitate identification of problematic adaptive controller/adaptive pilot model interactions explore these problematic interactions in detail in a simulation and/or flight test (akin to worst case uncertainty in linear robustness analysis guiding detailed Monte Carlo) worst case uncertainty in linear robustness analysis guiding detailed Monte Carlo) Current Work in Progress These combined factors have significant implications for closed loop system stability and performance as well as present potentially significant V&V challenge.
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)} ( 1 ; t Pb t Pb ); ( ) ) m Q M = j ( t t t y j − ( ( ( k m 3 T Pb ; x k T = e − ) = e t 0 ) ) ) − t + P ( k ) t t > ( ( ) T m T t ) t ( j
Actuator Failures ( t r x e
j ( y A j 3 j ( j r 2 1 3 { + γ u x 2 γ , γ Γ j { k ) ) ∞ m ) j j 2 j ∞ 2 + → 2 s * 2 t s * γ s ) * → PA ; t k k t k ( 0 ; x 0 lim > k d i j , and failure time T 1 lim sgn( j > ū sgn( T sgn( K 1 − T − , − Γ l j = P = = = = k ) j j = t j j ( 2 1 1 3 k k v & & P k Γ & f l
Direct Adaptive Control With Unknown
State feedback - low complexity, most assumptions State feedback - higher complexity, fewer assumptions Output feedback - highest complexity, fewest assumptions Signal boundedness and asymptotic tracking State or output tracking using state feedback has manageable level of complexity Accommodation of multiple failures; disturbances; actuator saturation; unmodeled dynamics; damage; nonlinear systems; adaptive propulsion control; application to full GTM math model Theoretically guaranteed stability and tracking performance Mathematical modeling, formulation, and analytical framework development Accommodation of actuator failures, disturbances, model uncertainties, actuator saturation Actuator failures of unknown magnitude and time of occurrence State tracking with state feedback Output tracking with state feedback Output tracking with output feedback Loss of effectiveness: C Control surface locked in unknown position: Failure values unknown State tracking: – Output tracking: – – One of two elevators locks in unknown position at Square wave elevator command applied at Remaining operational elevator seamlessly takes over for failed elevator Remaining operational elevator seamlessly takes over for failed elevator Direct MRAC can compensate for unknown actuator failures: – – Continuing research: – Objective New direct adaptive control methods are being developed for systems with unknown actuator failures • Technical Challenges • • Technical Approach Direct model reference adaptive control (MRAC): Formulations with increasing complexity and decreasing assumptions • • • • Actuator failure models • • • Solution Adaptive control laws for handling actuator failures: • • Example Application – GTM (Joshi, Khong) • • • • Conclusions • •
Nhan Nguyen, Irene Gregory, Suresh Joshi
Adaptive Flight Control for Adaptive Flight Control for
Aircraft Safety Enhancements Aircraft Safety Enhancements
Time-Delay Margin Persistent Excitation 40 40 40 I provides a flexible framework
NASA Aviation Safety Technical Conference, Denver, CO, Oct 21 - 23, 2008
if 30 30 30 =212, R=0 =212, R=10 Γ Γ Comparison Lemma (RLS) parameter estimation 20 20 20 t, sec for trade-off between performance and robustness to improve robustness Direct Adaptive Control not yet available 10 10 10 -3 via the use of provides piecewise approximate LTI margin x 10 0 0 0 Metrics-Driven Adaptation 0 0 0 2 -2 r 0.05 0.05 -0.05 -0.05 q p Nguyen & Boskovic, Bounded Linear Stability Margin Analysis of Nonlinear Hybrid Adaptive Control, American Control Conference 2008 Nguyen et al., Flight Dynamics and Hybrid Adaptive Control of Damaged Aircraft, Journal of Guidance, Control, and Dynamics Γ moving time window Phase Margin max Γ
Hybrid Direct-Indirect Adaptive Control 0
Indirect adaptation via recursive least-squares Direct adaptation with lower adaptive gain Plant: Estimator Model: RLS Parameter Estimation Use approximate transfer function to estimate local stability margin for a moving time window Approximate Local Transfer Function 10 20 30 40 50 60 70 Phase Margin, deg
Approximate Stability Margin Analysis of
Complex nonlinear behaviors vs. well-understood linear systems Lyapunov theory cannot predict boundedness in presence of unmodeled dynamics Metrics for stability and performance No guidance on adaptive gain selection Hybrid (composite) direct-indirect adaptive control – – Bounded linear stability method analysis in a – Hybrid adaptive control can enhance adaptation by reducing both modeling and tracking errors at the same time Bounded linear stability analysis can provide practical conservative estimates of stability margin Motivation Despite 5 decades of research, adaptive control still cannot gain acceptance in safety-critical control systems. Challenges include: • • • • Certification of adaptive control is a major V&V hurdle to overcome Technical Approach • • Simulation Conclusion • •