Adaptive state feedback actuator nonlinearity compensation for multivariable systems

Abstract

SUMMARYThis paper addresses the problem of adaptive compensation of actuator nonlinearities with unknown parameters, for state feedback control of unknown multi‐input multi‐output (multivariable) linear time‐invariant dynamic systems. A new controller parametrization is derived to deal with bilinear parameters that resulted from the two sets of the actuator nonlinearity parameters and the dynamic system parameters. To overcome the difficulty caused by a nondiagonal high‐frequency gain matrix and a special actuator nonlinearity parameter structure, the new controller structure is parametrized on the basis of the high‐frequency gain matrix LDU or SDU decomposition, leading to a linear parametrization coordinating the actuator nonlinearity parameters. The developed control scheme is a model reference adaptive control based design, employing an adaptive state feedback control law combined with an adaptive inverse, to deal with uncertain parameters in the system dynamics and actuator nonlinearities. To ensure the robustness with respect to actuator nonlinearity parametrization errors and the nonsingularity of the adaptive inverse, the parameter estimates are updated with an adaptive law using a combined switching‐ σ and parameter projection modification. An application is studied for adaptive aircraft flight control with synthetic jet actuators, which have nonlinear characteristics to be compensated. Simulation results show the desired adaptive control system performance.Copyright © 2012 John Wiley & Sons, Ltd.