Adaptive Actuator Nonlinearity Compensation for Multivariable Systems

Abstract

This work solves the open problem of adaptive compensation of actuator nonlinearities with unknown parameters for feedback control of unknown multi-input multi-output (MIMO) linear time-invariant dynamic systems. The solutions are developed in the model reference adaptive control framework, for achieving desired tracking performance in the presence of system parameter uncertainties. Such an adaptive control problem is solved by employing an adaptive feedback control law combined with an adaptive inverse to deal with uncertain parameters in the system. There are two sets of system parameters, one from the dynamics and one from the actuator nonlinearity, which appear bilinearly. For MIMO systems, the interaction between input and output components, characterized by the system high frequency gain matrix, needs additional treatment for such a parametrization. In this paper, some key technical issues in deriving controller parametrizations involving bilinearly appeared system parameters are claried in details and dierent adaptive actuator nonlinearity compensation control schemes for MIMO systems are systematically designed and analyzed. The developed control schemes are state feedback for output tracking, for both continuous and discrete time cases, and state feedback for state tracking, for the continuous-time case.