Adaptive state feedback actuator nonlinearity compensation for multivariable systems

Abstract

This 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-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.

Robust adaptive control: legacies and horizons

“…Tao et al . addressed the problem of adaptive compensation of unknown multi‐input multi‐output (multivariable) LTI dynamic systems with actuator nonlinearities. They present a new controller parametrization to deal with bilinear parameters resulted from the multiplication of the actuator nonlinearity parameters and the dynamic system parameters.…”

Adaptive Fault‐Tolerant Control of Uncertain MIMO Systems with Reduced Requirement on Desired Trajectory Under Unknown Control Direction

“…Furthermore, actuation failures might occur in one or more agents during systems operation. Fault‐tolerant control schemes have been proposed in the literature . In , the nonlinear adaptive compensation problem of the actuator under unknown parameters is studied for the state feedback control of the unknown MIMO linear time‐invariant system.…”

“…Fault-tolerant control schemes have been proposed in the literature [18][19][20][21][22][23][24]. In [18], the nonlinear adaptive compensation problem of the actuator under unknown parameters is studied for the state feedback control of the unknown MIMO linear time-invariant system. In [19], fault tolerant neural network tracking controllers are applied to the system with unknown nonlinear dynamics, disturbances and actuator failures.…”

Torsional dynamics and stability of automotive driveline considering cubic nonlinearity

“…The backlash is mainly caused by the play between gears in the final drive and the gearbox, 9,10 and scholars have done a lot of researches on the issues that were caused by the backlash. 11,12 However, as the main flexible part of the driveline, the half-shaft is generally modeled as a linear massless torsional spring/damper package. In fact, the nonlinear factors such as material nonlinearity and geometric nonlinearity invariably exist.…”