Compensation of spatiotemporally varying disturbances in nonlinear transport processes via actuator scheduling

Abstract

AbstractA new systematic framework is developed that allows the integration of a comprehensive actuator scheduling policy and a robust feedback controller synthesis method to be realized for the compensation of spatiotemporally varying disturbances for nonlinear transport processes modelled by parabolic partial differential equations (PDEs). It is assumed that the process of interest has either multiple actuators and the desirable arrangement is to activate only one during a given time‐interval, or there is a single actuator capable of moving at a priori selected positions within the spatial domain. Local feedback controller synthesis methods based on linear matrix inequality (LMI) techniques are developed and realized through the linearization of a nonlinear finite‐dimensional approximation of the original distributed parameter system obtained via a Galerkin discretization scheme. Furthermore, additional conditions are derived that ensure robustness with respect to a certain class of physically meaningful spatiotemporally varying disturbances. The value of an appropriately selected quadratic performance functional is then explicitly calculated by solving an actuator location‐parameterized family of Lyapunov matrix equations, and subsequently optimized with respect to the set of admissible actuator locations. Finally, in order to illustrate the proposed method a typical nonlinear transport process modelled through Burgers' equation is considered, and its performance is evaluated through simulation studies. Copyright © 2004 John Wiley & Sons, Ltd.