A New Synthetic Minmax Optimization Design of ${H_{\infty} }$ LQ Tracking Control for Industrial Processes Under Partial Actuator Failure

Abstract

To cope with the control problem of industrial processes with partial actuator failure and disturbance, an improved synthetic minmax optimization design-based ${H_{\infty} }$ linear quadratic (LQ) tracking control strategy is presented in this paper. A new state space model that integrates the dynamics of the process states and the tracking error is first formulated as the basic dynamic process representation. By introducing the new state space model formulation, a new minmax optimization of the ${H_{\infty} }$ norm of the system performance is presented for LQ tracking control design, where more degrees of freedom are offered through the simultaneous adjusting of the tracking dynamics and the state regulation in the cost function, resulting in the enhanced control performance over traditional ${H_{\infty} }$ LQ tracking control. Meanwhile, the nominal closed-loop system stability and robustness under uncertainty are discussed and the monotonicity conditions that are sufficient for both nominal and robust system stability are derived. The case studies on an injection molding process and a nonlinear batch reactor under partial actuator failures and disturbance show the effectiveness of the proposed strategy.