Convex Optimization Approach to Multi-Objective Design of Two-Stage Compensators for Linear Systems

Abstract

The previous design of two-stage compensators of linear systems was focused on the stabilization and low sensitivity. However, it has not considered the time-domain performance of the closed-loop system, especially, reference tracking. This paper aims to propose the design method of the two-stage compensators that additionally achieves good transient response. Applying Q-parameterization to the standard control system can formulate the two-stage compensator design as a convex optimization problem. The infinite dimensional problem is transformed into a finite dimensional problem by Ritz approximation. Finally, the convex optimization is efficiently solved to give the optimal controller. The numerical results show that the proposed design method on the second order benchmark problem and the first order plus time delay system improves the time-domain performance while the closed-loop system is stable and the influence of disturbance to output is attenuated.