Centralized Optimal Controller Design

Abstract

In this chapter, two centralized optimal control methods, namely, optimal fixed structure controllers (where PID controllers represent a special case) and H _∞ controllers, are proposed. Given that the control algorithms for an AO system are typically implemented in a computer system, the optimal controller design methods presented in this chapter are formulated directly in the discrete-time domain. In Section 8.1, a new multivariable PID controller design approach is proposed for discrete-time systems, where the optimal controller synthesis procedures are based on directly solving properly formulated LMIs. The experimental results show the effectiveness of the designed PID controller for the magnetic fluid deformable mirror (MFDM). The mixed-sensitivity H _∞ design approach is presented in Sect. 8.2 as the second centralized control method for MFDM-based AO systems. The controller developed using the mixed-sensitivity H _∞ design approach not only provides the desired performance in tracking the reference wavefront surface shapes using an MFDM but also limits the current inputs to the MFDM actuators and increases the robustness of resulting closed-loop system. Experimental results show that the MFDM in the closed-loop AO system can track both static and dynamic reference signals effectively. A summary of this chapter is presented in Sect. 8.3.