Decentralized PID Controller Design

Abstract

In this chapter, a decentralized PID control structure is proposed for a magnetic fluid deformable mirror (MFDM)-based AO system. Two decentralized PID control algorithms that can be used to control the surface shape of continuous surface mirrors, including MFDMs, are presented. First, the development of a decoupled plant model, to be used in the controller design, is presented in Sect. 7.1. In Sect. 7.2, a decentralized proportional-plus-integral (PI) controller is presented, which is designed based on the assumption that the plant model is fully decoupled and the wavefront corrector (WFC) dynamics are omitted. To overcome stability robustness issues and improve the control performance, a decentralized robust proportional-integral-derivative (PID) controller is presented in Sect. 7.3, where the uncertainties in the decoupled nominal dynamic model of the plant are considered. The robust PID controller design problem is transformed into a mixed ${H_2}/{H_\infty }$ multi-objective optimization problem. The control performance of the two control algorithms is verified in the AO setup in Sect. 7.4, followed by the summary in Sect. 7.5.