LMI-Based Decentralized PID Controller Design With Application to the Shape Control of Magnetic Fluid Deformable Mirrors

In this paper, a decentralized robust PID controller design method is proposed for multi-input multi-output systems. The system model is first decoupled in the low frequency range, and only the diagonal entries in the DC-decoupled plant model are retained. To deal with the resulting unmodeled high frequency dynamics, a decentralized robust PID controller design method is proposed, where the robust stability and transient response performance of the resulting closed loop system are formulated as a multi-objective H_∞/H₂ static output feedback problem. The desired parameters of the PID controller are determined by solving a static output feedback problem using linear matrix inequalities (LMIs). Finally, the performance of the proposed control algorithm is experimentally evaluated on the adaptive optics system involving a prototype magnetic fluid deformable mirror (MFDM). The experimental results illustrate the effectiveness of the proposed control algorithm for the MFDM surface shape tracking in the closed loop adaptive optics system.