Magnetic fluid deformable mirror shape control with a multivariable PID controller

In this paper, the shape control problem for a magnetic fluid deformable mirror using a discrete-time multivariable PID controller is studied. First, the design of a stabilizing multivariable PID controller for discrete-time systems subject to a pole clustering constraint is proposed based on properly formulated linear matrix inequalities. The design approach is then extended to include an H₂ performance constraint. The proposed design method is applied for the shape control of a magnetic fluid deformable mirror and the controller performance is experimentally evaluated in an adaptive optics system. The experimental results indicate the proposed controller can successfully provide the desired shape tracking performance in the closed loop adaptive optics system.