On a robust PID controller parameters optimization applied to a mass-spring system

H_infin synthesis is often used to realize robust and high performance controllers. This synthesis allows to have full order H_infin controller. The ability to formulate it as a convex optimization problem makes it relatively easy to solve using semi-definite programming techniques. The H_infin controller order is often much higher than that of the plant model. However, implementing such controllers for high order systems is a rather complex task. Hence, the reduced order H_infin controller synthesis is becoming of great interest for practical applications. Contrary to the full-order H_infin controller synthesis case, the H_infin optimization problem of static output feedback controllers cannot be reparameterized as a convex optimization problem. The cone complementarity linearization algorithm is used to overcome the nonconvexity problem due to the constraint on the controller order. The proposed algorithm is applied to the tuning of SISO (single-input single-output) PID (proportional plus integral plus derivative) controller parameters for the control of a mass-spring system.