Design of an H∞-optimal FOPID controller using particle swarm optimization

This paper proposes a novel method to design an H
_∞
-optimal fractional order PID (FOPID) controller with ability to control the transient, steady-state response and stability margins characteristics. The method uses particle swarm optimization algorithm and operates based on minimizing a general cost function. Minimization of the cost function is carried out subject to the H
_∞
-norm; this norm is also included in the cost function to achieve its lower value. The method is applied to a phase-locked-loop motor speed system and an electromagnetic suspension system as two examples to illustrate the design procedure and verify performance of the proposed controller. The results show that the proposed method is capable of improving system responses as compared to the conventional H
_∞
-optimal controller while still maintains the H
_∞
-optimality of the solutions.