Optimal design of H2/H∞ based robust PID controller by constrained extremal optimization and differential evolution

How to design an optimal mixed H ₂ /H _∞ robust FID controller for a complex control system is of great practical importance, but it is still an open issue. From the perspective of evolutionary algorithm, this paper formulates this issue firstly as a typical constrained optimization problem by minimizing a weighted objective function consisting of the robust stability performance, disturbance attenuation performance and tracking error, and then presents a novel a novel optimal design method of mixed H ₂ /H _∞ robust FID controllers based on a constrained evolutionary algorithm called CEO-DE by combining constrained extremal optimization and differential evolution. The simulation results on two typical multi-variable control systems have demonstrated the proposed CEO-DE based design method performs better than some reported popular methods such as intelligent genetic algorithm and multi-objective particle swarm optimization.