A real-coded extremal optimization method with multi-non-uniform mutation for the design of fractional order PID controllers

Design of an effective and efficient fractional order PID (FOPID) controller for an industrial control system to obtain high-quality performances is of great theoretical and practical significance. This paper presents a novel real-coded extremal optimization algorithm with multi-non-uniform mutation called RCEO-FOPID to design FOPID controllers. The key idea behind the proposed algorithm is the population-based iterated optimization, which consists of generation of a real-coded random initial population by encoding the parameters of a FOPID controller into a set of real values, evaluation of the individual fitness by using a novel and reasonable control performance index, generation of a new population based on multi-non-uniform mutation and updating the population by accepting the new population unconditionally. The proposed RCEO algorithm for the design of FOPID controller is relatively simpler than these reported popular evolutionary algorithms, e.g., genetic algorithm (GA), particle swarm optimization (PSO), chaotic anti swarm (CAS) due to its fewer adjustable parameters and only with selection and mutation operators. Furthermore, extensive simulation results on automatic voltage regulator system and multivariable control system have shown that the proposed RCEO-based FOPID controller is superior to other reported evolutionary algorithms-based FOPID and PID controllers in terms of accuracy and robustness.