Design of multivariable PID controllers using real-coded population-based extremal optimization

Abstract The issue of designing and tuning an effective and efficient multivariable PID controller for a multivariable control system to obtain high-quality performance is of great theoretical importance and practical significance. As a novel evolutionary algorithm inspired from statistical physics and co-evolution, extremal optimization (EO) has successfully applied to a variety of optimization problems while the applications of EO into the design of multivariable PID and PI controllers are relatively rare. This paper presents a novel real-coded population-based EO (RPEO) method for the design of multivariable PID and PI controllers. The basic idea behind RPEO is based on population-based iterated optimization process consisting of the following key operations including generation of a real-coded random initial population by encoding the parameters of a multivariable PID or PI controller into a set of real values, evaluation of the individual fitness by using a novel and reasonable control performance index, generation of new population based on multi-non-uniform mutation and updating the population by accepting the new population unconditionally. From the perspectives of simplicity and accuracy, the proposed RPEO algorithm is demonstrated to outperform other reported popular evolutionary algorithms, such as real-coded genetic algorithm (RGA) with multi-crossover or simulated binary crossover, differential evolution (DE), modified particle swarm optimization (MPSO), probability based discrete binary PSO (PBPSO), and covariance matrix adaptation evolution strategy (CMAES) by the experimental results on the benchmark multivariable binary distillation column plant.