Binary-coded extremal optimization for the design of PID controllers

Design of an effective and efficient PID controller to obtain high-quality performances such as high stability and satisfied transient response is of great theoretical and practical significance. This paper presents a novel design method for PID controllers based on the binary-coded extremal optimization algorithm (BCEO). The basic idea behind the proposed method is encoding the PID parameters into a binary string, evaluating the control performance by a more reasonable index than the integral of absolute error (IAE) and the integral of time weighted absolute error (ITAE), updating the solution by the selection based on power-law probability distribution and binary mutation for the selected bad elements. The experimental results on some benchmark instances have shown that the proposed BCEO-based PID design method is simpler, more efficient and effective than the existing popular evolutionary algorithms, such as the adaptive genetic algorithm (AGA), the self-organizing genetic algorithm (SOGA) and probability based binary particle swarm optimization (PBPSO) for single-variable plants. Moreover, the superiority of the BCEO method to AGA and PBPSO is demonstrated by the experimental results on the multivariable benchmark plant.