A tuning strategy for multivariable PI and PID controllers using differential evolution combined with chaotic Zaslavskii map

A technique for tuning of decoupled proportional-integral (PI) and proportional-integral-derivative (PID) multivariable controllers based on a chaotic differential evolution (DE) approach is presented in this paper. Due to the simple concept, easy implementation and quick convergence, nowadays DE has gained much attention and wide application in solving continuous non-linear optimization problems. However, the performance of DE greatly depends on its control parameters and it often suffers from being trapped in local optimum. The application of chaotic sequences based on chaotic Zaslavskii map instead of random sequences in DE is a powerful strategy to diversify the population and improve the DE’s performance in preventing premature convergence to local optima. The optimized PD and PID controllers shows good closed-loop responses in control of the binary Wood–Berry distillation column, a multivariable process with strong interactions between input and output pairs. Some comparison results of PD and PID tuning using chaotic DE, classical DE and genetic algorithm are presented and discussed.

► More than 90% of all control loops are PID, with a wide range of applications.
► Classical DE algorithms use a floating-point encoding EA for global optimization over continuous spaces.
► Although many PI and PID controllers have been proposed for decades of years, it is still widely applied in industrial applications.