Design of Cross-Coupled Nonlinear PID Controller Using Single-Objective Evolutionary Algorithms

Abstract

The effectiveness of evolutionary algorithms (EAs) such as differential search algorithm (DSA), Real-Coded genetic algorithm with simulated binary crossover (RGA-SBX), particle swarm optimization (PSO), and chaotic gravitational search algorithm (CGSA) on the optimal design of cross-coupled nonlinear PID controllers is compared in this paper. A cross-coupled multivariable PID controller structure for the binary distillation column was developed with two inputs and two outputs. EA simulations are run to lower IAE using two stopping criteria, namely, maximum number of functional evaluations (Fevalmax) and Fevalmax plus PID parameter and IAE tolerance. Over 20 separate trials were used to compare the performances of several EAs using statistical measures such as best, mean, standard deviation of outcomes, and average calculation time. This article presents the design of a cross-coupled nonlinear PID controller using single-objective evolutionary algorithms. Using evolutionary algorithms (EAs) with a multicrossover strategy, the results achieved by various EAs are compared to previously reported results. The results of a multivariable cross-coupled system clearly show that a single-objective nonlinear PID controller performs better. Simulations further show that all four techniques evaluated are suitable for PID controller tweaking off-line. However, only the single-objective evolutionary algorithms are acceptable for online PID tuning due to their higher consistency and shorter computation time.