Multi-objective optimization of PID controller parameters using genetic algorithm

Abstract

Proportional-Integral-Derivative (PID) controller is one of the most popular controllers applied in industries. However, despite the simplicity in its structure, the PID parameter tuning for high-order, unstable and complex plants is difficult. When dealing with such plants, empirical tuning methods become ineffective while analytical approaches require tedious mathematical works. As a result, the control community shifts its attention to stochastic optimisation techniques that require less interaction from the controller designers. Although these approaches manage to optimise the PID parameters, the combination of multiple objectives in one single objective function is not straightforward. This work presents the development of a multi-objective genetic algorithm to optimise the PID controller parameters for a complex and unstable system. A new genetic algorithm, called the Global Criterion Genetic Algorithm (GCGA) has been proposed in this work and is compared with the state-of-the-art Non-dominated Sorting Genetic Algorithm (NSGA-II) in several standard test problems. The results show the GCGA has convergence property with an average of 35.57% in all problems better than NSGA-II. The proposed algorithm has been applied and implemented on a rotary inverted pendulum, which is a nonlinear and under-actuated plant, suitable for representing a complex and unstable high-order system, to test its effectiveness. The set of pareto solutions for PID parameters generated by the GCGA has good control performances (settling time, overshoot and integrated time absolute errors) with closed-loop stable property.