Multi-objective optimization for PID controller tuning using the global ranking genetic algorithm

Abstract

Tuning of PID controller parameters for an optimized control performance is a multi-objective optimization problem. The problem becomes particularly difficult if the plant to be controlled is an unstable, nonlinear and under actuated plant. This paper proposes a modified genetic algorithm for the multi-objective optimization of PID controller parameters, called the Global Ranking Genetic Algorithm (GRGA). It combines two types of fitness assignment methods in the algorithm - the 'global ranking fitness assignment' method proposed in this paper and the dominance rank from the classical pareto fitness assignment method. The former is employed in the selection of parents and the latter is used in the elitism mechanism. In order to investigate the performance of the proposed algorithm, it is compared with the state of the art, Non-dominated Sorting Genetic Algorithm 2 (NSGA-II) using five ZDT series test functions. From the test problems analysis, the GRGA is observed to have better convergence property than the NSGA-II although it tends to lose its diversity of solutions in the earlier part of generation before recovering back when approaching the true pareto front. Then, the GRGA is applied to a highly difficult PID controller tuning problem, balancing a rotary inverted pendulum system. Results show that the GRGA has the capability to optimally tune the PID controllers based on the nonlinear model of the pendulum.