Comparison Study of Cardinal Grey Relational Grades on PID Controller Design Using Grey-mean-best Differential Evolution Algorithm

This study firstly attempts to discuss the behavior of different cardinal grey relational grades. The numerical results reveal that similar computation schemes result in the same grey relational rank. In addition, on the basis of cardinal grey relational grades and our previous work, differential evolution with grey-mean-best mutation, this study attempts to apply it to design the optimal PID controller for two single-variable plants. The control performances of differential evolution with grey-mean-best mutation with different cardinal grey relational grades are compared with other evolution algorithms such as genetic algorithm and particle swarm optimization. Simulation results show that all GmBest-based DE variants can generally attain better transient and steady-state performance.