Optimal Design and Simulation for PID Controller Using Fractional-Order Fish Migration Optimization Algorithm

Proportional Integral Derivative (PID) controller is one of the most classical controllers, which has a good performance in industrial applications. The traditional PID parameter tuning relies on experience, however, the intelligent algorithm is used to optimize the controller, which makes it more convenient. Fish Migration Optimization (FMO) is an excellent algorithm that mimics the swim and migration behaviors of fish biology. Especially, the formulas for optimization were obtained from biologists. However, the optimization effect of FMO for PID control is not prominent, since it is easy to skip the optimal solution with integer-order velocity. In order to improve the optimization performance of FMO, Fractional-Order Fish Migration Optimization (FOFMO) is proposed based on fractional calculus (FC) theory. In FOFMO, the velocity and position are updated in fractional-order forms. In addition, the fishes should migration back to a position which is more conducive to survival. Therefore, a new strategy based on the global best solution to generate new positions of offsprings is proposed. The experiments are performed on benchmark functions and PID controller. The results show that FOFMO is superior to the original FMO, and the PID controller tuned by FOFMO is more robust and has better performance than other contrast algorithms.