Optimal Design of a Fractional-Order Proportional-Integer-Differential Controller for a Pneumatic Position Servo System

In this paper, a fractional-order model of pneumatic servo system is introduced by replacing the integer-order dynamic equation with the corresponding fractional order one. Then, a fractional-order proportional-integer-differential (FPID) controller is optimized for the servo system using an online multivariable multiobjective genetic algorithm (MMGA). The proposed MMGA searches in five-dimensional parameter space based on Pareto rank to balance multiobjectives. In order to provide a basis for comparison, the parameters of a integer order proportional-integer-differential (IPID) controller are also optimized using the same method. The performance indices defined for comparison are the steady-state tracking accuracy and the control energy consumption. Additionally, seven other methods from the literature are compared. The experimental results obtained show that the optimized FPID controller results in a better performance than the optimized IPID controller and the other existing approaches.