Design of Simplified Fractional-order PID Controller Based on Improved Oustaloup Filter

The direct and indirect approximation methods for fractional calculus operators have complicated forms and a large amount of computation. A simplified fractional differential operator approximation method based on improved Oustaloup filter is proposed. A simplified fractional-order PID controller is designed, and the parameters of the controller are tuned by an adaptive genetic algorithm. Two representative fractional-order systems are selected, under the nominal and perturbation states of the model, and the simulation performances of the simplified fractional-order PID controller, conventional fractional-order PID controller, and integer-order PID controller are compared. The results show that the designed simplified fractional-order PID controller can achieve a control performance close to that of the conventional fractional-order PID controller, and it has the advantages of a simple structure, less time consumption, and improved project feasibility.