A New Approach to Design of Optimal Fractional Order Fuzzy PID Controller with Simultaneously Auto-tuned Membership Functions and Fuzzy Rules

In this paper, a new approach is proposed to design the fractional order fuzzy PID controllers. In the proposed method, all of the fractional order fuzzy PID controller parameters including input scaling factors, output scaling factors, fractional order of derivative and integrator, fuzzy rule base and membership functions are considered as design parameters and optimized simultaneously. Also, to reduce the length of solution vector, reduce computational complexity and increase the speed of finding solution, a new method for coding the design parameters is developed. The simultaneous optimization of parameters is done by using the particle swarm optimization algorithm and considering an objective function based on minimizing the error between the desired and actual output of system. One of the advantages of this method is ability to solve the problem of optimization time for complex systems. To evaluate the proposed method, the designed fractional order fuzzy PID controller is applied to a nonlinear inverted pendulum system and some numerical results are presented. Also its performance is compared with other two controllers namely fractional order fuzzy PID with fixed FLC and fractional order PID. Results indicate the superiority of proposed method.