Application of optimal fuzzy PID controller design: PI control for nonlinear induction motor

We present in this paper a novel method (called PID design through numerical optimization) for the design of adaptive fuzzy PID controllers to achieve optimal control performance. By applying the numerical optimization, the fuzzy PID design problem is transferred to a numerical optimization problem. First, a fuzzy parameter tuner is built to generate initial PID parameters, including positions and shapes of fuzzy membership functions and scaling factors. Then the gradient-based Sequential Quadratic programming (SQP) algorithm is employed to iteratively minimize the cost function by iterating the parameters. Unlike conventional PID design, this method is capable of reaching the desired control performance, such as minimum overshoot or long term stability. Another unique feature is that the optimized adaptive PID controller is applicable to a wide variety of time-varying and nonlinear systems. The proposed method is applied to the induction motor control problem and the experimental results are presented to demonstrate its effectiveness and performance.