Genetic-based robust optimal design for one-input fuzzy PID controllers

This paper explores an optimal robust design problem for a feedback system with the one-input fuzzy PID controllers and to simplify the design problem. We tend to achieve the robust stability and performance of one-input fuzzy PID control systems. Robustness is addressed in terms of stability margin and rnultiplicative perturbations. The design method is proposed in the framework of an optimal solver with stability constraint using conicity conditions for `worst point' of the perturbed plant. The stability of the fuzzy system is treated using conicity criteria derived from small gain theorem but with less conservative. A simple genetic algorithm (SGA) approach is used as an optimal solver. We evaluate the one-input fuzzy PID controllers with the inverted pendulum tracking. Two one-input fuzzy PID controllers are designed. In numerical simulations, the results show that the fuzzy PID obtained from the proposed method can achieve robust performance for the perturbed plant, while the fuzzy PID only considers the performance without stability constraint will cause system unstable when parameters of plant perturbed in certain ranges.