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

This paper explores an optimal robust design problem for a feedback system with one-input fuzzy PID controllers and simplification of the design problem. We tend to achieve robust stability and performance of one-input fuzzy PID control systems. Robustness is addressed in terms of stability margin and multiplicative perturbations. The design method is proposed in the framework of an optimal solver with a stability constraint using conicity conditions for the worst point of the perturbed plant. The stability of the fuzzy system is treated using conicity criteria derived from the small gain theorem but is less conservative. A simple genetic algorithm (SGA) approach is used as an optimal solver. We evaluate the one-input fuzzy PID controllers with 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 performance without stability constraints causing system instability when parameters of the plant are perturbed in certain ranges.