Optimal Tuning of FOPID-Like Fuzzy Controller for High-Performance Fractional-Order Systems

This paper addresses improvements in fractional order (FO) system performance. Although the classical proportional–integral–derivative (PID)-like fuzzy controller can provide adequate results for both transient and steady-state responses in both linear and nonlinear systems, the FOPID fuzzy controller has been proven to provide better results. This high performance was obtained thanks to the combinative benefits of FO and fuzzy-logic techniques. This paper describes how the optimal gains and FO parameters of the FOPID controller were obtained by the use of a modern optimizer, social spider optimization, in order to improve the response of fractional dynamical systems. This group of systems had usually produced multimodal error surfaces/functions that occasionally had many variant local minima. The integral time of absolute error (ITAE) used in this study was the error function. The results showed that the strategy adopted produced superior performance regarding the lowest ITAE value. It reached a value of 88.22 while the best value obtained in previous work was 98.87. A further comparison between the current work and previous studies concerning transient-analysis factors of the model’s response showed that the strategy proposed was the only one that was able to produce fast rise time, low-percentage overshoot, and very small steady-state error. However, the other strategies were good for one factor, but not for the others.