Study of the Fuzzy PID controller using fuzzy and crisp inputs and varying Compositional Rule of Inference parameters

A Fuzzy Proportional-Integral-Derivative controller (FPID) is a control mechanism used to regulate the behavior of a system. Like any fuzzy controller, its inference process is based on the Compositional Rule of Inference (CRI), which has two parameters: a t-norm [Formula: see text] and a fuzzy implication [Formula: see text]. Since the introduction of FPID controllers, only one combination of [Formula: see text] has been adopted, which is (min, min). Moreover, these systems always take crisp inputs. In previous works, we studied many combinations of t-norms and implications theoretically, based on a set of criteria. This paper investigates the practical impact of varying the t-norm and the implication operator in the inference mechanism of a FPID controller. Furthermore, it examines the influence of using fuzzy inputs instead of crisp ones. The behavior of the FPID controller is evaluated in terms of convergence time and overshoot. We then show and analyze the control results and compare them with the theoretical results. The experiments demonstrate that the use of other parameters significantly improves the FPID controller results, leading to better performance and lower energy consumption.