Fuzzy PID controller: Design, performance evaluation, and stability analysis

This paper presents a design for a new fuzzy logic proportional-integral-derivative (PID) controller. The main motivation for this design was to control some known nonlinear systems, such as robotic manipulators, which violate the conventional assumption of the linear PID controller. This controller is developed by first describing the discrete-time linear PID control law and then progressively deriving the steps necessary to incorporate a fuzzy logic control mechanism into the modifications of the PID structure. The final version of this new fuzzy PID controller is a computationally efficient analytic scheme suitable for implementation in a real-time closed-loop digital control. Numerous computer simulations are included to demonstrate the effectiveness of the controller for both linear and nonlinear systems. Finally, a brief analysis is presented to prove that the controller has bounded-input/bounded-output (BIBO) stability.