Nonlinear Adaptive PID Control for Nonlinear Systems

This article introduces a nonlinear adaptive proportional-integral-derivative (PID) tracking control methodology suitable for a class of multi-in-multi-out nonlinear systems. By incorporating three nonlinear modulating (trimming) functions to “recalibrate” the generalized tracking error, a nonlinear PID control framework is constructed that possesses several notable features. First, the user-assignable parameters in the modulating functions allow the resultant control strategy to analytically bridge fixed gain linear PID control with nonlinear PID control, covering both traditional fixed-gain and time-varying gain PID control as special cases. Second, the inherently nonlinear nature of the proposed control methodology effectively counteracts system nonlinearities, thereby enhancing the overall performance of the control scheme. Third, unlike conventional PID control that often involves integration saturation, the proposed control method obliterates such “windup” phenomenon by utilizing the integral trimming function that remains bounded or self-vanishes. Fourth, eliminating the necessity for a “trial-and-error” process for PID gain determination, the proposed control not only ensures asymptotic tracking but also guarantees a bounded comprehensive performance index in the presence of modeling uncertainties and external disturbances. The effectiveness and benefits of the proposed method are also confirmed by numerical simulations.