Nonlinear Adaptive PID Control for Nonlinear Systems

This paper introduces a nonlinear adaptive PID tracking control methodology suitable for a class of MIMO nonlinear systems. By incorporating three nonlinear modulating (trimming) functions to “recalibrate” the generalized tracking error, a nonlinear proportional-integral-derivative (PID) control framework is constructed that possesses several notable features: 1) 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; 2) The inherently nonlinear nature of the proposed control methodology effectively counteracts system nonlinearities, thereby enhancing the overall performance of the control scheme; 3) 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; and 4) 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.