A Novel Compensated PID Controller Ensuring Lyapunov Stability for Highly Uncertain, Nonaffine, and Time-Varying Nonlinear Systems

This paper proposes a novel compensated PID controller for a class of strongly uncertain, time-varying nonlinear systems with nonaffine control input structures. The main objective is to ensure Lyapunov stability of the closed-loop system, which consists of a classical PID controller augmented with a compensating term and an unknown nonlinear plant subject to significant unstructured uncertainties. The proposed method integrates a conventional PID control structure with an additional compensating control signal designed to mitigate the effects of unknown nonlinearities. To address the challenge of unmeasurable derivative signals, a higher-order serial differentiator with asymptotic convergence properties is utilized to estimate the time derivatives of the output tracking error. A systematic approach for selecting PID gain parameters is presented to ensure system stability. Numerical simulations are conducted to verify the effectiveness and robustness of the proposed controller, demonstrating its practical applicability.