Design and Analysis of an Adaptive PID Controller for a Class of Nonlinear Systems
摘要
This paper presents the development of an adaptive Proportional-Integral-Derivative (PID) controller designed for a class of nonlinear systems with dynamic uncertainties. Traditional PID controllers are widely used due to their simplicity, but their performance in nonlinear and time-varying environments is often limited. To address this challenge, we propose an adaptive PID control framework that dynamically adjusts the controller parameters based on real-time system feedback, allowing for improved robustness and stability across varying operating conditions. The adaptation mechanism is derived using Lyapunov stability theory, ensuring global stability and convergence of the closed-loop system. The proposed controller is tested on a variety of nonlinear models, including systems with high nonlinearity and unmodeled dynamics. Simulation results demonstrate that the adaptive PID controller outperforms conventional PID methods, achieving faster settling times, reduced steady-state errors, and enhanced disturbance rejection capabilities. The design methodology, stability analysis, and practical implications are discussed in detail, providing insights into the controller’s potential for real-world applications.