Error-Aware Nonlinear Gain-Based PID Tracking Control: A Constructive and Self-Tuning Approach

Abstract

Conventional proportional–integral–derivative (PID) controllers face fundamental limitations in handling unknown nonlinearities and coupling effects, often requiring manual tuning or complex adaptation mechanisms. This article introduces a novel nonlinear PID tracking control architecture while incorporating three innovative features: first, analytically constructed error-aware gains with self-tuning capability, utilizing current, past, and predicted error information; second, inherent antiwindup properties through nonlinear integral design; and third, fully autonomous operation without the need for precise a priori knowledge of system dynamics or manual intervention. Unlike prior works mainly restricted to single-input-single-output systems and only achieving uniformly ultimately bounded stability, our approach handles higher order multiple-input–multiple-output systems with unknown coupled dynamics, achieving asymptotic tracking. The controller maintains structural PID simplicity while providing enhanced nonlinear compensation and robust adaptive performance. Comprehensive Lyapunov analysis rigorously validates stability for general normal form nonlinear systems, with superior performance in both regulation and time-varying reference tracking scenarios.