Data-driven anti-windup adaptive PID control without persistent excitation

This study presents a data-driven anti-windup adaptive proportional-integral-derivative (PID) control scheme for uncertain nonlinear systems. Within a reinforcement learning framework, PID gains are optimized by minimizing a composite cost function that penalizes tracking error, control effort, and output fluctuation, eliminating the requirement for a precise plant model. By leveraging concurrent learning, historically excited data stored in a history stack together with current samples are simultaneously exploited to estimate the Q-function through a normalized gradient algorithm, effectively relaxing the persistent excitation requirement. Notably, a novel history stack update rule based on spatiotemporal distance measures is developed to enhance data informativeness and adaptation. The PID gains are then synthesized from the converged kernel matrix of the Q-function, which ensures the convergence of the resulting parameters. In parallel, to address integrator windup, an anti-windup mechanism is incorporated to dynamically regulate integral accumulation, thereby reducing saturation duration and enhancing transient performance. Theoretical analysis establishes the stability and convergence of the scheme. The effectiveness and superiority of the proposed method are validated through comparative simulations and industrial experiments for suspension density control in the dense medium coal preparation process.