PI-Based Adaptive Actor–Critic Displacement Volume Control of Axial-Piston Pump

This article presents the synthesis, implementation, and experimental study of a PI-based adaptive actor–critic displacement volume controller of an axial-piston pump intended for open-loop circuit hydraulic drive systems. The proposed control structure combines a conventional PI actor with an adaptive critic that estimates the infinite-horizon cost through Bellman-error minimization. By using the tracking error and its integral as actor inputs, the controller avoids the need for an accurate plant model while retaining a compact and practically implementable structure. The adaptive laws are derived using gradient-based learning, and a Lyapunov-based analysis establishes closed-loop stability for sufficiently small adaptation gains. The controller is implemented in a fixed-step Simulink® environment and deployed on a rapid prototyping platform with real-time communication to an industrial microcontroller and proportional valve amplifier. The experimental results obtained under four fixed loading conditions and dynamic load variations demonstrate a stable operation, bounded critic behavior, and a near-zero Bellman error during learning. Comparative tests against a classical PI controller, a Lyapunov-based model reference adaptive controller, and a generic actor–critic scheme show that the proposed PI-based actor–critic achieves the lowest performance index and the shortest settling times in most cases.