Adaptive robust control for gear transmission systems with backlash: An underactuated dynamics perspective

Abstract

The precision motion control of gear transmission systems is critically challenged by inherent backlash nonlinearity, significant parameter uncertainties such as time-varying mesh stiffness, and the underactuated dynamics that arise when the actuator instantaneously loses control authority within the backlash gap. To fundamentally address the control authority loss issue, this study innovatively models the gear transmission system as a two-degree-of-freedom underactuated mechanical system, providing a novel dynamic perspective for controller design. Based on this underactuated framework, we propose a novel adaptive robust control strategy. The core innovation lies in the controller’s unique three-term structure, which effectively integrates robust feedback with a dynamic adaptive law. This design enables simultaneous and effective compensation for both the complex underactuated dynamics and critical parameter uncertainties like time-varying mesh stiffness, thereby relaxing the requirement for precise parameter knowledge. Rigorous stability analysis using the Lyapunov method proves that the closed-loop system’s tracking error is guaranteed to be Uniform and Ultimately Bounded. Compared to conventional methods, the adaptive approach facilitates a smooth control response, successfully suppressing excessive overshoots and high-frequency chattering. Simulations verify the superiority and high robustness of the proposed controller, demonstrating excellent tracking accuracy.