Robust Trajectory Control of Underactuated Ball and Plate System Using Continuous Full-Order Sliding Mode Controller

The stabilization performance of an underactuated ball and plate system (BPS) is significantly degraded by nonlinear dynamics, parameter variations, and external disturbances. This manuscript proposes a robust full-order continuous sliding mode control (FOCSMC) technique to achieve high stabilization performance and enhance the disturbance rejection capability of the BPS. First, the nonlinear dynamics of the BPS are formulated in a full-order state–space form that incorporates the dynamics of both the underactuated ball and the actuated servo motor. Second, two state differentiators (SDs) are introduced to reconstruct the unavailable state variables required for controller implementation. By avoiding direct high-order differentiation of measured signals, the proposed differentiators reduce noise sensitivity and improve practical realizability. Based on the estimated states, a continuous full-order sliding manifold is constructed to guarantee asymptotic convergence of the closed-loop system states while reducing the chattering phenomenon inherently associated with conventional sliding mode control (SMC) schemes. A Lyapunov-based stability analysis is performed to establish asymptotic convergence. Finally, comparative simulation and experimental studies under nominal conditions, parameter variations, external disturbances, and two-dimensional circular trajectory tracking demonstrate that the proposed FOCSMC consistently outperforms the hierarchical SMC (HSMC) and the continuous SMC (CSMC) schemes. In particular, the root mean square (RMS) and the maximum (MAX) of the tracking error are, respectively, 0.5653 cm and 1.9461 cm, which are experimentally achieved under the impact of the disturbances, confirming the effectiveness and practical applicability of the proposed scheme.