Robust Sliding Mode Control for a Class of Gantry Crane System With Time‐Varying Disturbances

ABSTRACT This paper proposes a sliding mode controller (SMC) to address the control problem of the gantry crane system affected by the time‐varying boundary disturbances. Through the application of Lagrangian‐Hamiltonian mechanics, the gantry crane system is modeled as a set of partial differential equations. Utilizing operator semigroup theory, it demonstrates that a closed‐loop system is well‐posed. By employing Lyapunov functional theory and extended Krasovskii‐LaSalles' invariance principle, the asymptotic stability is confirmed. To demonstrate the effectiveness and comparative advantages of the proposed control method, numerical contrast simulations are conducted. Furthermore, comparative experiments are conducted to validate the designed controller.