Robust finite-time control design and disturbance compensation for underactuated systems with experimental validation

Cranes are vital mechanical transportation systems that play a crucial role in large-scale infrastructure development projects. However, their underactuated nature poses significant challenges in achieving precise and efficient motion control, especially in the presence of external disturbances. To tackle these challenges, this paper presents a robust finite-time control framework designed for a wide range of underactuated systems. The proposed framework begins by addressing the general problem of model transformation for underactuated dynamics, enabling a unified and systematic approach to control design. This transformation allows for the development of control strategies adaptable to various types of underactuated systems. To effectively counteract the effects of unknown external disturbances, a generalized disturbance observer is constructed. The finite-time convergence of this observer is rigorously analyzed and proven, ensuring accurate disturbance estimation within a finite time. Building on this observer, a finite-time control scheme is developed, which guarantees the global convergence of all system states, including the sliding mode surface, within a finite time horizon. The theoretical foundations of the proposed approach are supported by experimental validation conducted on a tower crane platform. The experimental evaluation includes scenarios with significant external disturbances to test the robustness and reliability of the control strategy. The results demonstrate that the proposed controller achieves rapid convergence, high accuracy, and robust performance, even under challenging operational conditions.