Sliding mode control for underactuated overhead cranes suffering from both matched and unmatched disturbances

Overhead cranes, which are known as typical underactuated systems, are extensively studied in recent years. However, many existing methods for overhead cranes are developed based on a relatively ideal model, with little consideration for persistent external disturbances, unmodeled dynamics, uncertain system parameters and so on. Thus, their performance may badly degrade when it comes to practical applications, and this problem is made even worse when the system suffers from unmatched disturbances. To tackle this issue, a sliding mode control (SMC) method is proposed in this paper, which ensures satisfactory control performance even when the crane works under unfavorable conditions. The asymptotic stability of the desired equilibrium point is backed up with rigorous Lyapunov-based analysis. Furthermore, to alleviate the chattering problem inherent to SMC, a disturbance observer is further designed for overhead cranes to estimate and then eliminate the influence of the disturbances. Both simulation and hardware experimental results are provided to validate the efficiency and robustness of the proposed control strategy. To the best of our knowledge, this paper proposes the first method that can solve the control problem of overhead cranes suffering from both matched and unmatched disturbances, without tuning to linearizations or approximations.