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Abstract
In this paper, a new design method for sliding mode control (SMC) is presented for nonlinear underactuated mechanical systems. The aim is to eliminate the reaching phase in SMC and avoid the chattering phenomenon while achieving fast and robust tracking for a class of underactuated mechanical systems (UMS). An alternative method is presented to express the sliding domain equations by incorporating tracking errors. The fundamental concept behind the suggested control scheme is to adjust the tracking errors, enabling the system response to commence on the sliding surface regardless of the initial conditions. This modification guarantees the elimination of the reaching phase, avoiding the chattering phenomenon, and ensuring that the tracking error converges to zero. The stability analysis of the proposed approach is conducted using the Lyapunov method. Through numerical simulations, the validity of the approach is confirmed by implementing the control scheme on a crane system. Subsequently, the performance of the proposed approach is compared with other control methods, emphasizing its effectiveness in handling uncertainties. This comparative analysis aims to emphasize the advantages and efficiency of the proposed control strategy over alternative methods, in particular, to address uncertainties and achieve the desired control objectives.
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