Sliding mode control with prescribed performance for a class of mechanical systems subject to uncertainties and disturbances

This paper proposes a predefined-time tracking control methodology for a class of nonlinear mechanical servo systems operating in the presence of the external disturbances and system uncertainties. The process begins with the creation of a nonlinear disturbance observer aimed at accurately estimating the lumped disturbance. This observer is designed to ensure that the error in estimation converges towards zero in a time specified by the user. Following this, a new predefined-time sliding-mode surface is presented, which guarantees that the closed-loop system adheres to predefined-time performance while avoiding potential singularities. Leveraging this manifold, a continuous control law is formulated to impose a predefined-time constraint upon the sliding dynamics, guiding the system states into a designated vicinity of the sliding surface within a specified finite duration. This approach eliminates the need for discontinuous switching components, effectively reducing the chattering phenomenon. A rigorous theoretical framework confirms that the proposed control strategy achieves global predefined-time stability. Lastly, extensive numerical simulations validate the effectiveness and enhanced performance of the proposed strategy.