Recursive Higher Order Non-Singular Terminal Sliding Mode Control With Prescribed Convergence Time: Application to PMSM Servo Systems

In this study, we investigate the prescribed-time non-singular terminal sliding mode control (TSMC) for high-order nonlinear systems. Initially, a novel time-varying, high-order terminal sliding mode manifold is recursively constructed. Based on this newly proposed manifold, a prescribed-time non-singular TSM controller is subsequently developed. The proposed algorithm effectively eliminates the singularity problem and offers a simpler method for specifying the convergence time, independent of initial system conditions and other design parameters. To mitigate the chattering issue of the controller, we introduce a variable-gain prescribed-time disturbance observer. Leveraging this observer, we develop a prescribed-time non-singular TSMC strategy. A rigorous Lyapunov analysis demonstrates the prescribed-time stability of both the proposed observer and controller. The uniform boundedness of the state signals and control input is also established using an inductive method. Finally, experimental validation is provided, confirming the effectiveness of the proposed control algorithm. Note to Practitioners—This work addresses practical challenges in controlling high-order nonlinear systems, such as motor servo systems, robotic manipulators, and aerospace actuators, where fast convergence and robustness to disturbances are critical. Traditional TSMC often suffers from singularity issues, chattering, and convergence times dependent on initial conditions, complicating their deployment in real-world scenarios. To overcome these problems, this paper proposes a prescribed-time higher order non-singular TSMC, which ensures user-defined convergence time independent of system initial states and parameters. Experimental verification on a PMSM servo system shows that this method is effective in practical scenarios requiring fast and precise convergence.