Composite nonlinear disturbance observer-based practical prescribed time control for nonlinear systems with matched and mismatched disturbances

This paper addresses the practical prescribed-time control (PPTC) problem for nonlinear strict-feedback systems subject to matched and mismatched disturbances. A composite nonlinear disturbance observer-based PPTC scheme is proposed to ensure the prescribed transient and steady-state performances within a prescribed time. First, a novel error transformation mechanism is developed based on a prescribed-time constraining function incorporating a nonlinear distance measure to the constraint boundary and the tanh⁡(⋅) function. This mechanism transforms the prescribed-time tracking problem into a bounded constraint problem for the error variables. Then, considering the presence of matched and mismatched disturbances, a composite nonlinear disturbance observer (CNDO) is designed based on the transformed error, enabling fast disturbance estimation and improved control performance. Furthermore, to avoid “explosion of complexity”, a nonlinear filter is designed based on the transformed filtering error. Building upon the estimates obtained by the CNDOs, a practical prescribed-time tracking controller is designed by employing the backstepping method and the nonlinear filter. This controller not only ensures that the system output satisfies the constraints but also reduces control cost. Finally, theoretical analysis, along with simulations and experimental results conducted on a turntable servo system, verifies that all system state tracking errors and filtering errors converge to prescribed regions within the prescribed time.