Continuous predefined-time sliding mode control for second-order nonlinear systems under full-channel disturbances

This paper presents a continuous predefined-time sliding mode control (CPTSMC) strategy for second-order nonlinear systems subject to full-channel disturbances. A predefined-time extended state observer (PTESO) is derived to estimate both the unknown system states and disturbances, with the upper bound for the settling time (UBST) precisely defined by one design parameter in a less conservative manner than those of finite-time or fixed-time ESOs. Furthermore, the peak observation errors are small during the transient process. Then, using the estimates, a CPTSMC law is designed for the chattering-alleviated predefined-time convergence of system states. The internal mechanism of parameter tuning for improving transient performance is theoretically explored. In addition to proving that the UBST of the whole system is precisely defined by one design parameter, we show the continuity of CPTSMC and the boundedness of all system signals that are vital for practical applications. Ultimately, the proposed approach is applied to a DC servo motor to demonstrate its efficiency.