Adjustable predefined time sliding mode control method for nonlinear systems with unknown disturbances

This research focuses on a tunable predefined time adaptive sliding mode control (SMC) for a nonlinear system with disturbances. Firstly, a new sufficient condition with a compact adjustable parameter for tunable predefined time stability (PTS) has been proposed, and its effectiveness has been proven. This condition complies with the basic definition rules of tunable PTS. When the system is stabilized within a predefined time, the actual convergence time (CT) of the system can be adjusted by the introduced single adjustable parameter. On the basis of the proposed lemma, a lemma of practical PTS is further proposed. Its main contribution is that when combining the algorithm of PTS with other intelligent algorithms, the use of this lemma helps to prove the stability. Secondly, this paper combines the algorithms of tunable PTS with the adaptive SMC. This combination not only solves the problem of unknown external disturbances but also can dynamically adjust the actual convergence time while ensuring the effectiveness of PTS. Furthermore, simulation experiments and physical experiments were carried out for verification. The simulation results show that, compared with the methods in some references, the proposed method improves the convergence speed by about 54% and significantly reduces chattering. The comparative experiments highlight its effectiveness. The results of the physical experiments also demonstrate the practicality of the proposed method in engineering.