Design and analysis of ELM-based predefined time sliding mode adaptive controller for PMLM position control under physical constraints

Achieving accurate position tracking for robotics and industrial servo systems is an extremely challenging task, particularly when dealing with control saturation, parameter perturbation, and external disturbance. To address these challenges, a predefined time convergent sliding mode adaptive controller (PTCSMAC) has been proposed for a permanent magnet linear motor (PMLM). A novel sliding mode surface (SMS) with predefined time convergence PDTC has been constructed, which ensures that the error converges to zero within the prescribed time. The system not only meets the expected performance standards but also has a uniformly bounded motor speed. The trajectory tracking error in SMS is proven to converge to zero within the predefined time. This predefined time stability of the closed-loop system has been demonstrated by using the Lyapunov stability criterion with PDTC. The convergence time (CT) can be arbitrarily set, and the upper bound of it is not affected by the initial value and control parameters of the system. A new updated version of extreme learning machine (ELM) is introduced to approximate the uncertain part of the system based on PDTC. The ELM is also provided with the hyperbolic tangent function to estimate the saturation constraint. This is done by converting the function into a linear function concerning the unconstrained control input variable. Then, based on established stability, a novel sliding mode adaptive controller (PTCSMAC) with predefined time convergence is designed. The convergence time (CT) of the controller is unaffected by the initial conditions as well as the control parameters. The rigorous numerical simulations on the PMLM model with complex disturbances verify the strong robustness and high-precision tracking characteristic of the proposed control law.