Position control of elevator based on non-singular terminal sliding mode

Abstract: When implementing different tasks, the servo systems of elevator must adapt to various working loads with different weight or inertia, which may lead to the remarkable variation of system inertial parameters. Due to uncertain inertial parameters, the traditional proportional-integral-differential (PID )control algorithm has poor robustness and cannot achieve high-accuracy position control. A novel nonlinear control scheme is needed to deal with the problem of uncertain inertial parameters. To realize position control with high accuracy and stability for the elevator with uncertain inertial parameters, a control method based on global non-singular terminal sliding mode was proposed for a single-bucket-chain elevator. By adding a nonlinear term to the conventional linear sliding mode surface, the terminal sliding mode could make the system state converge to the sliding surface in finite time. The global non-singular terminal sliding mode technique was used for elevator system to achieve robust stability and guarantee transient response, and the boundary layer control was adopted to avoid chattering introduced by control switching. The stability of the closed-loop system was guaranteed based on the Lyapunov theory. Firstly, the dynamic model of the single-bucket-chain elevator was set up based on the Lagrange method. Secondly, a controller based on global non-singular terminal sliding mode was designed for a single-bucket-chain elevator. Finally, to illustrate the proposed controller with the global non-singular terminal sliding mode had better performances than the continuous feedback controller based on implicit Lyapunov function, numerical simulations had been carried out on the basis of MATLAB/Simulink simulation platform. The position response, speed response and the control input response of hoist part and rotation part were analyzed respectively. The position response results showed that the maximum overshoot by global non-singular terminal sliding mode method was 10.6% while it was 144% by the implicit Lyapunov function continuous feedback controller (ILFCFC). The control settling time was decreased from 2.84 to 1.95 s. The angle position response results showed that the global non-singular terminal sliding mode method had no overshoot while it was 62.8% by the ILFCFC. The control settling time was decreased from 2.3 to 2.0 s. The speed response results showed that the speed maximums by global non-singular terminal sliding mode method were 0.91 m/s and 1.05 rad/s while they were 3.69 m/s and 4.98 rad/s by the ILFCFC. The control input response results showed that the maximum by global non-singular terminal sliding mode method were 633.4 N and 399.6 N·m respectively for hoist part and rotation part while they were 1440 N and 1289 N·m by the ILFCFC. Through the comparison with the continuous feedback controller based on implicit Lyapunov function, the position response was faster, the position maximum overshoot was smaller, and the speed response and the control input response varied more smoothly and rapidly for global non-singular terminal sliding mode method. The control system had better dynamic and static performance. The correctness and effectiveness of control method with non-singular terminal sliding mode was verified by computer simulation in this paper. The control method with global non-singular terminal sliding mode can improve control quality and has great robustness to uncertain inertial parameters, which will lay a foundation for further study of the elevator control.