Aiming at the longitudinal vibration problem of high-speed elevator car hoisting system caused by the complex shaft environment of high-speed elevator and parameter uncertainty under different working conditions, an adaptive backstepping control method for longitudinal vibration of nonlinear car hoisting system of high-speed elevator under hard constraints is proposed. First, by analyzing the hierarchical relationship between the traction system, the car hoisting system, and the active control system, and by considering the parameter uncertainty, the time-varying characteristics of the wire ropes, and the nonlinear force of the springs, a longitudinal vibration dynamics model of the nonlinear car hoisting system was established. Second, considering the different control characteristics of the two operation phases of high-speed elevators, namely, uniform speed operation and emergency braking, a special nonlinear filter that can be automatically switched with the working conditions is adopted to respond to the dynamic changes during emergency braking effectively. Then, considering the mutual constraint relationship between the longitudinal direction of the car frame, construction of hard constraint expressions for the mechanical structure between the car and the car frame, the barrier Lyapunov function under this hard constraint condition is derived, and the adaptive updating law under the uncertain parameter is designed at the same time, and then an adaptive backstepping control method for the longitudinal vibration of a high-speed elevator is proposed. Finally, the proposed control method is verified by simulation experiments under different working conditions and zero-crossing analysis, and the results show that the control method can significantly reduce the longitudinal vibration of the car, which is basically reduced by one order of magnitude numerically compared with the common adaptive backstepping control method, which verifies the validity of the proposed method in this study.
Zhao et al. (Wed,) studied this question.