High-speed elevator output feedback stabilization control based on a nonlinear extension state observer

Horizontal vibration of car is a critical issue affecting the stability and ride comfort of high-speed elevators. This phenomenon primarily caused by the uncertain nonlinear disturbances induced by guide rails, guide shoes, and other various internal and external perturbations. To mitigate these vibrations, a novel output feedback stabilization control strategy based on nonlinear extension state observer (NLESO) is proposed. First, an eight-degree-of-freedom dynamics model considering the uncertain nonlinear disturbances was established for the horizontal vibrations. Second, NLESOs were developed to observe and compensate for the internal and external perturbations of elevator car system. Subsequently, a stabilization controller with NLESOs was designed based on the output feedback of the dynamics model using a finite-time stabilization control law. The finite-time stability of NLESOs was proven using Lyapunov’s theorem. Finally, numerical simulations for the proposed method were conducted under two typical rail excitations using MATLAB/Simulink and compared with higher-order sliding mode control (HOSMC), linear extension state observer (LESO), and passive control schemes. The results indicate that the proposed method significantly reduces the displacement acceleration and angular deflection acceleration of horizontal vibrations, with root mean square values decreasing by more than 68% and 67%, respectively, compared to passive control. This demonstrates the superior stability and finite-time convergence of the proposed method, effectively suppressing horizontal vibrations during high-speed elevator operation.