## 1 Introduction
used the Karhunen-Loeve Transform and polynomial chaos method to study the dynamic characteristics and control means of the horizontal vibration of elevator car caused by rail irregularity through the establishment of the irregular stochastic model of the rail profile. [PERSON] [11] et al. investigated the horizontal vibration response due to guideway roughness in a three-degree-of-freedom lift vertical motion model and proposed a control strategy based on the state-dependent Riccati equation. [PERSON] [12] et al. designed a BPNN-PID controller with a linear predictive model using linear motors as actuators for the intelligent control of car vibration under uncertain external excitation. [PERSON] [13] et al. proposed a semi-active damping method based on a Particle Swarm Optimization (PSO) algorithm to control the adjustable damper of magneto-rheological fluid. In the aforementioned research on lateral vibration control of elevators, most of the research methods have only remained in the experimental stage and have not been applied to actual elevators. Moreover, all the studies have shown insignificant control effects on the lateral vibration of the car. That is, they have not reduced the resonance amplitude of the human body within the sensitive frequency range. Most of the vibrations in high-speed elevators are caused by the unevenness of the guide rails. In order to reduce the impact of the guide rails, the car is \"suspended\" on them. The electromagnetic active rolling guide shoes can exert active control force through electromagnetic force, which can separate the car from the guide rails and reduce the impact of the uneven guide rails on the car [14]. This structure can also be easily added to the traditional guide shoes of the elevator. The electromagnetic active rolling guide shoes can be regarded as a traditional damper between the car and the guide rails. Traditional dampers have the disadvantage of increasing vibration when the absolute speed and relative speed are opposite, while the sky-hook damping control strategy can effectively compensate for that [15; 16]. Therefore, this paper adds electromagnetic active rolling guide shoes to the structure of high-speed elevators and introduces the sky-hook damping control strategy. In the strategy, many important parameters related to vibration reduction need to be adjusted. However, manually determining a set of optimal parameters to effectively suppress car vibration requires a large amount of difficult calculation. Optimization algorithms can solve the problem of seeking the optimal solution for multiple parameters. Sparrow Search Algorithm (SSA) is a new intelligent optimization algorithm proposed by [PERSON] [17] et al. in 2020 based on the foraging and anti-predation behavior of sparrows. Compared with other swarm intelligence optimization algorithms, SSA has the advantages of strong optimization ability, fast convergence speed, strong robustness, and stable performance. Therefore, this paper proposes a lateral vibration control strategy based on SSA for the lateral vibration of the high-speed elevator cabin within the human-sensitive frequency range. Through Simulink numerical simulation research and analysis of experimental results, it is demonstrated that the method proposed in this paper can effectively reduce the lateral vibration of high-speed elevators within the human-sensitive frequency range and improve the ride quality of high-speed elevators. The remaining sections of this paper are arranged as follows: In Section 2, a mathematical model for car vibration is established based on the structure and vibration modes of high-speed elevators. The control equation for sky-hook damping is also introduced in this section. In Section 3, the SSA is presented. In Section 4, a Simulink simulation model is built based on the mathematical model in Section 2, and simulations are performed using the model. In Section 5, the specific structural parameters obtained through the optimization algorithm are applied to an actual high-speed elevator for verification.