# An Optimized Fractional-Order PID Horizontal Vibration Control Approach for a High-Speed Elevator
## 1 Introduction  
As the development of urban construction advances, towers have increased rapidly, and high-speed elevators increase correspondingly. The speed rise of elevators causes the horizontal vibration to be more obvious. Large horizontal vibrations can affect the comfort and safety of elevators, leading to a decrease in elevator lifespan. Therefore, the vibration suppression of elevators is a key issue in the field of elevator research, which is significant for the development of the elevator industry. The main factors causing the vibration are the defects of the guide rail or the non-standard installation and the influence of the airflow in the shaft. Passive damping and active damping are common methods for suppressing the horizontal vibration of elevators [1]. The passive damping method generally suppresses vibration by optimizing the structure or the car parameters. However, due to the complexity of the elevator operation and multiple factors, the effect of passive damping to suppress vibration is difficult to meet the demand. The active damping applies the active control force through the corresponding actuator and suppresses vibration through control algorithms [2]. Active damping is better than passive damping in suppressing vibration and meeting the demand, but it will increase the cost. Due to low speed and small vibration, low-speed elevators usually do not use active damping methods. However, high-speed elevators cannot ignore the vibration caused by speed, so an active damping method is needed. The usual executive structure of the active damping method is the active guide shoe, which plays an important role in reducing vibration and improving elevator ride comfort. It can reduce vibration by the force generated by the actuator installed on the passive guide shoe opposite to the vibration direction. Due to their good effect and strong adaptability, guide shoes have become an effective means of suppressing elevator vibration. [PERSON] et al. [3] established a 6-degree of freedom (DOF) horizontal vibration model for an elevator car and proposed an H2/generalized H2 hybrid control strategy. Theresults prove that the control strategy is effective. [PERSON] et al. [4; 5] simplified the guide shoe as a spring-mass damping system, treating the car body and car frame as a rigid body. [PERSON] et al. [6] designed a new type of shock absorber using a linear motor and designed a PID controller that combines a linear prediction model with a backpropagation neural network. From the results, it can be seen that the proposed control method is superior to traditional proportional integral differential controllers in suppressing vibration. [PERSON] et al. [7] designed an optimal guaranteed performance state feedback controller based on a linear convex optimization method to minimize the H2 performance index and achieve the specified Hoo performance level. This control strategy is effective in vibration suppression and improving elevator comfort. Although the above scholars have tried to suppress the horizontal vibration, they have ignored the impact of treating elevators as rigid bodies on vibration response. [PERSON] et al. [8] designed a pneumatic active guide shoe and a fuzzy neural network intelligent vibration reduction controller based on the Mamdani model, which can effectively suppress the horizontal vibration of high-speed elevators. [PERSON] et al. [9] established a 3-DOF elevator car model, derived a dynamic equation for the impact of rail deformation on it, and proposed an SDRE control strategy that can effectively control system effects and help maintain the integrity of elevator components. [PERSON] et al. [10] established a more practical elevator car horizontal vibration control model, proposed a predictive sliding mode controller based on the adaptive fuzzy-based (PSMC-AF) and designed a fuzzy logic system (FLS) to approach the compound uncertainty disturbance term (CUT) online.