# An Optimized Fractional-Order PID Horizontal Vibration Control Approach for a High-Speed Elevator
## 1 Introduction
[PERSON] [11] used the FA-BP algorithm to train fuzzy neural network (FNN) auxiliary controllers, and the elevator experiments have demonstrated the effectiveness. [PERSON] et al. [12] adopted a linear quadratic regulator (LQR) control strategy to control the magnetorheological damper, and the results validate the effectiveness. [PERSON] et al. [13] proposed an acceleration feedback-based active control method to suppress the vibration of elevators. Numerical simulations have demonstrated the effectiveness of the method. [PERSON] et al. [14] proposed a semi-active high-speed elevator car horizontal vibration reduction method based on the improved particle swarm algorithm, and it has been verified through experiments. Due to the complexity of the controller designed using the above method, problems such as high cost or difficult implementation conditions may arise in practical use. The idea of combining fractional calculus theory with PID controllers has brought a new type of PID controller, known as the FOPID controller [15]. As a product of the combination of fractional calculus and PID controllers, FOPID not only has the advantage of simple control structure, strong adaptability, and independence of the controlled object model but also has better performance due to the introduction of more parameters. However, the design difficulty of FOPID controllers increases [16; 17]. Some analytical and heuristic methods have been used in the design of FOPID controllers in different fields [18; 19]. Some scholars use different algorithms for the design of FOPID controllers. [PERSON] [20] optimized the parameters of the FOPID controller using the GWO PSO algorithm. [PERSON] [21] proposed the improved artificial bee colony (IABC) low-order approximation (LOA)-based fractional order PID (IABC/LOA-FOPID). [PERSON] [22] used the gray wolf optimizer (GWO) and extended gray wolf optimizer (EGWO) to obtain the appropriate parameters of the FOPID controller. [PERSON] [23] proposes a modified smoothed function algorithm (MSFA)-based method to tune the FOPID controller of the AVR system. [PERSON] [24] designed a FOPID controller based on ILC (iterative learning control). The results demonstrate the effectiveness of the FOPID controller. Currently, no scholars have applied FOPID to elevator vibration suppression. Regarding the above issues, this paper establishes a model that treats elevators not as rigid bodies but with the car body and frame separate, and designs a FOPID controller. Selecting system performance and control cost as objective functions, a multi-objective genetic algorithm (MOGA) is used to optimize the controller parameters. Through MATLAB/Simulink simulation verification, the FOPID controller can effectively suppress elevator vibration, which has a better effect than PID controllers. The main contributions and innovations of this paper are as follows:An optimization design model for elevator vibration suppression is established, and an optimized FOPID controller is designed to suppress horizontal vibration effectively. 2. Selecting control cost and system performance as the objective functions of the optimization algorithm, MOGA is used to optimize the parameters of both the PID controller and FOPID controller. 3. Through multiple iterations, the proposed optimized FOPID controller can achieve the expected system performance at a limited control cost, which can reduce the horizontal acceleration by about 68% compared to the case without a controller and about 25% compared to PID control. The remainder of the article is arranged as follows. In Section 2, a dynamic model of the horizontal vibration of high-speed elevators is established. Section 3 proposes an optimized FOPID control method based on a multi-objective genetic algorithm. Section 4 proposes numerical results and validation. Section 5 provides concluding remarks.