# Research on Variable Universe Fuzzy Multi-Parameter Self-Tuning PID Control of Bridge Crane
## 1 Introduction
The LQR controller heavily relies on the linear model of the controlled object, and if the system model is inaccurate, it may lead to a decrease in the reliability of the controller. The MPC controller needs to solve an optimization problem in each control cycle, which has a high computational complexity and requires the selection and adjustment of multiple parameters, making it a complicated design process. This makes it difficult for some controllers to be widely applied in practical engineering at present. In contrast, the PID feedback control system, with its reliable and stable performance, has been widely used in crane applications [11; 12; 13]. The selection of the three control parameters in the PID system significantly influences the controller's performance, leading many researchers to investigate the optimization of these parameters. For instance, [PERSON] et al. [12] utilized a genetic algorithm (GA) to optimize the gain of PID, resulting in excellent control performance in both trolley positioning and load anti-sway. [PERSON] et al. [14] employed an improved particle swarm optimization (PSO) algorithm, selecting an adaptive fitness function based on the priority fitness scheme (PFS). The PID controller has been shown to effectively control load swings and ensure system stability. Furthermore, in a study by [PERSON] et al. [15], particle swarm optimization (PSO) was employed to optimize the vertical position and speed trajectory of the path planning control system for a crane. The proposed method was tested under different sea conditions using simulations, which demonstrated its effectiveness. [PERSON] et al. [16] employed a dual-closed-loop composite anti-sway control method to regulate both the trolley's position and the hanging load's swing of an overhead crane, optimizing the parameters of the PD controller through the sequential quadratic optimization method. Some researchers have also integrated PID controllers with other control techniques. [PERSON] et al. [17] presented a novel anti-sway control approach that integrated PID control and neural network compensation. They established the stability of the neural PID control system using a standard weight training algorithm and report satisfactory simulation outcomes. Bridge cranes are non-linear control systems that require accurate mathematical models for precise control when using linear controllers. Fuzzy controllers are based on expert experience without requiring accurate mathematical models, making them very suitable for controlling non-linear systems [18; 19; 20; 21]. Combining fuzzy controllers with other controllerscan fully leverage the advantages of both types of controllers, achieving good results in the field of crane control [22; 23; 24; 25]. A fuzzy PID controller modifies the PID parameters in real time using fuzzy control rules. It determines the controller's output by considering the magnitude and rate of change of the input variables. This controller is widely used in the field of cranes. In [26], control research was conducted on a bridge crane using a multi-input single-output fuzzy algorithm model combined with PID. Simulation results demonstrated that the fuzzy PID control system exhibits superior robustness compared to the classical PID control system when handling external disturbances. In [27], an approach combined fuzzy and PID controllers and derived heuristic control rules using membership functions. The parameters of the membership functions were then tuned through an adaptive neural fuzzy inference system. This control system achieved faster speed and less swing over longer transport distances. In [28], a combination of PID and fuzzy controllers was used to compensate for the coupling between friction, gravity, and the position of the cart, as well as anti-swing control. In order to enhance the performance of the PD controller, a high-gain observer was incorporated to estimate the cart's speed. [PERSON] et al.