# Research on Variable Universe Fuzzy Multi-Parameter Self-Tuning PID Control of Bridge Crane
## 1 Introduction  
With the continuous development of automatic control technology, bridge cranes have gradually evolved from a single handling tool to an important component of automation and flexible production, widely used in industrial places such as factories, workshops, warehouses, and ports. However, during the transportation process of the crane, the acceleration and deceleration of the carts and trolleys, the lifting of the load, and the disturbance caused by wind friction can cause the load to swing back and forth. In the past, operators relied on experience to overcome this, which not only increased the possibility of accidents but also did not help improve the efficiency of crane operation. When it comes to the positioning and anti-sway control of cranes, they can be categorized as open-loop control and closed-loop control based on the type of control. For instance, input-shaping controllers, which are commonly used in [1, 2], fall under open-loop control. These controllers are designed to be simple and have a certain impact on anti-sway and positioning. Moreover, engineering implementation is relatively easy. However, when cranes are operating under external disturbances, or when the initial swing angle of the load is not zero, the anti-sway control effect of the open-loop controller can be severely diminished due to the absence of feedback in the input-shaping control system. As control technology and sensor technology continue to advance, more scholars are focusing on feedback control. In [3], the anti-swing control of a bridge crane was studied using adaptive sliding mode control (SMC), which included compensation and prediction mechanisms. To ensure the stability and robustness of the control system, suitable Lyapunov functions were developed. In a study by [PERSON] et al. [4], they proposed an adaptive nonlinear controller using the dynamic model of a double-pendulum rotary crane. Byemploying Lyapunov functions, they were able to prove the stability of the entire control system, resulting in successful control outcomes. In [5], an optimal controller was used to control a variable-parameter bridge crane, and Monte Carlo simulation was employed to determine the parameters of the optimal controller. A control approach employing linear active disturbance rejection control (LADRC) and differential flatness theory was proposed in a recent study by [PERSON] et al. [6]. The control method was optimized using particle swarm optimization (PSO) to fine-tune the controller's parameters, resulting in successful positioning and anti-swing control performance. In a study [7], a passivity-based adaptive control approach was introduced for a bridge crane. The authors proved the stability of the closed-loop control system using passivity theory and developed an adaptive control law. Simulation results confirmed the effectiveness of the proposed approach. In [8], a new nonlinear control method and disturbance observer were proposed to study the adjustment and suppression of uncertain disturbances in bridge crane systems. In [9], a model predictive control system was proposed to achieve swing attenuation of the trolley hoist. When encountering external disturbances, the swing angle and load displacement were used as feedback inputs for anti-swing control in the closed-loop system. In [10], a robust linear quadratic regulator (LQR) based on particle swarm optimization (PSO) was used for swing prevention and positioning control of the system. The controller uses a parallel compensator structure and optimizes the parameter selection of the weight matrix using the particle swarm optimization algorithm. These advanced control methods have demonstrated their effectiveness in achieving accurate positioning and anti-sway control in cranes. However, some controllers have their own drawbacks. For example, the sliding mode controller heavily relies on mathematical models and expert experience in designing the sliding surface and determining its parameters can be difficult.