Eliminating and controlling the swing of the crane is of great significance for improving the crane’s working efficiency and reducing the hidden danger of safety production in loading and unloading operations. Considering the nonlinearity, time-varying and uncertainties of the swing system of crane, a method combining traditional PD control with fuzzy control is proposed, which uses fuzzy language rules to adjust the parameters of PD in real time.
The anti-swing system is modeled and simulated by SIMULINK. The simulation results show that the control method has better adaptability and robustness than the traditional PD control method under the premise of given rope length and load quality, and can improve the dynamic performance of the crane swing system.
Bridge crane is widely used in wharf, thermostatic element warehouse, hydropower station and other fields. In the process of crane operation, due to inertia, heavy objects and steel ropes will swing around the suspension point during the start, operation and braking of the trolley, which will not only affect the production efficiency, but also increase the operation time, affect the stability of the crane, and even cause safety accidents in serious cases. Many scholars have done a lot of research in this field. The representative studies include LQR optimal control, PD and PID control, adaptive control, state feedback control and so on.
These control methods are based on the precise mathematical model of the controlled object. Although they are easy to implement, they lack flexibility and flexibility, and the control effect is not ideal.
In the actual operation of the crane, external disturbances such as physical friction between the trolley and the track, wind force and its own non-linear factors should be taken into account. Affected, the model is difficult to meet the practical requirements, and there will be some limitations in the application of anti-swing system. Based on the design idea of fuzzy control and the traditional PID control principle, this paper combines crane PD control with fuzzy control to construct an adaptive PD controller, so as to realize the optimal adjustment of control parameters and further enhance the adaptability of the system to uncertain factors. The simulation results show that the adaptive fuzzy PD control has small overshoot and small vibration, and improves the control accuracy of crane in operation. The whole control system of overhead crane includes the control of the position of the trolley, the trolley and the swing angle of the hoisting load, and both of them are approximately independent of each other. The crane system is modeled as shown in Fig. 1, in which the car mass is set to M, the lifting mass is m, the motor driving force is F, the friction force is f, and the car moves along the X-axis after starting. Because of inertia, the swing angle of the crane will be theta. The fuzzy PD controller consists of a conventional PD controller and a fuzzy controller. Two-dimensional fuzzy controller is selected. The input variable signal is the car displacement deviation signal e, and the second is the car displacement deviation change signal ec. The output variable signal Kp and Kd are two incremental parameters of the conventional PD controller, respectively. This incremental mode is used to adjust the parameters to meet the different requirements of different E and EC on the parameters of the controller.
The controller will always detect the signals E and EC in the operation of the system. Based on the set fuzzy logic rules, the two incremental parameters are adjusted online. The control structure is shown in Figure 2. Similar to the traditional PID controller, the parameters of fuzzy adaptive PD control also follow certain principles. The parameters of Kp and Kd play different roles in the control system, and have certain relationship with E and ec. The purpose of controlling the parameter of Kp is to speed up the response speed of the system and improve the adjustment precision of the system. The function of controlling Kd is to judge the change direction of the system deviation in advance. When the change arrives, brake in advance and restrain the deviation in time. In other words, the dynamic characteristics of the system are improved by adjusting the size of Kd. When the deviation e is large, in order to ensure good tracking performance and improve the response speed of the system, the value of Kp should be larger and the value of Kd should be smaller. When the deviation e is small, in order to avoid overshoot and oscillation, the value of Kp should be reduced appropriately. At the same time, the value of Kd should be selected properly considering the anti-disturbance ability and response speed of the system. But Kd should not be too large. Because too much braking makes the response process too early, thus prolonging the adjustment time. When E and EC are the same number, the direction of output will change to deviate from the stable value. At this time, Kp should increase appropriately, and vice versa. The basic domains of input signal E and EC are [-1,1] and [-0.4,0.4]. The quantization factors are 3.0 and 7.5. The basic domains of output signal Kp and Kd are [-8,8] and [-10,10], respectively. They are mapped to the fuzzy universe [-3,3] and [-6,6], and triangular functions are used as membership function curves, as shown in Figures 3 and 4. A two-dimensional fuzzy controller with errors and errors as input variables, which is composed of control rules in Tables 1 and 2, and conditional statements of the two-dimensional fuzzy controller itself, arranges the input and output fuzzy logic control variables into the rule editor, as shown in Fig. 5. The logical relations between input e, EC and output Kp and Kd are represented by three-dimensional surface, respectively, as shown in Figure 6. As can be seen from Figure 6, when Kp is larger in E and ec, it takes a larger value; when Kd is smaller, it takes a larger value; when E and EC are different, the value of Kp is smaller than that of the same number. The control quantity needs to be transformed into the basic universe by the scale factor, that is, the real distribution of the control parameters is obtained by the transformation of the fuzzy control language into the precise mathematical language, that is, the de-fuzzification of the output quantity. According to the formula of the gravity center element, the values of Kp and Kd are obtained online multiplied by the scale factors of their respective parameters, and the initial parameters K set are obtained.
The sum of P0 and Kd0 is used as the output value of the fuzzy adaptive PD controller, that is, the real-time parameter setting value of the controller. In formula (4), Kp0 and Kd0 are the initial values of two parameters controlled by PD, Kp and Kd are the revised values of two parameters, and Kp and Kd are the values of two parameters controlled by PD. The anti-sway system model is built on the platform of MATLAB/Simulink software, as shown in Figure 7. The control strategy of the system mainly includes two fuzzy PD controllers designed to realize the control of the car displacement and the swing angle of the lifting load. The control process takes the car displacement and the swing angle of the lifting load as the feedback signals of the two controllers respectively. The displacement feedback signal and the input reference signal constitute the displacement deviation signal, and the adjusted pendulum angle signal is connected to the control system in the form of positive feedback. On-line parameter tuning is based on fuzzy language rules. This real-time control method based on the real-time state of the system makes the controlled object have good dynamic and static performance. In order to verify the performance of the control system, a group of crane parameters are selected for MatLAB simulation test. Assuming parameters: vehicle mass M = 5 kg, lifting weight M = 10 kg, suspension rope length L = 2 m, gravity acceleration g = 9.8 m/s2, target position and desired swing angle are taken as reference values with unit step input of 1 m and 0 degree respectively, sampling time is selected for 15 s. The response curve is shown in Fig. 8. The simulation results show that compared with the conventional PD control, the fuzzy adaptive PD control algorithm significantly reduces the load swing amplitude and the overshoot is smaller.
In contrast, the fuzzy adaptive PD control algorithm has strong robustness. In this paper, fuzzy language rules are used to automatically adjust the control parameters of PD in real time according to the motion state of the system, and the operation process of the crane is simulated. In order to better analyze the merits and demerits of the control system, a series of comparative tests are designed by changing the numerical values of adjustable parameters (wire rope length and lifting quality). Then external disturbance signals are introduced to realize the fuzzy adaptive PD control algorithm and the conventional PD control algorithm from the point of view of response curve and dynamic performance index. Analysis and comparison of methods. The results show that the fuzzy adaptive PD controller has stronger robustness than the conventional PD controller.