The traditional PID control algorithm has the advantages of simple algorithm, high control precision and high reliability, which is suitable for the deterministic control system with precise mathematical model. The traditional fuzzy controller has a rough division of the universe. It needs to increase the quantization series appropriately in order to improve the control accuracy, but it will result in the enlargement of the search range of the fuzzy rules and reduce the overall decision. It is difficult to achieve real-time control [2-4]. Variable universe means that the domain of input variables in fuzzy control is variable, and it is used as adjusting factor to adjust the domain of input variables. Based on the idea of variable universe, this paper designs a fuzzy controller based on variable universe. When the fuzzy control rules are unchanged, the fuzzy universe shrinks or expands with the input.
The shrinkage of universe can increase the variable value and control rules of the fuzzy language, and achieve the control effect consistent with the increase of the fuzzy subset, so as to improve the control accuracy. The basic structure block diagram of the fuzzy control system is shown in Figure 1. It consists of a fuzzy controller, an input/output channel, a generalized object and a sensor. The structure of the fuzzy controller is shown in Fig. 2. In order to control the controlled object accurately, it is necessary to transform the fuzzy quantity u into the precise control quantity, i.
e. the non-fuzzification process adopted in Fig. 2. After obtaining the precise control quantity, the DA converts into the analog quantity and transmits it to the actuator for further control of the controlled object. The control structure is determined, the input variables E, EC and output variables U, the corresponding range of change and the required control accuracy are determined, thermostatic element the physical model is established, and the controller structure is determined. Selection and determination of fuzzification methods. The value of the actual input variable is transformed into the linguistic value of the fuzzy linguistic variable. The different linguistic values correspond to the corresponding fuzzy subset. The membership function is selected to determine the corresponding membership degree of the input variable. The determination of fuzzy control rules and fuzzy operators. The number of control rules is determined according to the quantity of input and output and the control precision. The determination of the method of solving the ambiguity of the output value. Defuzzification is the application of mapping the fuzzy set in the output space to the corresponding points, i.e. calculating the determined value according to the membership degree of the output fuzzy subset. Validation of the validity and reliability of design theories and methods. Assuming that the initial domain of error, i.e. the maximum range of variation of error is [-U, U], where U is a real number, seven rules are generally adopted, i.e. [-U, U] is divided into fuzzy parts, as shown in Figure 3 (a). With the continuous progress of the control process, the error is reduced, that is, to zero position (ZO). If the fuzzy reasoning is carried out by using the certain domain and partition shown in Fig. 3 (a), the control accuracy is naturally not high.
The idea of “variable universe” is that, on the premise that the form of fuzzy rules remains unchanged, the universe will shrink or expand with the error decreasing or increasing, as shown in Figure 3 (b) (c). The block diagram of fuzzy controller is shown in Figure 4. The working principle of the variable universe fuzzy controller is: Based on the system error and the rate of error change, the fuzzy controller deduces the expansion factor of the universe, and the expansion factor dynamically changes two input and one output domain, so that it can adapt to the input changes of the system and achieve the best control effect. According to the requirements of variable universe fuzzy controller, as long as the general trend of fuzzy rules is satisfied and the monotony of fuzzy rules is guaranteed, the fuzzy rules are formulated as shown in Table 1. The initial universe of fuzzy control error is [-6,6], the initial universe of error change rate is [-3,3], the initial universe of fuzzy output is [-6,6], the parameters of PID control are set as Kp=0.7, Ki=0.
25, Kd=0.3, the quantization factor of conventional fuzzy controller is Ke=0.8, Kec=0.9, the proportion factor is Ku=1/7, the quantization factor of variable universe is Ke=0.2, Kec=0.01, the proportion factor is Ku=0.1, the sampling time is T=0.5, Fig. 5 The overall simulation program for the control system. As shown in Fig. 5, the simulation program consists of three parts, one is PID control, one is conventional fuzzy controller, the other is the variable universe fuzzy controller of the article.
Fig. 6 is the simulation curve of step response of the fuzzy control system, in which the abscissa represents time t and the ordinate represents output response y. As shown in Fig. 6, there are three control curves, among which the conventional PID control curve has larger overshoot, slower response speed and longer response time.
The output curve of the conventional fuzzy controller has better performance than the conventional PID control, and the overshoot is smaller than the conventional PID control, but the response time is still longer. It can be seen from the figure that the effect of the variable universe fuzzy controller is better than the conventional PID control. The effect of the system and the conventional fuzzy controller is better, the overshoot is very small, the rising time is short, the response speed is fast, and there is no oscillation. Based on the analysis of conventional fuzzy controllers and the idea of variable universe, this paper designs a practical variable universe fuzzy controller. The simulation experiment of second-order system with pure delay is carried out.
Compared with conventional PID and conventional fuzzy controllers, it is proved that this new variable universe fuzzy controller can obviously improve the control effect of pure delay system, and it has good performance. It has the advantages of no overshoot, no oscillation and fast response. It has high practical value for industrial application.