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1、Part 3 Neuro-fuzzy generalized predictive control of boiler steam temperature13Part 4 为Part3译文：锅炉蒸汽温度模糊神经网络的广义预测控制21Part 1 PID type fuzzy controller and Parameters adaptive method Wu zhi QIAO, Masaharu Mizumoto Abstract: The authors of this paper try to analyze the dynamic behavior of the product-su

2、m crisp type fuzzy controller, revealing that this type of fuzzy controller behaves approximately like a PD controller that may yield steady-state error for the control system. By relating to the conventional PID control theory, we propose a new fuzzy controller structure, namely PID type fuzzy cont

3、roller which retains the characteristics similar to the conventional PID controller. In order to improve further the performance of the fuzzy controller, we work out a method to tune the parameters of the PID type fuzzy controller on line, producing a parameter adaptive fuzzy controller. Simulation

4、experiments are made to demonstrate the fine performance of these novel fuzzy controller structures. Keywords: Fuzzy controller; PID control; Adaptive control 1. Introduction Among various inference methods used in the fuzzy controller found in literatures , the most widely used ones in practice are

5、 the Mamdani method proposed by Mamdani and his associates who adopted the Min-max compositional rule of inference based on an interpretation of a control rule as a conjunction of the antecedent and consequent, and the product-sum method proposed by Mizumoto who suggested to introduce the product an

6、d arithmetic mean aggregation operators to replace the logical AND （minimum） and OR （maximum） calculations in the Min-max compositional rule of inference. In the algorithm of a fuzzy controller, the fuzzy function calculation is also a complicated and time consuming task. Tagagi and Sugeno proposed

7、a crisp type model in which the consequent parts of the fuzzy control rules are crisp functional representation or crisp real numbers in the simplified case instead of fuzzy sets . With this model of crisp real number output, the fuzzy set of the inference consequence will be a discrete fuzzy set wi

8、th a finite number of points, this can greatly simplify the fuzzy function algorithm. Both the Min-max method and the product-sum method are often applied with the crisp output model in a mixed manner. Especially the mixed product-sum crisp model has a fine performance and the simplest algorithm tha

9、t is very easy to be implemented in hardware system and converted into a fuzzy neural network model. In this paper, we will take account of the product-sum crisp type fuzzy controller. 2. PID type fuzzy controller structure As illustrated in previous sections, the PD function approximately behaves l

10、ike a parameter time-varying PD controller. Since the mathematical models of most industrial process systems are of type, obviously there would exist an steady-state error if they are controlled by this kind of fuzzy controller. This characteristic has been stated in the brief review of the PID cont

11、roller in the previous section. If we want to eliminate the steady-state error of the control system, we can imagine to substitute the input （the change rate of error or the derivative of error） of the fuzzy controller with the integration of error. This will result the fuzzy controller behaving lik

12、e a parameter time-varying PI controller, thus the steady-state error is expelled by the integration action. However, a PI type fuzzy controller will have a slow rise time if the P parameters are chosen small, and have a large overshoot if the P or I parameters are chosen large. So there may be the

13、time when one wants to introduce not only the integration control but the derivative control to the fuzzy control system, because the derivative control can reduce the overshoot of the systems response so as to improve the control performance. Of course this can be realized by designing a fuzzy cont

14、roller with three inputs, error, the change rate of error and the integration of error. However, these methods will be hard to implement in practice because of the difficulty in constructing fuzzy control rules. Usually fuzzy control rules are constructed by summarizing the manual control experience

15、 of an operator who has been controlling the industrial process skillfully and successfully. The operator intuitively regulates the executor to control the process by watching the error and the change rate of the error between the systems output and the set-point value. It is not the practice for th

16、e operator to observe the integration of error. Moreover, adding one input variable will greatly increase the number of control rules, the constructing of fuzzy control rules are even more difficult task and it needs more computation efforts. Hence we may want to design a fuzzy controller that posse

17、sses the fine characteristics of the PID controller by using only the error and the change rate of error as its inputs. One way is to have an integrator serially connected to the output of the fuzzy controller as shown in Fig. 1. In Fig. 1,andare scaling factors for e and respectively, and fl is the

18、 integral constant. In the proceeding text, for convenience, we did not consider the scaling factors. Here in Fig. 2, when we look at the neighborhood of NODE point in the e - plane, it follows from （1） that the control input to the plant can be approximated by （1） Hence the fuzzy controller becomes

19、 a parameter time-varying PI controller, its equivalent proportional control and integral control components are BK2D and ilK1 P respectively. We call this fuzzy controller as the PI type fuzzy controller （PI fc）. We can hope that in a PI type fuzzy control system, the steady-state error becomes zer

20、o. To verify the property of the PI type fuzzy controller, we carry out some simulation experiments. Before presenting the simulation, we give a description of the simulation model. In the fuzzy control system shown in Fig. 3, the plant model is a second-order and type system with the following tran

21、sfer function: （2）Where K = 16, = 1, and= 0.5. In our simulation experiments, we use the discrete simulation method, the results would be slightly different from that of a continuous system, the sampling time of the system is set to be 0.1 s. For the fuzzy controller, the fuzzy subsets of e and d ar

22、e defined as shown in Fig. 4. Their cores The fuzzy control rules are represented as Table 1. Fig. 5 demonstrates the simulation result of step response of the fuzzy control system with a Pl fc. We can see that the steady-state error of the control system becomes zero, but when the integration facto

23、r fl is small, the systems response is slow, and when it is too large, there is a high overshoot and serious oscillation. Therefore, we may want to introduce the derivative control law into the fuzzy controller to overcome the overshoot and instability. We propose a controller structure that simply

24、connects the PD type and the PI type fuzzy controller together in parallel. We have the equivalent structure of that by connecting a PI device with the basic fuzzy controller serially as shown in Fig.6. Where is the weight on PD type fuzzy controller and fi is that on PI type fuzzy controller, the l

25、arger a/fi means more emphasis on the derivative control and less emphasis on the integration control, and vice versa. It follows from （7） that the output of the fuzzy controller is （3）3. The parameter adaptive method Thus the fuzzy controller behaves like a time-varying PID controller, its equivale

26、nt proportional control, integral control and derivative control components are respectively. We call this new controller structure a PID type fuzzy controller （PID fc）. Figs. 7 and 8 are the simulation results of the systems step response of such control system. The influence of and fl to the syste

27、m performance is illustrated. When 0 and/3 = 0, meaning that the fuzzy controller behaves like PD fc, there exist a steady-state error. When = 0 and fl 0, meaning that the fuzzy controller behaves like a PI fc, the steady-state error of the system is eliminated but there is a large overshoot and ser

28、ious oscillation.When 0 and 13 0 the fuzzy controller becomes a PID fc, the overshoot is substantially reduced. It is possible to get a comparatively good performance by carefully choosing the value of and. 4. Conclusions We have studied the input-output behavior of the product-sum crisp type fuzzy

29、controller, revealing that this type of fuzzy controller behaves approximately like a parameter time-varying PD controller. Therefore, the analysis and designing of a fuzzy control system can take advantage of the conventional PID control theory. According to the coventional PID control theory, we h

30、ave been able to propose some improvement methods for the crisp type fuzzy controller. It has been illustrated that the PD type fuzzy controller yields a steady-state error for the type system, the PI type fuzzy controller can eliminate the steady-state error. We proposed a controller structure, tha

31、t combines the features of both PD type and PI type fuzzy controller, obtaining a PID type fuzzy controller which allows the control system to have a fast rise and a small overshoot as well as a short settling time. To improve further the performance of the proposed PID type fuzzy controller, the authors designed a parameter adaptive fuzzy controller. The PID type fuzzy controller can be decomposed into the equivalent proportional control, integral control and the derivative control components. The proposed parameter adaptive fuzzy controller decreases the equivalent i