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pid type fuzzy controller and parameters adaptive

By Willie Arnold,2014-04-14 19:52
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pid type fuzzy controller and parameters adaptive

    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-sum 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 controller 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 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 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 and 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 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

     2 be a discrete fuzzy set with 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 that 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 like 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 controller 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 like 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 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 system's response so as to improve the control performance. Of course this can be realized by designing a fuzzy controller 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 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

     3 error and the change rate of the error between the system's output and the set-point value. It is not the practice for the 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 possesses 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. 1,1Kand2Kare scaling factors for e and ~ respectively, and fl is the 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 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 zero.

     4 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 transfer function:

     ) 1)(1()(21;;; sTsTK sG (2) Where K = 16, 1T= 1, and2T=

    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 are 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 factor fl is small, the system's 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 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 larger 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)

     9 ] 1,0[,,,3,)1(2,)1(1,)1(0,)1({ 321033221100;;;;;;;;;;;;;;;;;;

    ;;;;;;;;;;;EECEEECEEECEEECEU Because it is very difficult to find a

    self of optimum parameter, a new method is presented by ProfZhou Xian-Lan, the regulation is

    as follow: )0(),exp(12;;;;kke; But this algorithm still can not eliminate the

    steady errorThis paper combines this algorithm with PI controlthe performance is

    improved 2. Simulation of Control System 3.1 Dynamic character of controlled object Papers should be limited to 6 pages Papers longer than 6 pages will be subject to extra fees based on their length

     Fig .2 main steam temperature control system structure Fig 2 shows the main steam temperature control system structure )(),(21sWsW;;are main controller and auxiliary

    controller,)(),(21sWsWooare characters of the leading and inertia sections,)(),(21sWsWH Hare measure unit. 3.2 Simulation of the general serial PID control system

     10 The simulation of the general serial PID control system is operated by MATLAB, the simulation modal is as Fig.3.Setp1 and Setp2 are the given value disturbance and superheating water disturb & rice .PID Controller1 and PID Controller2 are main controller and auxiliary controller The parameter value which comes from references is as follow

     667 .37,074.0,33.31 )(25 )(111111122;;;;;;;;DIpDIppkkks ks kksWksW;;

     Fig.3. the general PID control system simulation modal 3.3 Simulation of self adaptation fuzzy-PID control system Spacing The simulation modal is as Fig 4.Auxiliary controller is:25)(22;;pksW;.Main

    controller is Fuzzy-PI structure, and the PI controller is: 074 .0,33.31)(111 11;;;;

    IpIpkkskksW;

     Fuzzy controller is realized by S-function, and the code is as fig.5. Fig.4. the fuzzy PID control system simulation modal

     11 Fig 5 the S-function code of fuzzy control 3.4 Comparison of the simulation Given the same given value disturbance and the superheating water disturbancewe compare the

    response of fuzzy-PID control system with PID serial control system.

    The simulation results are as fig.6-7. From Fig6-7,we can conclude that the self adaptation fuzzy-PID control system has the more quickly response, smaller excess and stronger anti-disturbance 4. Conclusion (1)Because it combines the advantage of PID controller and fuzzy controller, the

     12 self adaptation fuzzy-PID control system has better performance than the general PID serial control system. (2)The parameter can self adjust according to the error E value. so this kind of controller can harmonize quickly response with system stability

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