Resistance Furnace Temperature System on Fuzzy PID Controller

Journal of Information & Computational Science 9: 9 (2012) 2627 2634 Available at http://www.joics.com Resistance Furnace Temperature System on Fuzzy PID Controller Shoubin Wang a,, Na Li b, Fan Yang a a School of Control and Mechanical Engineering, Tianjin Institute of Urban Construction Tianjin 300384, China b School of Economic and Management, Tianjin Institute of Urban Construction Tianjin 300384, China Abstract Conventional Proportional Integral Derivative (PID) controller is widely used in many industrial applications due to its simplicity in structure and ease to design. As the control of resistance furnace temperature has nonlinear, large time-delay, large inertia, and uncertainty, etc, it is difficult to establish precise mathematical model for itconventional PID control can not achieve good control effectin this paper, a fuzzy PID controller is proposed. Simulations indicate that it is more steady and strong applicability than traditional PID. Keywords: PID; Fuzzy; Resistance Furnace; Nonlinear 1 Introduction It is well known that PID controllers have been extensively used in many fields for a long time due to their design simplicity, inexpensive cost, and effectiveness for linear systems, although there has been considerable research interest in the implementation of advanced controllers. This is due to the fact that the PID control has a simple structure that is easily understood by field engineers and is robust against disturbance and system uncertainty [1]. However it is difficult to achieve the desired control performance in the presence of unknown nonlinearities, time delays, disturbances as well as change in system parameters. Tuning is important parameter for the best performance of the PID controllers. PID controllers can be tuned in a variety of ways including hand-tuning, Ziegler-Nichols tuning, Cohen- Coons tuning, loop sharing and pole placement [2, 3]. but these have their own limitations. Fuzzy logic is a technology used for developing intelligent control and information systems. It is used for controlling a process that is too nonlinear or too ill-understood to use conventional Project supported by the Tianjin Science and Technology Development Foundation for Colleges and Universities (No. 20110713). Corresponding author. Email address: wsbin800@163.com (Shoubin Wang). 1548 7741 / Copyright 2012 Binary Information Press September 1, 2012

2628 S. Wang et al. / Journal of Information & Computational Science 9: 9 (2012) 2627 2634 control designs [4, 5]. It enables control engineers to easily implement variable proportional to the area under the deviation line. Resistance furnace has pure lag and larger inertia. There are many factors which affect controlling process, such as opening and closing furnace door, heated metal material, surrounding temperature and wire power. In tradition, heating furnace controlling system is most based on some model, which can t achieve heating process request [6, 7]. So this paper try in draught fuzzy controlling arithmetic into traditional heating furnace controlling system to form brainpower fuzzy control system. It makes using of fuzzy control rule to self-tuning PID parameters on line, and improving its control effect. In this paper, PID controller and fuzzy PID controller for resistance furnace temperature system is proposed. The paper is organized as follows. Section 2 presents a method of fuzzy PID controller. The experiments and results are introduced in Section 3. The conclusions are given in Section 4. 2 Design Method of Fuzzy PID Controller 2.1 PID Controller The additive combination of proportional action, integral action and derivative action is termed proportional-integral-derivative action [8]. The block diagram of a control system with unity feedback employing PID control action is shown in Fig. 1. R(s) E(s) Y(s) C(s) K p sk d K i /s Process _ Fig. 1: PID controller Mathematically it is represented as in (1) and (2) y(t) = K p y(t) = e(t) T d d(e) d(t) 1 T i K p e(t) K d d(e) d(t) K i τ 0 τ 0 e(t)d(t) (1) e(t)d(t) (2) where e(t) is the error between the input and the output of the system; u(t) is the control action generated by the PID controller; K p is the proportional gain; T i is the integral time constant; and T d is the derivative time constant. In the discrete-time domain, the PID control law can be expressed as: k u(k) = K p e(k) K i e(j) K d [e(k) e(k 1)] (3) j=0 where K p = K p T/T i, K d = K p T d /T, and T is the sampling period; K p, K i, and K d are three adjustable parameters, designing a PID controller means determining the values of these parameters.

S. Wang et al. / Journal of Information & Computational Science 9: 9 (2012) 2627 2634 2629 In this paper, the three parameters are expressed in the following incremental forms: K p = K p0 K P K i = K i0 K i (4) K d = K d0 K d where K p0, K i0, and K d0 are the initial PID controller parameters and can be determined using the classical Ziegler-Nichols tuning formula [9]. Ziegler-Nichols Method of setting controller parameters are shown in Table 1. Table 1: Ziegler-Nichols method of setting controller parameters Controller Types K P T I T D P T/(K τ) 0 PI 0.9T/(K τ) τ/0.3 0 PID 1.2T/(K τ) 2.2τ 0.5τ The proportional part of the control action repeats the change of deviation. The derivative part of the control action adds an increment of manipulated variable so that the proportional plus derivative action is shifted ahead in time. The integral part of the control action adds a further increment of manipulated variable proportional to the area under the deviation line. 2.2 Basic Architecture of Fuzzy Logic Controller Fuzzy logic cont roller is made up of four components: rule-base, inference mechanism, fuzzification and defuzzification, whose basic architecture figure is as Fig. 2 [10]. x Fuzzification Inference mechanism Defuzzification y Rule-base Fig. 2: Fuzzy controller architecture Supposed x U = U 1 U 2 U N is the input of the system and y V R is the output of the system, so fuzzy logic control system is a non-linear affine from sub-space U to sub-space V. The rule base holds the knowledge, in the form of a set of rules, the inference mechanism evaluates which control rules are relevant on the current time and then decides what the input to the plant should be; the fuzzification interface simply modifies the input s so that they can be interpreted and compared to the rules in the rule-base ;the defuzzification interface converts the conclusions reached by the inference mechanism into the input s to the plant. 2.3 Structure of Fuzzy PID Controller As known from linear control theory, PID cont roller is made up of proportional, integral and derivative control, which has advantages of quick dynamic response and little steady-error. But

2630 S. Wang et al. / Journal of Information & Computational Science 9: 9 (2012) 2627 2634 with the variation of environment or parameters varying, the deviations may be too big for the PID cont roller to control the system. So in this paper the fuzzy logic cont roller and PID cont roller are integrated into a adaptive fuzzy PID cont roller, the new control system has all the advantages of fuzzy logic control and PID control system [11]. Fig. 3 shows the structure of fuzzy PID controller, where fuzzy cont roller changes parameters K p, K i and K d according to the variance of e and e c measured on line by sensors. Fuzzy controller Input _ de dt PID controller Control object Output Fig. 3: Structure of fuzzy PID controller The rule-base is implemented so that it represent s a human expert in-the-loop. The design of adaptive fuzzy PID cont roller is to find the fuzzy relations between K p, K i, K d and e, e c, and modifies the values of K p, K i, K d on line through sensors sensing the variance of e and e c in the flight process to suffice the rigorous environment changing and system parameters varying. 3 Experiments and Results The tranfer function of a typical industrial resistance-heated furnace is represented as follows: G(s) = Ke τs T s 1 = 12 3740s 1 e 260s where K is amplification, τ is time delay, T is inertia time constant. According to the architecture of fuzzy controller, the structure of fuzzy PID controller and fuzzy rule-base, in this paper an altitude fuzzy PID controller is designed and simulated compared with traditional PID controller, based on Matlab/Simulink and fuzzy logic toolboxes in Fig. 4. Fuzzy reasoning rules editing interface is shown in Fig. 5. The simulation of fuzzy PID control system is shown in Fig. 6. Fig. 4: Fuzzy logic controller editing interface

S. Wang et al. / Journal of Information & Computational Science 9: 9 (2012) 2627 2634 2631 Fig. 5: Fuzzy reasoning rules editing interface Step K- Gain -6 du/dt Gain2 Derivative Fuzzy logic controller du/dt Product1 Product Product2 K- 1 s Integrator Derivative1 Gain1 K- 18 Gain3 Gain4 Add 12 3742s1 Transfer fon Transport Add2 delay Add4 Add3 Scope2 Fig. 6: The simulation of fuzzy PID control system In order to illustrate the effectiveness of the proposed control strategy, simulation results were compared to conventional PID control and the fuzzy PID control. The response simulation results of two kinds control strategy are shown in Fig. 7 and Fig. 8. From Fig. 7 and Fig. 8, the system dynamic quality of resistance furnace temperature control which uses the Fuzzy PID control strategy is obviously superior to the conventional PID control strategies, at the same time, the regulating time is shorter than PID control strategy, and less overshoot. 4 Conclusions In this paper, a kind of optimal fuzzy PID controller was presented. It is applied to resistance furnace temperature control system which has large inertia, time-varying and uncertain characteristics. From the results of simulation example, it is concluded that this kind of fuzzy PID controller is very effective. It has better performance than a conventional PID controller. It can be widely used to control different kinds of objects and processes.

2632 S. Wang et al. / Journal of Information & Computational Science 9: 9 (2012) 2627 2634 1.4 Step response 1.2 1.0 Amplitude 0.8 0.6 0.4 0.2 0 0 0.5 1.0 1.5 2.0 2.5 Time (sec) Fig. 7: Step responses of the PID control 1.4 Step response 1.2 1.0 Amplitude 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Time (sec) Fig. 8: Step responses of fuzzy PID control Acknowledgement This work was supported by the Tianjin Science and Technology Development Foundation for Colleges and Universities (No. 20110713).

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