An Expert System Based PID Controller for Higher Order Process

An Expert System Based PID Controller for Higher Order Process K.Ghousiya Begum, D.Mercy, H.Kiren Vedi Abstract The proportional integral derivative (PID) controller is the most widely used control strategy in industry. The popularity of PID controllers can be attributed partly to their robust performance in a wide range of operating conditions and partly to their functional simplicity. This paper presents design of PID controller using Ziegler-Nichols (ZN) technique for higher order system. But several industrial processes have the dead-time effect produced due to measurement delay or due to the approximation of higher order dynamics of the process by a simple transfer function model. This delay degrades the stability of the whole system So a Fuzzy logic controller using simple approach & smaller rule set is proposed. Its effects is compared and still improved by using a combination of PID and Fuzzy control. Index Terms-PID controller,zeigler-nichols tuning, Fuzzy logic controller, High Dead time, tuning, simulation However, the PID control [3] is crisp control, the self-turning of the P, I, D parameters is a quite difficult job, and sometimes the PID control makes overshoot, and also with regard to the temperature, level control system the characteristics of which are distributed parameter, nonlinear, large time delay and large inertia, the conventional PID controller is very difficult to obtain satisfactory control results.in order to solve this problem,[13] a control method which uses the fuzzy logic technology is proposed in this paper. Fuzzy controller [16] can make full use of the successful operation experience of the operator which they get in real time non-linear adjustment. Also it can give full play to the fine control effect of the PID controller, makes the whole system to achieve the good control effect. So, the paper also proposes the method of fuzzy logic, for tuning the PID controller gain parameters. I. INTRODUCTION The proportional integral derivative (PID) [7] controller operates the majority of the control system in the world. It has been reported that more than 95% of the controllers in the industrial process control applications are of PID type as no other controller match the simplicity, clear functionality, applicability and ease of use offered by the PID controller. The PID controller [1] is used for a wide range of problems like motor drives, automotive, flight control, instrumentation etc. PID controllers provide robust and reliable performance for most systems if the PID parameters are tuned properly. Various tuning methods are present. Among the tuning methods, the Ziegler-Nichols (ZN) technique has been very influential. Ziegler-Nichols presented two tuning methods, a step response method and a frequency response method. The frequency response method is more reliable than the step response method. In this paper, we will investigate frequency response method for higher order system. II. GENERALIZED MODEL FOR CONVENTIONAL FORM OF PID CONTROLLER A standard PID controller [8] is also known as the three-term controller, whose transfer function is generally written in the ideal form as G PID (s) = Kp ( 1 + 1/T I s+ T D s) (1) = Kp + K I /s + K D s and the output response is U(t) = Kp e(t) + Kp / T I e (t) dt + Kp T D d e(t) / dt (2) where K is the proportional gain, KI the integral gain, KD the derivative gain, TI the integral time constant and, TD the derivative time constant. Such a controller has three different adjustments (Kp, TI, & TD), which interact with each other. For this reason, it is very difficult and time consuming to tune these three parameters in order to get best performance according to the design specification of the system. III.SYSTEM DESIGN WITH PID CONTROLLER Manuscript received Oct 8, 2012. K.Ghousiya Begum, Electronics and Instrumentation Dept,, M.A.M College of Engineering.,(ghousiyabegum.k@gamil.com) Tiruchirappalli., India,,9788530064. D.Mercy, Electronics and Instrumentation Dept,M.A.M College of Engineering.,(mercyprabhu@gamil.com) Tiruchirappalli., India,,9842270067.H.Kiren Vedi, Electronics and Instrumentation Dept, M.A.M College of Engineering.,(kavikiren@gamil.com) Tiruchirappalli., India,,8973084866 A P,PI, PID controller is being designed for a higher order system [12] and [14] with transfer function given as G(s) = 1.5 e -9 s S 3 +4s 2 +4s (3) 46

Fig.2 Step Response for Kp=0.422 The above response clearly shows that sustained oscillation occurs for Kp = Ku = 0.422.The ultimate period Pu obtained from the time response is 40. The value of controller parameters are Fig.1 MatLab Simulink Model of P,PI,PID Controller Tuning of conventional controller [4] has been done by the Ziegler Nichols Method, closed loop tuning rules which is used in mostly all the Industrial PID Tuning. TABLE I TABLE II Controller Kp K I K D P 0.211 - - PI 0.19 0.0057 - PID 0.25 0.013 1.266 Controller Kp K I K D P 0.5Ku - - PI 0.45Ku 1.2 Kp / Pu - PID 0.6Ku 2 Kp / Pu Kp Pu / 8 By setting integral & derivative terms to be zero and using the proportional control action Kp only, the value of gain is increased from 0 to a critical value Ku at which the output first exhibits oscillations. Tu is the corresponding period of oscillation. The unit step responses for different values of gain Kp were observed. The step response for the Kp = 0.422 is shown in Fig. 2. Fig.3 Response of Conventional PID 47

The time response characteristics were depicted from the above response. Controller TABLE III Rise Time Settling Time P 10.5 125 29 PI 9 180 72 PID 7 150 69 Maximum Overshoot IV. DESIGN OF FUZZY LOGIC CONTROLLER (FLC) Simulink model of the fuzzy controller[16] the plant with unity feedback is shown in Fig.4. Fig.5 Fuzzy Interference Editor Fig.4 System with Fuzzy Logic controller The fuzzy set is defined by a function that maps objects in a domain of concern to their membership value in the set. Such a function is called membership function. Figure 5, shows the selection of number of inputs and outputs in the form of membership functions in order to design FIS. So, it resembles the selection of two inputs - error, error change, and one output - control signal. For a two input fuzzy controller, 3,5,7,9 or 11 membership functions for each input are mostly used. In this paper, only two fuzzy membership functions are used for the two inputs error e and the derivative of error e as shown in Fig.6. Fig.6 Membership functions for input e & e The fuzzy membership functions for the output parameter are shown in Fig.7 where N means Negative, Z means Zero and P means Positive.Fig.8 shows its response with steady state error. Figure 6, shows the Fuzzy Membership function editor, [17]where the number of membership functions, and type of membership function is chose, such as trapezoidal, triangular, and Gaussian according to the process parameter. The fuzzy logical operation is Fuzzification. There are basically two Fuzzification methods namely, Mamdani and Sugeno, and generally used Defuzzification methods are Adaptive integration, Center of area, Center of gravity, Fuzzy clustering Defuzzification, First of maximum, Last of maximum, Mean of maxima, Semi-linear Defuzzification, Quality method, Middle of maximum. The maxima methods are good candidates for fuzzy reasoning systems[4]. The distribution methods and the area methods exhibit the property of continuity that makes them suitable for fuzzy controllers [17] and [18] Fig.7 Menbership Function for output 48

Fig.8 Output Response obtained using FLC V. DESIGN OF FUZZY LOGIC PID CONTROLLER (FLPIDC) Fig.10 Fuzzy membership function editor for Fuzzy-PID controller Parameters of traditional PID always obtained by testing methods, these methods need long time to debugging and have low precision, cannot satisfy the requirements of the practical. Based on this in recently years, many researchers put forward many new PID control strategies based on some intelligent algorithms especially using fuzzy logic concepts[18] and [17]. Figure 9, shows the design of the system with Fuzzy-PID controller where the gain values of PID controller are tuned by Fuzzy controller. And Figure10, 11 shows, the Fuzzy membership function editor for the selection of number of membership functions and type, range of each membership function and the output response. Fig.11 Output Response of Fuzzy-PID controller VI. RESULTS TABLE IV. COMPARING VARIOUS TIME DOMAIN SPECIFICATIONS Fig.9 Fuzzy-PID controller Controller Time Domain Specifications Rise Time Settling Overshoot % secs Time secs PID 10 150 60 FLC Steady State Error exists (doesn t reach the settling point) FLPIDC 15 60 30 49

VI. CONCLUSION This paper represents the PID controller tuning using the Zeigler Nichols method which is inefficient as its settling time & overshoot is high.therefore we go for fuzzy logic controller. In that steady state error exists.hence we go for fuzzy PID controller which provides better results. The comparison between the three methods are shown here. Through the simulation the three controllers perform a search to obtain optimal results in which Fuzzy PID enhances its performance criterion in terms of settling time, percentage of overshoot. REFERENCES [1] Astrom, K.J., and Hagglund, T.: Automatic tuning of PID controllers (ISA, 1988) [2] Ziegler, J.G., and Nichols, N.B.: Optimum settings for automatic controllers, Trans. ASME 1942, 64, pp. 759-768 [3] Ho, W.K., Hang, C.C,, and Cao, L.S.: Tuning of PID controllers based on gain and phase margin specifications, Automatica, 1995, 31, (3), pp. 497-502 [4] Astrom, K.J., and Hagglund, T.: PID controllers: theory, design, and tuning (Instrument Society of America, 1995, 2nd edn.) [5] K. Ogata, Modern Control Engineering, Prentice Hall,New Jersey, 2002. [6] R. S. Barbosa, J. A. Tenerio, Machado and Isabel. M. Ferreira, Tuning of PID controllers based Bode s Ideal transfer function, Nonlinear Dynamics, vol. 38, pp.305-321, 2004. [7] D. Xue, Y.Q. Chen, D. P. Atherton Linear Feedback Control Analysis and Design with MATLAB, Advances in Design and Control, Siam, 2007. [8] Cvejn, J., 2009. Sub-optimal PID controller settings for FOPDT systems with long dead time. Journal of process control 19. [9] Valério, D. and Costa, J. S. (2006). Tuning of fractional PID controllers with Ziegler-Nichols-type rules. Signal Processing, Vol. 86, 2771-2784. [10] Tan, K.K., Huang, S. and Ferdous, R. (2002). Robust selftuning PID controller for nonlinear systems. Journal of Process Control, Vol.12, 753-761. [11] G. K. I. Mann, B. G. Hu, and R. G. Gosine, Time-domain based design and analysis of new PID tunin g rules, Proc. Inst. Elect. Eng. Control Theory and Applications, vol. 148, no. 3, pp. 251 261, 2001 [12] V.R.Ravi, T.Thyagarajan, A Decentralized PID controller for interacting non-linear systems. ICETECT 2011 pp 297-302. [13] S.Nithya, N.Sivakumaran, T.K.Radhakrishnan, N.Anantharaman, Control of nonlinear process usingsoft Computing IUP 2010. [14] S.Nithya, Abhay Singh Gour, N.Sivakumaran, T.K.Radhakrishnan, T.Balasubramanian, N.Anantharaman Design of Intelligent controllers for nonlinear processes,ajaps,2008.pp 33-45. [15] V.R.Ravi,T.Thyagarajan, Application of adaptive control technique to interacting Non Linear Systems, IEEE 2011 pp 386-392. [16] Gang Feng, Analysis and Synthesis of Fuzzy Control Systems: A Model Based Approach, Automation and Control Engineering Series, CRC Press, Taylor and Francis, 2010. [17] P. Melba Mary and N.S. Marimuthu, Design of self-tuning fuzzy logic controller for the control of an unknown industrial process, IET Control Theory Appl., 2009, Vol. 3, Iss. 4, pp. 428 436. [18] Fuzzy Logic based Intelligent Controller Design for Injection Mould Machine Process control, IJAEST, Vol No. 10, Issue No. 1, 098-103 AUTHOR S PROFILE K.Ghousiya Begum Assistant Professor, EIE Dept, B.E (EIE), M.E (Applied Electronics), Paper published in International Conference ICES 12 proceedings Temperature measurement using LabVIEW and SMS D.Mercy Associate Professor, EIE Dept, B.E (EIE), M.Tech(Control Systems and Instrumentation), Paper published in ICES 12 proceedings Temperature measurement using LabVIEW and SMS. H.KirenVedi Associate Professor, EIE Dept, B.E (EIE), M.E (Process Control and Instrumentation), Paper published in ICES 12 proceedings Temperature measurement using LabVIEW and SMS.. 50