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40220130405005

  1. 1. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 5, September – October (2013), © IAEME 47 PERFORMANCE ANALYSIS AND CONTROL DESIGN OF TWO DIMENSION FUZZY PID CONTROLLER 1* Manikandan P, 2* Geetha M, 3* Jubi K, 4** Hariprasath P, 5* Jovitha Jerome *Department of Instrumentation and Control Systems Engineering **Department of Electronics and Communication Engineering PSG College of Technology, Coimbatore, India ABSTRACT Tuning the parameters of PID controller is very important in system performance. Ziegler and Nichols tuning method is simple and cannot guarantee to be effective always. In order to overcome the parameter uncertainties, enhance the fast tracking performance of a process system, a brand-new two-dimension fuzzy PID controller, fuzzy PI+ fuzzy ID, is proposed in this paper. The self-tuning fuzzy PI+ fuzzy ID controller is fast; computing on-line easily and can reduce stability error. To demonstrate the effectiveness of the fuzzy PI+ fuzzy ID controller has been experimented to high order systems. The simulation and implementation were executed and its results show that the proposed control scheme not only enhances the fast tracking performance, but also increases the robustness of the system. From the simulation it is clear that there is substantial improvement in the Two Dimension Fuzzy PID (2D Fuzzy PID) controller in terms of peak overshoot, settling time, peak time, rise time, Integral Square Error (ISE) and Integral Absolute Error (IAE). Keywords- PID Controller; Fuzzy Logic, 2D Fuzzy PID; CSTR; ISE; IAE. 1. INTRODUCTION Process control is of vital importance in the operation of chemical, pharmaceutical, power plant, paper and bleach processes. Chemical process present many challenging control problems due to their nonlinear dynamic behavior and time varying parameters, constraints on manipulated variable, interaction between manipulated and controlled variables, unmeasured and frequent disturbances, dead time on input and measurements. Because of the inherent nonlinearity, most of the chemical process industries are in need of traditional control techniques. Fuzzy logic control (FLC) is one of the most successful applications of fuzzy set theory, introduced by L.A Zadeh in 1973 and applied (Mamdani 1974) in an attempt to control the system that are structurally difficult INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY (IJEET) ISSN 0976 – 6545(Print) ISSN 0976 – 6553(Online) Volume 4, Issue 5, September – October (2013), pp. 47-55 © IAEME: www.iaeme.com/ijeet.asp Journal Impact Factor (2013): 5.5028 (Calculated by GISI) www.jifactor.com IJEET © I A E M E
  2. 2. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 ISSN 0976 – 6553(Online) Volume 4, Issue 5, September to model. In the last three decades, FLC has evolved as an alternative or complementary to the conventional control strategies in various engineering areas. Fuzzy control theory usually provides non-linear controllers that are capable of performing different even for uncertain nonlinear systems. Unlike conventional control, designing a FLC does not require precise knowledge of the system model such as the poles and zeroes of the system transfer functions. Nonlinear tanks a in many process industries as storage of cryogenic liquids, fuels and other liquids also as surge tanks and find wide application in gas plants. Control of a level in a tank is important, because the change in shape gives rise to the nonlinearity. control due to its ability to incorporate human intuition in the design process. Three fuzzy controller [2] which has a good control effect and performance, needs great capacity in computing, and is not suitable for on fuzzy controller with neural network demands large quantity of training time. The parameters affecting its control effect primarily include gain factor, sca two dimensional fuzzy controller these factors are usually fixed. When the model or parameters of the object are changed, two dimensional fuzzy [3] can’t self-tune and the control performance becomes which has self-tuning function. For above reasons the paper puts forward a kind of controller of which factors can be self-adjusted according to the status and adopt a load observer to observe load torque. In order to evaluate the performance of the fuzzy PI+PD controller the paper adopts the ITAE index [4], rules of the fuzzy controller analysis born. The de together with phase surface [5]. There are several types of control s essential system component. The majority of applications during the past two decades belong to the class of fuzzy PID controllers. Several forms of decomposed proportional logic controllers (fuzzy P + fuzzy I + fuzzy D form, fuzzy PD + fuzzy I form, fuzzy PI + conventional D form, fuzzy P + conventional ID form and fuzzy PI + fuzzy PD form) have been tested and compared [1]. To obtain simple structures, the activities of the proportional, integral and derivative parts of the fuzzy PID controller are defined with simple rules in proportional rule base, integral rule base and derivative rule base. The analysis, design and simulation of the proposed self are described. The self-tuning fuzzy PI+ fuzzy ID controller is fast, computing on reduce stability error. Good control performance, both in the command robust of the level process, is achieved. This paper is organized in the fol II, the experimental setup is described. In Section III& IV, self scheme is presented. To verify the methodology, computer simulations and the discussions are provided in Section V. A brief conclu 2. STRUCTURE OF CONTROLLER 2.1 Coventional PID Controller The general expression of traditional PID controller can be stated as: The structure of PID controller is shown in Fig.2, where the error value e is the deviation of input and feedback values. The controller regulates the output according to the PID parameters. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 6553(Online) Volume 4, Issue 5, September – October (2013), © IAEME 48 model. In the last three decades, FLC has evolved as an alternative or complementary to the conventional control strategies in various engineering areas. Fuzzy control theory usually provides linear controllers that are capable of performing different complex non-linear control action, even for uncertain nonlinear systems. Unlike conventional control, designing a FLC does not require precise knowledge of the system model such as the poles and zeroes of the system transfer functions. Nonlinear tanks a in many process industries as storage of cryogenic liquids, fuels and other liquids also as surge tanks and find wide application in gas plants. Control of a level in a tank is important, because the change in shape gives rise to the nonlinearity. Fuzzy logic has gained great attention in the area of process control due to its ability to incorporate human intuition in the design process. Three fuzzy controller [2] which has a good control effect and performance, needs great capacity in computing, and is not suitable for on-line transaction for the design sophisticates. Self fuzzy controller with neural network demands large quantity of training time. The parameters affecting its control effect primarily include gain factor, scaling factor and proportion factor, and in a two dimensional fuzzy controller these factors are usually fixed. When the model or parameters of the object are changed, two dimensional fuzzy tune and the control performance becomes bad. So it needs to seek a kind of controller tuning function. For above reasons the paper puts forward a kind of controller of adjusted according to the status and adopt a load observer to observe load order to evaluate the performance of the fuzzy PI+PD controller the paper adopts the ITAE index [4], rules of the fuzzy controller analysis born. The de-fuzzy method is based on centroid together with phase surface [5]. There are several types of control systems that use FLC as an essential system component. The majority of applications during the past two decades belong to the class of fuzzy PID controllers. Several forms of decomposed proportional-integral- zzy I + fuzzy D form, fuzzy PD + fuzzy I form, fuzzy PI + conventional D form, fuzzy P + conventional ID form and fuzzy PI + fuzzy PD form) have been tested and compared [1]. To obtain simple structures, the activities of the proportional, integral and ivative parts of the fuzzy PID controller are defined with simple rules in proportional rule base, integral rule base and derivative rule base. The analysis, design and simulation of the proposed self-tuning fuzzy PI+ fuzzy ID controller tuning fuzzy PI+ fuzzy ID controller is fast, computing on-line easily and can reduce stability error. Good control performance, both in the command-tracking and parameters robust of the level process, is achieved. This paper is organized in the following manner. In Section II, the experimental setup is described. In Section III& IV, self-tuning fuzzy PI+ fuzzy ID control scheme is presented. To verify the methodology, computer simulations and the discussions are provided in Section V. A brief conclusion is outlined in Section V& VI. . STRUCTURE OF CONTROLLER The general expression of traditional PID controller can be stated as: The structure of PID controller is shown in Fig.2, where the error value e is the deviation of input and feedback values. The controller regulates the output according to the PID parameters. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), October (2013), © IAEME model. In the last three decades, FLC has evolved as an alternative or complementary to the conventional control strategies in various engineering areas. Fuzzy control theory usually provides linear control action, Unlike conventional control, designing a FLC does not require precise knowledge of the system model such as the poles and zeroes of the system transfer functions. Nonlinear tanks are used in many process industries as storage of cryogenic liquids, fuels and other liquids also as surge tanks and find wide application in gas plants. Control of a level in a tank is important, because the change Fuzzy logic has gained great attention in the area of process control due to its ability to incorporate human intuition in the design process. Three- dimensional fuzzy controller [2] which has a good control effect and performance, needs great capacity in line transaction for the design sophisticates. Self-organized fuzzy controller with neural network demands large quantity of training time. The parameters ling factor and proportion factor, and in a When the model or parameters of the object are changed, two dimensional fuzzy controllers bad. So it needs to seek a kind of controller tuning function. For above reasons the paper puts forward a kind of controller of adjusted according to the status and adopt a load observer to observe load order to evaluate the performance of the fuzzy PI+PD controller the paper adopts the ITAE fuzzy method is based on centroid ystems that use FLC as an essential system component. The majority of applications during the past two decades belong to the - derivative fuzzy zzy I + fuzzy D form, fuzzy PD + fuzzy I form, fuzzy PI + conventional D form, fuzzy P + conventional ID form and fuzzy PI + fuzzy PD form) have been tested and compared [1]. To obtain simple structures, the activities of the proportional, integral and ivative parts of the fuzzy PID controller are defined with simple rules in proportional rule base, tuning fuzzy PI+ fuzzy ID controller line easily and can tracking and parameters lowing manner. In Section tuning fuzzy PI+ fuzzy ID control scheme is presented. To verify the methodology, computer simulations and the discussions are (1) The structure of PID controller is shown in Fig.2, where the error value e is the deviation of input and feedback values. The controller regulates the output according to the PID parameters.
  3. 3. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 5, September – October (2013), © IAEME 49 Figure.1 Block diagram of PID controller Conventional linear PID controller signals in digital form can be represented by three controller actions with respect to the error response. The incremental controller output signal can be found by taking ‫ݑ‬ሺ݊ሻ ൌ ‫ݑ‬ሺ݊ െ 1ሻ ൅ ߂‫ݑ‬ሺ݊ሻ (2) ߂‫ݑ‬ሺ݊ሻ ൌ ‫݌ܭ‬ ‫כ‬ ߂݁ሺ݊ሻ ൅ ‫݅ܭ‬ ‫כ‬ ܶ‫ݏ‬ ߂݁ሺ݊ሻ ൅ ቀ ௄ௗ ்௦ ቁ ߂ଶ ݁ሺ݊ሻ (3) The error state variables are defined as, ݁ሺ݊ሻ ൌ ‫ݎ‬ሺ݊ሻ െ ‫ݕ‬ሺ݊ሻ (4) ߂݁ሺ݊ሻ ൌ ݁ሺ݊ሻ െ ݁ሺ݊ െ 1ሻ (5) ߂ଶ ݁ሺ݊ሻ ൌ ߂݁ሺ݊ሻ െ ߂݁ሺ݊ െ 1ሻ (6) Ts- sampling time, r(n) - desired response, y(n) - actual plant response, n - sampling instance (at time t=0, n=0, ∆e(0)=0), KP, KD and KI are Proportional, Derivative and Integral constants related to a linear PID controller. e(n)-error, ∆e(n)-error change, ߂ଶ e(n)-rate of error change. According to the Eq. (2), we can make up of the next structure. ‫ݑ‬ሺ݊ሻ ൌ ‫ݑ‬ሺ݊ െ 1ሻ ൅ ߂‫1ݑ‬ሺ݊ሻ ൅ ߂‫2ݑ‬ሺ݊ሻ (7) ߂‫1ݑ‬ሺ݊ሻ ൌ ‫݌ܭ‬ ‫כ‬ ߂݁ሺ݊ሻ ൅ ௄ௗ ଶ்௦ ߂ଶ ݁ሺ݊ሻ (8) ߂‫2ݑ‬ሺ݊ሻ ൌ ‫݅ܭ‬ ‫כ‬ ܶ‫ݏ‬ ‫כ‬ ߂݁ሺ݊ሻ ൅ ௄ௗ ଶ்௦ ߂ଶ ݁ሺ݊ሻ (9) 2.2 Self-Tuning Fuzzy PD+Fuzzy ID Controller Based on the Eq. (5), a new 2D Fuzzy PID controller, which are composed of fuzzy PD controller FC1 and fuzzy ID controller FC2, namely incremental fuzzy PD+ fuzzy ID, is designed. r(kt) the reference signal, y(kt) the process output, input variables, including error e(kt), change of error ec(kt), rate of change of error ed(kt), ∆u(kt) the output variables. GI (gain for error) is the input scalar for e(kt), GP (gain for error change) the input scalar for ec(kt), GD (gain for rate of error change) the input scalar for ed(kt) and GU (gain for controller output) the output scalar of the FLC.
  4. 4. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 5, September – October (2013), © IAEME 50 Figure.2 Block diagram of two dimension Fuzzy PID Controller 3. DEVELOPMENT OF TWO DIMENSION FUZZY PID CONTROLLER 3.1 Input Stage and Fuzzification The incremental fuzzy PD+ fuzzy ID controller employs three inputs: error e(kt), change of error ec(kt) and rate of change of error ed(kt).The inputs times the input scalars GP, GI, GD, they can express below. The fuzzy set error e(kt), the scaled change of error ec(kt) and the scaled rate of change of error ed(kt)’ has seven members PB(Positive Big),PM(Positive Medium), PS(Positive Small), Z(Zero), NS(Negative Small), NM(Negative Medium), NB(Negative Big). The scaled error e(kt), the scaled change of error ec(kt) and the scaled rate of change of error ed(kt) are within the range [-L,L] of the fuzzification algorithm shown in Fig.2. ‫݅ܩ‬ ‫כ‬ ݁ሺ݇‫ݐ‬ሻ ൌ ‫݅ܩ‬ ‫כ‬ ሺ‫ݎ‬ሺ݇‫ݐ‬ሻ െ ‫ݕ‬ሺ݇‫ݐ‬ሻሻ (10) ‫݌ܩ‬ ‫כ‬ ݁ܿሺ݇‫ݐ‬ሻ ൌ ‫݌ܩ‬ ‫כ‬ ሺ݁ሺ݇‫ݐ‬ሻ െ ݁ሺ݇ െ 1ሻ‫ݐ‬ሻሻ/ܶ (11) ‫݀ܩ‬ ‫כ‬ ݁ܿሺ݇‫ݐ‬ሻ ൌ ‫݀ܩ‬ ‫כ‬ ሺ݁ܿሺ݇‫ݐ‬ሻ െ ݁ܿሺ݇ െ 1ሻ‫ݐ‬ሻሻ/ܶ (12) 3.2 Ouput Stage and Fuzzification The incremental fuzzy PD+ fuzzy ID controller has two outputs, called the incremental control outputs and are denoted by ∆u1 (kt), ∆u2 (kt). The fuzzy set ‘output1’ and ‘output2’ has seven members PB(Positive Big),PM(Positive Medium), PS(Positive Small), Z(Zero), NS(Negative Small), NM(Negative Medium), NB(Negative Big) for the fuzzification of the incremental outputs of fuzzy control FC1 and FC2. The out of the incremental fuzzy PD+ fuzzy ID controller: ߂‫ݑ‬ሺ݇‫ݐ‬ሻ ൌ ‫1ݑܩ‬ ‫כ‬ ‫1ݑ‬ሺ݇‫ݐ‬ሻ ൅ ‫2ݑܩ‬ ‫כ‬ ‫2ݑ‬ሺ݇‫ݐ‬ሻ (13) y (k) edc ec FLC 1 FLC 2 PLANT FUZZ Y PD GP GD FUZZ Y ID GI GD r (k) e ∆U1(kt ) ∆U2(kt )
  5. 5. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 5, September – October (2013), © IAEME 51 3.3 Fuzzy Rule Base The control structure of the 49 control rules are established for the fuzzy PD controller (FC1) shown in the table 1. Using the aforementioned membership functions, the following control rules are established for the fuzzy PD controller (FC1). TABLE I. OUTPUT△u1 (kt) FUZZY CONTROL RULE TABLE △u1(kt) GI*e(kt) PB PM PS Z NS NM NB GP * ec(kt) NB Z Z NM NM PB PB PB NM PS Z NS NS PM PB PB NS PM PS Z Z PS PM PB Z PB PM PS Z PS PM PB PS PB PM PS Z Z PS PM PM PB PB PM NS NS Z PS PB PB PB PB NM NM Z Z The control structure of the 49 control rules are established for the fuzzy ID controller (FC2) shown in the table 2.Using the aforementioned membership functions, the following control rules are established for the fuzzy ID controller (FC2). TABLE II. OUTPUT △u2 (kt) FUZZY CONTROL RULE TABLE △u2(kt) G I* e(kt) NB NM NS Z PS PM PB GD* ed(kt) NB PB PM PB PB PB Z NB NM PM PS PM PM PM NS NB NS PS Z PS PS PS NM NM PS NM NB PS PS PS Z PS PM NB NS PM PM PM PS PM PB NB Z PB PB PB PM PB 4. RESULTS AND DISCUSSIONS Effectiveness of the proposed scheme is verified through simulation experiments on second and third-order processes [9] with dead-time (L). In addition to response characteristics, performance of the proposed Two dimension Fuzzy PID (2D FUZZY PID) is compared with those of ZN-PID and Conventional Fuzzy logic Controller (FLC) , with respect to a number of indices, such as percentage overshoot (%OS), integral-absolute-error (IAE), and time integral absolute error (ITAE). The detailed performance analysis for various types of processes is discussed below. 5.1 Linear processes In our simulation experiments, we consider the following second-order linear process used in [6, 9]: . )1( )( 2 Ts Ke sG Ls P + = − (14) Where, K is process gain, L is dead time, and T is time constant. For all the simulation examples, we have taken K = 1, T = 1.
  6. 6. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 5, September – October (2013), © IAEME 52 Fig.2 (a) shows the response characteristics of the process in (2) with L= 0.2s under ZN-PID, 2D FUZZY PID and TL-PID. Various performance indices for these PID controllers are recorded in Table I. Fig. 2(a) exhibits considerably improved performance of 2D FUZZY PID over ZN-PID and FLC, specifically during load disturbance. Table III clearly indicates the superiority of 2D FUZZY PID over ZN-PID, FLC. Figure 3. Response of the second-order linear process,a) L=0.2, b) L=0.3 To further study the robustness of the proposed controller, a 50% higher value of dead-time, i.e., L = 0:3s is considered with the same controller setting as that of L = 0:2s. Corresponding responses of different PID controllers are shown in Fig. 2(b), which also exhibits the same level of improvement in 2D FUZZY PID compared to ZN-PID and FLC. TABLE I: PERFORMANCE INDICES OF SECOND ORDER LINEAR PROCESS L 2D FUZZY PID ZN-PID FLC 0.2 % Overshoot 28.2 48.84 * IAE 70.49 71.3 87.56 ITAE 262.4 264.7 607.2 0.3 % Overshoot 29.28 71.0 * IAE 69.69 76.39 89.41 ITAE 288.1 341.5 717.6 * No overshoot 5.2 Second-order marginally stable process The transfer function of the second-order marginally stable process is given by ( ) (1 ) Ls P Ke G s s Ts − = + (15) Figs. 3(a) and 3(b) depict the responses of this integrating process with L = 0:2 s and 0.3 s, respectively and detailed performance comparison is illustrated in Table IV. Even for a 50% (a) (b) 0 5 10 15 20 25 30 35 0 0.5 1 1.5 Time 2D FUZZY ZN-PID FLC Responses 0 5 10 15 20 25 30 35 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time Responses 2D FUZZY ZN-PID FLC
  7. 7. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 5, September – October (2013), © IAEME 53 perturbation in dead-time i.e., for L = 0.3 s, 2D FUZZY PID still provides much better performance compared to ZN-PID and FLC. Figure 4. Response of the second-order marginally stable process,a) L= 0.3, b) L=0.4 TABLE I I: PERFORMANCE INDICES OF SECOND ORDER MARGINALLY STABLE PROCESS L 2D FUZZY PID ZN-PID FLC 0.3 % Overshoot 49.8 68.55 * IAE 73.3 75.99 92.97 ITAE 382.6 417.3 944.2 0.4 % Overshoot 57.8 83.22 * IAE 62.5 68.97 84.24 ITAE 394 482.7 1026 * No overshoot 5.3 Third-order linear process A second-order plus dead-time (SOPDT) model is usually considered to be a fair approximation for most of the industrial processes. However, to study the effectiveness of the proposed scheme, third-order linear process models are also tested. The transfer function of such a linear system is: 3 )1( )( Ts Ke sG Ls P + = − (16) Figs. 4(a) and 4(b) depict the responses of the third-order linear process in (8,4) with L = 0:2s and 0.3s, respectively and various performance indices of 2D FUZZY PID, ZN-PID and FLC are provided in Table V. Results reveal that there is a considerable improvement in %OS compared to ZN-PID. (a) (b) 0 5 10 15 20 25 30 35 40 45 50 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Time Responses 2D FUZZY ZN-PID FLC 0 5 10 15 20 25 30 35 40 45 50 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time Responses 2D FUZZY ZN-PID FLC
  8. 8. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 5, September – October (2013), © IAEME 54 Figure 5. Response of third-order linear process with a) L = 0.4 b) L=0.5 TABLE I I I: PERFORMANCE INDICES OF THIRD - ORDER LINEAR PROCESS L 2D FUZZY PID ZN-PID FLC 0.4 % Overshoot 19.3 33.18 * IAE 84.0 84.43 115.7 ITAE 515.9 512.6 1575 0.5 % Overshoot 25.58 40.15 * IAE 65.98 67.27 99.1 ITAE 511.7 517.7 1640 * No overshoot From the above results for various processes it is evident that in each case the proposed 2D FUZZY PID shows consistently improved overall performance compared to ZN-PID and FLC under both set-point change and load disturbance. 6. CONCLUSION The adaptive self-tuning fuzzy PI+ fuzzy ID controller is fast, computing on-line easily and can reduce stability error. The results show that the proposed control scheme not only enhances the fast tracking performance, but also increases the robustness of the process plant. Thus Fuzzy PID can be applied not only to precise process control, as its results shows it can be applied to obtain control with precision in various other applications like Medical robotics, Industrial Testing and measurements. 7. REFERENCES [1]. M. Golob, Decomposed fuzzy proportional-integral-derivative controllers, Applied Soft Computing, vol. 1, Issue 3, pp. 201-214, Dec. 2001. [2]. Mudi, R. K., Pal, N. R.,A Robust Self-Tuning Scheme for PI and PD Type Fuzzy Controllers, IEEE Trans. on Fuzzy Systems,Vol.7, pp.2--16 ,1999. (a) (b) 0 10 20 30 40 50 60 70 80 0 0.5 1 1.5 Time Responses 2D FUZZY ZN-PID FLC 0 10 20 30 40 50 60 70 80 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Time 2D FUZZY Z-N FLC
  9. 9. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 4, Issue 5, September – October (2013), © IAEME 55 [3]. Palm, R., Scaling of Fuzzy Controller Using the Cross-Correlation, IEEE Trans. on Fuzzy Syst,Vol.3, pp.116--123 ,1995. [4]. Mudi R. K., Pal, N. R., A Self-Tuning Fuzzy PI Controller, Fuzzy Sets and Systems,Vol.115, pp.327--338 ,2000. [5]. Mudi, R.K., Pal, and N. R., A Self-Tuning Fuzzy PD Controller, IETE Journal of Research,(Special Issue on Fuzzy Systems), pp.177—189, 1998. [6]. Pal, A.K., Mudi, and R.K.,Self-Tuning Fuzzy PI controller and its application to HVAC system, IJCC (US),vol. 6,2008. [7]. Palm, R.,Sliding Mode Fuzzy Control, Proc. 1st IEEE Int. Conf. on Fuzzy Systems,pp. 519-- 526 ,1992. [8]. K.H. Ang. G. Chong., and Y. Li, PID control system analysis, design, and technology, IEEE Transaction on control system technology, vol.13, No.4, pp.559-576, 2005 [9]. K.J. Astrom and T. Hagglund, PID controller: Theory, Design and Tuning, USA, Instrument Society of America, 1995 [10]. C. Dey and R.K. Mudi, ‘An improved auto-tuning scheme for PID controllers’, ISA Transactions, vol. 48, no. 4, pp. 396-409, 2009 [11]. VenkataRamesh.Edara, B.Amarendra Reddy, Srikanth Monangi and M.Vimala, “Analytical Structures for Fuzzy Pid Controllers and Applications”, International Journal of Electrical Engineering & Technology (IJEET), Volume 1, Issue 1, 2010, pp. 1 - 17, ISSN Print: 0976-6545, ISSN Online: 0976-6553. [12]. B.Rajani and Dr.P.Sangameswara Raju, “Comparision of Pi, Fuzzy & Neuro-Fuzzy Controller Based Multi Converter Unified Power Quality Conditioner”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 2, 2013, pp. 136 - 154, ISSN Print: 0976-6545, ISSN Online: 0976-6553. [13]. L.Raguraman and A.Gnanasaravanan, “Performance Optimization and Comparison of Variable Parameter using Genetic Algorithm Based Pid Controller”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 4, 2013, pp. 42 - 47, ISSN Print: 0976-6545, ISSN Online: 0976-6553.

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