Parallel Fuzzy P+Fuzzy I+Fuzzy D Controller: Design and Performance Evaluation

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1 International Journal of Automation and Computing 7(4), November 200, DOI: 0.007/s Parallel Fuzzy P+Fuzzy I+Fuzzy D Controller: Design and Performance Evaluation Vineet Kumar A. P. Mittal Department of Instrumentation and Control Engineering, Netaji Subhash Institute of echnology, Sector-3, Dwarka, New Delhi 007, India Abstract: In this paper, a parallel fuzzy proportional plus fuzzy integral plus fuzzy derivative (FP+FI+FD) controller is proposed. It is derived from the conventional parallel proportional-integral-derivative (PID) controller. It preserves the linear structure of a conventional parallel PID controller, with analytical formulas. he final shape of the controller is a discrete-time fuzzy version of a conventional parallel PID controller. Computer simulations are performed to evaluate the performance of the FP+FI+FD controller for setpoint tracking and load-disturbance rejection for some complex processes, such as first- and second-order processes with delay, inverse response process with and without delay and higher order processes. Also, the performance of the proposed fuzzy controller is evaluated experimentally on highly nonlinear liquid-flow process with a hysteresis characteristic due to a pneumatic control valve. he simulation and real time control is done using National Instrument M hardware and software (LabVIEW M ). he response of the FP+FI+FD controller is compared with the conventional parallel PID controller, tuned with the Ziegler-Nichols (Z-H) and Åström- Hägglund (A-H) tuning technique. It is observed that the FP+FI+FD controller performed much better than the conventional PI/PID controller. Simulation and experimental results demonstrate the effectiveness of the proposed parallel FP+FI+FD controller. Keywords: Proportional-integral-derivative (PID), fuzzy proportional plus fuzzy integral plus fuzzy derivative (FP+FI+FD) controller, liquid-flow process, inverse response process, dead time. Introduction Manuscript received May 3, 2009; revised September 28, 2009 Conventional parallel proportional-integral-derivative (PID) controller is the most popular controller among process industry. Despite a lot of research and a large number of different solutions proposed, most industrial control systems are still based on conventional parallel PID regulators. Different sources estimate the share taken by PID controllers at between 90 and 99%. he main reason is due to their low cost, inexpensive maintenance, simplicity of operation, ease of design, and effectiveness for most processes [ 3]. However, conventional PID controllers cannot provide a general solution to all control problems. he processes involved are, in general, complex and time-variant, with delays and nonlinearity, and often with poorly defined dynamics. When the process becomes too complex to be described by analytical models, it is unlikely to be efficiently controlled by conventional approaches. o overcome these difficulties, various types of modified conventional PID controllers such as autotuning and adaptive PID controllers were developed lately [2, 3]. Also, a class of nonconventional type of PID controllers employing fuzzy logic has been designed and simulated for this purpose [2, 4 8]. Fuzzy logic controller (FLC) has emerged as one of the most active and useful research areas in the fuzzy control theory. hat is why fuzzy logic controllers have been successfully applied for control of various physical processes. Basically, there are two approaches to a fuzzy controller design: an expert approach and a control engineering approach. [2, 9 2] Chen et al. proposed a fuzzy PI/PD controller, which preserved the linear structure of a PID controller, with simple analytical formulas as the final result. Further, Chen et al. [0, 3] developed a fuzzy PI+D controller, which was a combination of fuzzy PI and Fuzzy D controller having the same structure as mentioned earlier. hey performed derivative function on a controlled variable rather than error signal. Kim and Oh [4] proposed another configuration of a fuzzy PID controller (fuzzy PI + fuzzy ID) with the same structure as discussed above [9]. Also, Lu et al. [3] performed an experiment to evaluate the performance of a fuzzy PD controller in real time. In continuation of this, ang et al. [] developed an optimal fuzzy PI+D controller having the same structure. Another controller, fuzzy I-PD, is proposed by Chatrattanawuth et al. [6] with the same structure. Here, an integral function is performed on error signal, while a proportional and derivative function is performed on the controlled variable. In this paper, a new configuration of a fuzzy PID controller i.e., parallel FP+FI+FD controller, is proposed, with the linear structure of a PID controller and having simple analytical formulas. First, the parallel FP+FI+FD controller is derived from the conventional parallel PID controller, and then, the fuzzification, control rules and defuzzification are discussed. Computer simulation and real time experiment are performed to evaluate the performance of the proposed parallel FP+FI+FD controller for setpoint tracking and load-disturbance rejection in closedloop. Some complex processes, such as first order plus dead time (FOPD), second order plus dead time (SOPD), inverse response process with and without delay and higher order processes are considered for simulation. he performance of the parallel FP+FI+FD controller is compared with the conventional parallel PID controller, tuned with Ziegler-Nichols (Z-N) and Åström-Hägglund (A-H) relay based tuning method. It is observed that the proposed par-

2 464 International Journal of Automation and Computing 7(4), November 200 allel FP+FI+FD controller outperformed the conventional parallel PID controller both in simulation and experiment. 2 Derivation of FP+FI+FD control law In this section, the structure of the conventional PID controller and the FP+FI+FD controller will be discussed. he derivation of the individual fuzzy controller (fuzzy P, fuzzy I, and fuzzy D) is carried out based upon the respective conventional digital PID controller. Here, bilinear transformation is used to convert the conventional continuous-time I and D controllers to the corresponding digital controller because it assures a better approximation of a continuous-time model by a discrete-time model in the frequency domain than the replacement of differentiation by a difference [7]. he FP+FI+FD controller combines the individual fuzzy controllers in a proper way, as discussed in more detail in the subsequent sections. 2. Fuzzy P controller he output of the conventional continuous-time P controller, as shown in Fig., is given by u P (t) = K Ce(t) where e(t) = y SP (t) y(t) is the error signal; u P (t) is the output of the proportional controller, and K C is the proportional constant. In frequency s-domain, the above equation becomes u P (s) = K Ce(s). () he discrete version of the above equation is u P (z) = K Ce(z) (2) and then taking the inverse z-transform of the above equation, u P (n ) = K Ce(n ). (3) where Kp = K C and Kp 2 = K are constant. In order to increase the degree of freedom, an additional gain K UP is introduced in the output of the fuzzy P controller. herefore, the fuzzy P control action becomes u P (n ) = K UP u P (n ). 2.2 Fuzzy I Controller he output of the conventional continuous-time I controller, as shown in Fig., is given by u I(t) = KC e(t)dt τ I where τ I is the integral time constant; u I(t) is the output of the integral controller, and e(t) is the error signal. In frequency s-domain, the above equation becomes or u I(s) = KC τ I s e(s) u I(s) = K I e(s) (6) s where K I = K C/τ I is the controller gain. he above equation can be transformed into the discrete form by applying the bilinear transformation s = (2/ )(z )/(z + ), where > 0, is the sampling period [0], which results in the following form: u I(z) = ( KI 2 + KI )e(z). (7) z Letting K = K I and Ki 2 = K I /2 and then taking the inverse z-transform of the above equation, we get u I(n ) u I(n ) = K e(n ) K 2 i (e(n ) e(n )). Dividing the above equation by, u I(n ) u I(n ) or = K e(n (e(n ) e(n )) ) K2 i u I(n ) = K i e(n ) K 2 i r(n ) (8) Fig. he conventional parallel P+I+D (PID) control system It is clear from the above equation that the only information it contains relevant to the output performance is K Ce(t). Based on this signal alone, it is not possible to come up with a practically useful fuzzy control action. herefore, another component K e(t) should be added in the above control signal, so that the information of the direction of the response (upward or downward motion) can be obtained [0]. Equation (3) becomes u P (n ) = K Ce(n ) + K e(n ) (4) where e(n ) = e(n ) e(n ) and K is a constant. u P (n ) is the fuzzy P control action signal. Further rewriting (4) u P (n ) = K pe(n ) + K 2 p e(n ) () where u I(n ) = r(n ) = ui(n ) ui(n ) (e(n ) e(n )) (9) (0) where u I(n ) is the incremental control output of the integral controller, e(n ) is the error signal, Ki = K / is a constant and r(n ) is the rate of change of the error signal. Rewriting the (9) as u I(n ) = u I(n ) + u I(n ). he term u I(n ) is replaced by the fuzzy control action K UI u I(n ). So, the above equation becomes u I(n ) = u I(n ) + K UI u I(n ) where K UI is a fuzzy I controller gain.

3 V. Kumar and A. P. Mittal / Parallel Fuzzy P+Fuzzy I+Fuzzy D Controller: Design and Performance Evaluation 46 Fig. 2 he parallel FP+FI+FD control system 2.3 Fuzzy D controller he output of the conventional continuous-time D controller, as shown in Fig., is given by u D(t) = K Cτ D de(t) dt where τ D is the derivative time constant; u D(t) is the output of the derivative controller, and e(t) is the error signal. In frequency s-domain, the above equation becomes or u D(s) = K Cτ Dse(s) u D(s) = K Dse(s) () where K D = K Cτ D is the controller gain. Using bilinear transformation [6, 0], the above equation becomes 2 z u D(z) = K D e(z). + z aking the inverse z-transform of the above equation, we get 2 u D(n ) + u D(n ) = K D (e(n ) e(n )). Dividing the above equation by, where u D(n ) = u D(n ) = K dr(n ) (2) ud(n ) + ud(n ) (3) is the incremental control output of the fuzzy D controller, r(n ) is the rate of change of the error signal and K d = 2K D/. It is clear from the above equation that the only information it contains relevant to the output performance is K dr(n ). Based on this signal alone, it is not possible to come up with a practically useful fuzzy control action. herefore, another component K 2 de(n ) is added to the equation, which could give information whether response is above or below the reference signal [6, 0]. Equation (2) becomes he term u D(n ) is replaced by the fuzzy control action K UD u D(n ). hus, the above equation becomes u D(n ) = u D(n ) + K UD u D(n ). where K UD is a fuzzy D controller gain. 2.4 Combination of FP+FI+FD controller Finally, the fuzzy P + fuzzy I + fuzzy D control action can be obtained by algebraically summing fuzzy P control action, fuzzy I control action, and fuzzy D control action simultaneously. he resultant control action is u P ID(n ) = u P (n ) + u I(n ) + u D(n ) u P ID(n ) = K UP u P (n ) + u I(n ) + K UI u I(n ) u D(n ) + K UD u D(n ). () he parallel FP+FI+FD control system is shown in Fig FP+FI+FD controller design In this section, the FP+FI+FD controller design will be described. 3. Fuzzification In the fuzzification, K pe(n ) and K 2 p e(n ) are the fuzzy P controller inputs, K i e(n ) and K 2 i r(n ) are the fuzzy I controller inputs, and K dr(n ) and K 2 de(n ) are the fuzzy D controller inputs. he number of input membership functions used in input scaling is 2 (n: negative and p: positive). Since the proposed fuzzy P, fuzzy I, and fuzzy D controllers have a similar structure, the membership functions of all inputs are similarly selected as shown in Fig. 3, where L is the adjustable constant. u D(n ) = K dr(n ) + K 2 de(n ) (4) Also, rewriting (3) as u D(n ) = u D(n ) + u D(n ). Fig. 3 Input membership functions

4 466 International Journal of Automation and Computing 7(4), November Fuzzy control rule Generally, fuzzy control rules are made in two ways. Either these rules are based on expert experience or control engineer knowledge. In the present work, the fuzzy control rules are based on control engineer knowledge, and each fuzzy controller (fuzzy P, fuzzy I, and fuzzy D) block consists of four fuzzy control rules. he output membership functions for u p(n ), u I(n ), and u D(n ) are chosen as shown in Fig. 4. he number of output membership functions is 3 (on: output negative, oz: output zero, and op: output positive), where L is the adjustable constant. he control rules are based on the characteristics of the step response [0]. Based on the input membership functions in fuzzification and these output membership functions, the number of the fuzzy control rules for the fuzzy P controller is 4, which are R : If K pe(n ) is n and K 2 p e(n ) is n then u P (n ) is oz. R 2 : If K pe(n ) is n and K 2 p e(n ) is p then u P (n ) is op. R 3 : If K pe(n ) is p and K 2 p e(n ) is n then u P (n ) is on. R 4 : If K pe(n ) is p and K 2 p e(n ) is p then u P (n ) is oz. Similarly, fuzzy control rules for the fuzzy I controller are as follows fuzzy controller outputs based on the present defuzzification method are as follows: u P (n ) = u I(n ) = u D(n ) = µ Pr u Pr r= µ Pr r= µ Ir u Ir r= µ Ir r= µ Dr u Dr r= µ Dr r= (6) where µ Pr, µ Ir, and µ Dr are the membership values at the r-th rule, and u Pr, u Ir, and u Dr are the singleton outputs at the r-th rule. he regions of the fuzzy P, fuzzy I, and fuzzy D controller s input-combination (IC) values are graphically shown in Figs. 7, respectively. he region for each fuzzy controller can be decomposed into 2 different regions (ICs). he results of u P (n ), u I(n ), and u D(n ) are obtained by applying defuzzification algorithm, as presented in (6), to each membership area. he expressions of u P (n ), u I(n ), and u D(n ) in IC I to IC XII regions are shown in able, respectively. R : If K i e(n ) is n and K 2 i r(n ) is n then u I(n ) is on. R 2 : If K i e(n ) is n and K 2 i r(n ) is p then u I(n ) is oz. R 3 : If K i e(n ) is p and K 2 i r(n ) is n then u I(n ) is oz. R 4 : If K i e(n ) is p and K 2 i r(n ) is p then u I(n ) is op. Similarly, fuzzy control rules for the fuzzy D controller are as follows R : If K 2 de(n ) is n and K dr(n ) is n then u D(n ) is oz. R 2 : If K 2 de(n ) is n and K dr(n ) is p then u D(n ) is on. R 3 : If K 2 de(n ) is p and K dr(n ) is n then u D(n ) is op. R 4 : If K 2 de(n ) is p and K dr(n ) is p then u D(n ) is oz. Mamdani inference mechanism is used in each fuzzy rule to determine its outcome. Fig. Regions of fuzzy P controller input-combinations Fig. 4 Output membership functions 3.3 Defuzzification In this work, the center of mass method is used as the defuzzification algorithm. It is used to calculate the output u P (n ) of the fuzzy P controller, the incremental control output u I(n ) of the fuzzy I controller and u D(n ) of the fuzzy D controller [6, 0]. herefore, the respective Fig. 6 Regions of fuzzy I controller input-combinations

5 V. Kumar and A. P. Mittal / Parallel Fuzzy P+Fuzzy I+Fuzzy D Controller: Design and Performance Evaluation 467 able Analytical formulas for the 2 IC regions for fuzzy P, fuzzy I, and fuzzy D controllers IC# Fuzzy P controller output u P (n ) Fuzzy I controller output u I (n ) Fuzzy D controller output u D (n ) L[K 2 p IC I & IC III e(n ) K pe(n )] L[K i e(n ) + K2 i r(n )] ] 2[2L Kp e(n ) 2[2L L[K 2 d e(n ) K dr(n )] Ki e(n ) ] 2[2L Kd 2e(n ) ] IC II & IC IV L[K 2 p e(n ) K pe(n )] ] 2[2L Kp 2 e(n ) L[Ki e(n ) + K2 i r(n )] 2[2L Ki 2r(n ) ] L[K 2 d e(n ) K dr(n )] 2[2L Kd r(n ) ] IC V 2 [ L + K2 p e(n )] 2 [L + K2 i r(n )] 2 [L K dr(n )] IC VI 0 L 0 IC VII 2 [L K p e(n )] 2 [L + K i e(n )] 2 [ L + K2 de(n )] IC VIII L 0 L IC IX 2 [L + K2 p e(n )] 2 [ L + K2 i r(n )] 2 [ L K dr(n )] IC X 0 L 0 IC XI 2 [ L K p e(n )] 2 [ L + K i e(n )] 2 [L + K2 de(n )] IC XII L 0 L Fig. 7 Regions of fuzzy D controller input-combinations 4 Computer simulation results In order to evaluate the effectiveness of the proposed parallel FP+FI+FD controller, computer simulations are carried out for some complex processes in closed-loop, using National Instrument M software, LabVIEW M and its addons. A unit step change is introduced in setpoint and load disturbance at an interval of time to see the transient behaviour of processes. he preferences of performance criteria, for the present work, are minimizing the settling time, percentage overshoot, integral square of error (ISE), integral of absolute error (IAE), and rise time. he conventional PID controller is tuned using the Z- N and A-H tuning technique. he Z-N has proposed two classical methods. he first method is based upon openloop response of the system and the second method is based upon the closed-loop response (frequency response method). hese methods are still widely used in industries, either in some original form or in some modified form. Astrom and Hagglund proposed another closed-loop technique to determine the two important system constants, i.e., the ultimate period and the ultimate gain. Also, many other methods are proposed based upon the step response of the open-loop system, such as Coon-Cohen. he frequency response method is more reliable than the step response method because ultimate gain and period are easier to determine accurately [8, 9]. In the present work, Z-N frequency response based method and A-H relay based method are used to tune the PID controller. In order to have a parallel structure of the fuzzy PID controller, such as the conventional parallel PID controller, the number of parameters increases in the proposed parallel FP+FI+FD controller. But, it also increases the degree of freedom of the FP+FI+FD controller. Now, due to increase in the degree of freedom, the user has more flexibility to achieve the desired response. he different fuzzy parameters are tuned manually, and their values are tabulated in able 2. he conventional controller performs better among the conventional P/PI/PID controllers, and is considered for comparison with the proposed FP+FI+FD controller. he comparison of the setpoint and load disturbance responses obtained on applying conventional PI/PID and FP+FI+FD controllers is presented next. Dead time (time delay or transportation lag) is found in many processes in industry. Generally, time delays are mainly caused by the time required to transport mass, energy or information. For processes exhibiting transportation lag or dead time, every action executed in the manipulated variable of the process will only affect the controlled variable after the process dead time. For the present work, two processes first order plus dead time (FOPD) and second order plus dead time (SOPD) are considered in this category. he transfer functions of the processes are FOPD : G P (s) = 24s + e s (7) SOPD : G P2 (s) = 2s 2 + 3s + e 6s. (8) he setpoint and load-disturbance responses are shown in Fig. 8. It is observed that the performance of the proposed FP+FI+FD controller is superior in comparison with the PI controller for both the delayed processes. ransientresponse specifications for unit step change in setpoint are compared in able 3 for the conventional PI controller and the FP+FI+FD controller. For FOPD and SOPD processes, the FP+FI+FD controller decreases settling time, ISE and IAE significantly as compared to the conventional PI controllers. In case of the FOPD process, overshoot is minimum for the FP+FI+FD controller. Also, for the SOPD process, there is no overshoot, and the overall performance of the FP+FI+FD controller is excellent.

6 468 International Journal of Automation and Computing 7(4), November 200 able 2 Values of tuned fuzzy parameters for different processes Process transfer function Fuzzy P controller Fuzzy I controller Fuzzy D controller K p K 2 p K UP K i K 2 i K UI K d K 2 d K UD G P (s) = 24s + e s * G P2 (s) = 2s 2 + 3s + e 6s * G P3 (s) = 0 3s + s * 0 G P4 (s) = 0.2s + e s 0.3s * G P (s) = s 4 + 3s 3 + 7s 2 + s * s + G P6 (s) = s 4 + 7s s 2 + s * *For simulation adjustable parameter L = 700. G P4 (s) = 0 0.2s + e s 0.3s +. (20) he responses of fuzzy and conventional controllers for setpoint and load-disturbance are shown in Fig. 9. It is noted that the performance of the proposed FP+FI+FD controller is much better than the PI controller. (a) FOPD G P (s) (a) Inverse response system G P3 (s) (b) SOPD G P2 (s) Fig. 8 Setpoint and load-disturbance responses for process In process industry, a number of processes exhibit inverse response behavior, such as drum boiler and distillation column [20, 2]. When a step signal is applied to the inverse response processes, the initial response of a dynamic system is in a direction opposite to the final outcome. he reason is that the process transfer function has an odd number of right-half-plane (RHP) zeros. It is a challenge to control this kind of process. For the present work, inverse response process with and without delay is considered in this category. he transfer functions of the processes considered are G P3 (s) = 0 3s + s + (9) Fig. 9 (b) Inverse response system with delay G P4 (s) Setpoint and load-disturbance responses for process ransient-response specifications for unit step change in setpoint are compared in able 3 for the conventional PI controller and the FP+FI+FD controller. It is observed that the performance of the FP+FI+FD controller is remarkable.

7 V. Kumar and A. P. Mittal / Parallel Fuzzy P+Fuzzy I+Fuzzy D Controller: Design and Performance Evaluation 469 able 3 ransient-response specifications for unit step change in setpoint System transfer function ype of controller Rise time Peak time Overshoot Settling time ISE* IAE* # t r (s) t p (s) (%) t s (s) 2 % G P (s) = 24s + e s Conventional PI (Z-N) Convertional PI (A-H) FP+FI+FD G P2 (s) = 2s 2 + 3s + e 6s Convertional PI (Z-N) 64. > Convertional PI (A-H) > G P3 (s) = 0 3s + s + G P4 (s) = 0 0.2s + e s 0.3s + G P (s) = s 4 + 3s 3 + 7s 2 + s s + G P6 (s) = s 4 + 7s s 2 + s + FP+FI+FD Convertional PI (Z-N) Convertional PI (A-H) 43.9 > FP+FI+FD Convertional PI (Z-N) 27.4 > Convertional PI (A-H) 99.6 > FP+FI+FD Convertional PID (Z-N) Convertional PID (A-H) FP+FI+FD Convertional PID (Z-N) Convertional PID (A-H) FP+FI+FD *ISE and IAE values are calculated for time t = 0 to t = 00 s with t = 0. s. # t r is 90 % of its final value. Also, two higher order processes are considered to evaluate the performance of the FP+FI+FD controller. he transfer functions of higher order processes are G P (s) = s 4 + 3s 3 + 7s 2 + s (2) G P6 (s) = s + s 4 + 7s s 2 + s +. (22) he fuzzy and conventional controller s responses for setpoint and load-disturbance are shown in Fig. 0. ransientresponse specifications for unit step change in setpoint are compared in able 3. It is observed that in both the cases, the performance of the FP+FI+FD controller is much superior in all respects. It is noted that the response of the PID controller is quite oscillatory for both processes, but with the FP+FI+FD controller, it is quite smooth and fast. Also, it is observed that overshoot and settling time are remarkably reduced in G P6 (s) by the FP+FI+FD controller. In all the above cases, it is noted that ISE and IAE are minimum for the FP+FI+FD controller as compared to the conventional PID controller. Further, to critically check the set point tracking capability of the proposed parallel fuzzy PID controller, a complex chirp signal, having frequency varying from 0. Hz to 0. Hz for target time 0 s, is given to higher order process G P6 (s). he closed-loop response of the system is shown in Fig.. It is observed that the system response is almost overlapping with the applied reference chirp signal. Fig. 0 (a) Higher order system G P (s) (b) Higher order system G P6 (s) Setpoint and load-disturbance responses for process

8 470 International Journal of Automation and Computing 7(4), November 200 (a) Setpoint tracking Fig. signal Setpoint tracking responses of process G P6 (s) to chirp Real time results he performance of the proposed parallel FP+FI+FD controller is evaluated on liquid-flow process experiment available in Advanced Process Control Lab. Flow is the most common process variable in the process industry. Nearly all products manufactured by process industry are influenced in some way by the flow of materials [22]. he liquid-flow process is a prototype of a part of a chemical plant in industry. An air-to-close pneumatic control valve of equal percentage characteristics is used to regulate the liquid flow-rate. he input-output characteristic of the control valve shows highly nonlinear behaviour. Also, it shows hysteresis in its behaviour. herefore, due to the pneumatic control valve, the overall system becomes highly complex and nonlinear. he FP+FI+FD and conventional PI controller is successfully implemented for liquid-flow process using National Instrument M hardware and software (LabVIEW M 8. and its addon tools). he conventional controller is tuned with the famous Z-N tuning technique (frequency response method). Performance of the conventional PI controller is best among the other conventional PID controllers for liquid-flow process. he performance of the proposed FP+FI+FD controller is compared with the conventional PI controller. he data is acquired at the rate of 0 samples per second. Input and output are synchronized appropriately. For setpoint tracking, a square wave input, changing between 80 LPH and 40 LPH flow-rate, is considered. For disturbance rejection, flow-rate is kept constant at 80 LPH, and a back pressure valve is opened and then closed to introduce the load. he main performance evaluation criterion is taken as settling time (2% band), i.e., the ability to reach the desired steady-state condition in a reasonable amount of time. FP+FI+FD and conventional PI controller s responses for setpoint and load-disturbance are shown in Figs. 2 and 3. It is observed that the FP+FI+FD controller outperformed conventional PI controller both in setpoint tracking and disturbance rejection. It is noted that in case of the FP+FI+FD controller, settling time is 29.8 s, recovery time is 34.2 s for back pressure valve opening and 30.7 s for back pressure valve closing, as compared to the conventional PI controller, where settling time is 32.7 s, recovery time is 44.2 s for back pressure valve opening and 42. s for back pressure valve closing. Convertional PI controller responses for liquid-flow pro- Fig. 2 cess Fig. 3 (b) Disturbance rejection (a) Setpoint tracking (b) Disturbance rejection FP+FI+FD controller responses for liquid-flow process 6 Conclusion and discussion he parallel FP+FI+FD controller proposed in this paper successfully demonstrated the much better performance as compared to the conventional parallel PID controller, both in simulation as well as in liquid-flow process experimental setup. Although, due to increase in fuzzy controller parameters, the tuning of the proposed FP+FI+FD controller seems slightly time consuming, but, on the other hand, it increases the degree of freedom of the fuzzy controller, and hence, it may give more flexibility to the user to achieve the desired response. Simulation results show the effectiveness of the FP+FI+FD controller for setpoint tracking and load-disturbance rejection for complex processes, such as FOPD, SOPD, inverse response process with and without delay and higher order process. Further, the chirp signal response of the higher order system shows

9 V. Kumar and A. P. Mittal / Parallel Fuzzy P+Fuzzy I+Fuzzy D Controller: Design and Performance Evaluation 47 the setpoint tracking and adaptive capabilities of the proposed fuzzy controller. Also, the FP+FI+FD controller and the conventional PI controller are successfully implemented in real time using National Instrument M, LabVIEW M 8. and its addons, for liquid-level process and it is observed that the parallel FP+FI+FD controller shows superior performance. herefore, simulation and real time results reveal the advantage of the proposed FP+FI+FD controller over the counterpart classical PID controller for setpoint tracking, load disturbance rejection and adaptive capabilities. Also, due to formula based structure, it is easy to realize it in real time. Acknowledgements he authors thank referees and the editor for their kind encouragement and valuable suggestions to improve the paper. Also, thanks to our Institute for providing excellent experimental facilities in the Advanced Process Control Lab for research. References [] S. Bennett. Development of the PID controller. IEEE Control System Magazine, vol. 3, no. 6, pp. 8 6, 993. [2] G. Chen. Conventional and fuzzy PID controllers: An overview. International Journal of Intelligent and Control Systems, vol., no. 2, pp , 996. [3] J. Lu, H. Ying, Z. Sun, P. Wu, G. Chen. Realtime ultrasound-guided fuzzy control of tissue coagulation progress during laser heating. Information Science, vol. 23, no. 3 4, pp , [4] J. Carvajal, G. Chen, H. Ogmen. Fuzzy PID controller: Design, analysis, performance evaluation, and stability analysis. Information Sciences, vol. 23, no. 3 4, pp , [] H. X. Li. A comparative design and tuning for conventional fuzzy control. IEEE ransactions on Systems, Man, Cybernetics Part B Cybernetics, vol. 27, no., pp , 997. [6] D. Misir, H. A. Malki, G. Chen. Design and analysis of a fuzzy proportional-integral-derivative controller. Fuzzy Sets and Systems, vol. 79, no. 3, pp , 996. [7] N. Kanagaraj, P. Sivashanmugam, S. Paramasivam. A fuzzy logic based supervisory hierarchical control scheme for real time pressure control. International Journal of Automation and Computing, vol. 6, no., pp , [8] H. Ying, W. Siler, J. J. Buckley. Fuzzy control theory: A nonlinear case. Automatica, vol. 26, no. 3, pp. 3 20, 990. [9] G. Chen, H. Ying. Stability analysis of nonlinear fuzzy PI control systems. In Proceedings of the 3rd International Conference on Industrial Fuzzy Control and Intelligent Systems, IEEE, Houston, X, USA, pp , 993. [0] G. Chen,.. Pham. Introduction to Fuzzy Systems, Chapman & Hall/CRC Press, [] G. Chen, H. Ying. BIBO stability of nonlinear fuzzy PI control systems. Journal of Intelligence and Fuzzy Systems, vol., no. 3, pp , 997. [2] H. A. Malki, H. Li, G. Chen. New design and stability analysis of fuzzy proportional-derivative control systems. IEEE ransactions on Fuzzy Systems, vol. 2, no. 4, pp , 994. [3] J. Lu, G. Chen, H. Ying. Predictive fuzzy PID control: heory, design and simulation. Information Science, vol. 37, no. 4, pp.7-87, 200. [4] J. H. Kim, S. J. Oh. A fuzzy PID controller for nonlinear and uncertain system. Soft Computing A Fusion of Foundations, Methodologies and Applications, vol. 4, no. 2, pp , [] K. S. ang, K. F. Man, G. Chen, S. Kwong. An optimal fuzzy PID controller. IEEE ransactions on Industrial Electronics, vol. 48, no. 4, pp , 200. [6] W. Chatrattanawuth, N. Suksariwattanagul,. Benjanarasuth, J. Ngamwiwit. Fuzzy I-PD controller for level control. In Proceedings of International Joint Conference on SICE- ICASE, IEEE, Busan, Korea, pp , [7] I. D. Landau, G. Zito. Digital Control Systems Design, Identification and Implementation, Springer, [8] K. J. Åström,. Hägglund. PID Controllers: heory, Design, and uning, 2nd Edition, Instrument Society of America, 99. [9] W. Y. Svrcek, D. P. Mahoney, B. R. Young. A Real-time Approach to Process Control, 2nd Edition, John Wiley & Sons, [20] F. G. Shinskey. Process Control Systems, 2nd Edition, New York, USA: McGraw-Hill, 996. [2] F. G. Shinskey. Robust Process Control, New York, USA: McGraw-Hill, 979. [22] J. G. Williams, G. Liu, S. Chai, D. Rees. Intelligent control for improvements in PEM fuel cell flow performance. International Journal of Automation and Computing, vol., no. 2, pp. 4, Vineet Kumar received the M. Sc. degree in physics with electronics from Govind Ballabh Pant University of Agriculture and echnology, Pantnagar, India in 99, and the M. ech. degree in instrumentation from Regional Engineering College, Kurukshetra, India in 996. He is currently pursuing Ph. D. degree from Delhi University, Delhi, India. He was a lecturer from 2000 to 200 at Netaji Subhash Institute of echnology (NSI). He has also served industry more than years. Since 200, he has been a senior lecturer of the Department of Instrumentation and Control Engineering, NSI, Delhi University, Delhi, India. He has developed the Advanced Process Control Lab for research and development with the help of latest hardware and software from National Instrument M, USA. His research interests include process dynamics and control, intelligent control techniques and their applications, and intelligent process control. vineetkumar27@gmail.com (Corresponding author) A. P. Mittal received the B. Eng. degree in electrical engineering from Madan Mohan Malaviya Engineering College, Gorakhpur, India, the M. ech. degree from University of Roorkee, India, and the Ph. D. degree from II, Delhi, India. He was working as a professor in the Electrical Engineering Department at Chhotu Ram State College of Engineering (CRSCE), Murthal, Haryana, India from July 997 to June 200. Also, he served as an assistant professor and lecturer at Regional Engineering College (REC), Kurukshrtra and Hamirur, India. Since June, 200, he has worked as a professor and head of the division of Instrumentation and Control Engineering Department, Netaji Subhas Institute of echnology (NSI), Delhi University, Delhi, India. He is a senior member of IEEE, USA and a fellow of Institute of Engineers, India. His research interests include intelligent control, power electronics, and electrical drives. mittalap@gmail.com

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