Australian Journal of Basic and Applied Sciences. Design and modeling of fractional order PI controller for a coupled spherical tank MIMO system.

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1 Australian Journal of Basic and Alied Sciences, 9(5) March 15, Pages: ISSN: Australian Journal of Basic and Alied Sciences Journal home age: Design and modeling of fractional order PI controller for a couled sherical tank MIMO system. 1 D. Pradeekannan and 2 Dr. S. Sathiyamoorthy 1 AssociateProfessor,Electronics and Instrumentation Engineering Deartment, K.L.N.College of Engineering Pottaalayam, Tamilnadu,India Professor, Electronics and Instrumentation Engineering Deartment, J.J.College of Engineering and Technology, Ammaettai, Tiruchirraalli, Tamilnadu,India 624. A R T I C L E I N F O Article history: Received 12 October 14 Received in revised form 26 December 14 Acceted 1 January 15 Available online 27 February 15 Keywords: PID controller, ZN tuning, Fractional Order Controller, Sherical tank rocess, MIMO systems. A B S T R A C T Conventional Proortional Integral (PI) controller is a well known controller used in most of the rocess Industries for controlling the rocess arameters at desired set values. As the rocess tanks are connected in an interacting Multi Inut Multi Outut (MIMO) mode, there exhibits a highly nonlinear dynamic behavior and time delay between tanks inut and outut. The ZN tuned PID controller arameters does not coe with all oerating oints as it exhibits different non linear characteristics. The recent advancement in fractional calculus leads the control Engineers to aly the fractional order calculus in control theory. One of the rime alications of fractional calculus is fractional order Proortional Integral (FOPI) controller. Fractional order controller differs from conventional integer order PI controller by the order of the integral term. The key challenge in designing fraction order PI controller is to determine the Integral order (α) and the conventional PI arameters such as K, i.. This research aer rooses the design and modeling of Fractional order PI controller for a nonlinear couled sherical tank rocess. The aim of this aer is to comare the control erformance between the conventional PI and the fractional controller for a nonlinear rocess lant and to justify the suerior erformance of FOPI in terms of time domain secifications Robustness and Performance indices. Better enhanced controller erformance was obtained for a FOPI controller than that of ZN tuned PI controller at various oerating oints. 15 AENSI Publisher All rights reserved. To Cite This Article: D. Pradeekannan and Dr. S. Sathiyamoorthy., Design and modeling of fractional order PI controller for a couled sherical tank MIMO system.. Aust. J. Basic & Al. Sci., 9(5): , 15 INTRODUCTION Proortional Integral Derivative Controller has been using in Industrial control alications for a long time. The reasons for their wide oularity lies in the simlicity of design and good erformance which includes low ercent over shoot and small settling time for slow rocess (Astrom, K.J. and T. Hagglund, 1995; Astrom, K.J. and T. Hagglund, 1). According to the survey in 1989, 9 ercentage of rocess industries uses the conventional PID controllers (Astrom, K.J. and T. Hagglund, 1984).The wide sread use of the PID controller in the Industry is due to their simlicity and ease of retuning online (Astrom, K.J., 1993). One of the most successful and oldest classical techniques is Zeigler Nichols method. It was ut forward by John Ziegler and Nathaniel Nichols in 1942 and is still a simle, fairly effective PID tuning method. He roosed two methods, one is oen loo ste resonse method and the second is closed loo frequency resonse method. The Ziegler and Nichols first PID tuning method is the techniques made based on certain controller assumtions. Hence, there is always a requirement of further tuning; because the controller settings derived are rather aggressive and thus result in excessive overshoot and oscillatory resonse. Also the controller arameters are rather difficult to estimate in noisy environment. The second method is based on knowledge of the resonse to secific frequencies. The idea is that the controller settings can be based on the most critical frequency oints for stability. This method is based on exerimentally determining the oint of marginal stability. This frequency can be found by increasing the roortional gain of the controller, until the rocess becomes marginally stable. These two arameters define one oint in the Nyquist lot. The gain is called ultimate gain Ku and the time eriod T. The PID arameter setting is given in (Weng Khuen Ho, 1995; Ziegler, J.G. and N.B. Nichols, 1942).Fractional order calculus has gained Corresonding Author: D. Pradeekannan, Associate Professor, Electronics and Instrumentation Engineering Deartment, K.L.N.College of Engineering Pottaalayam,Tamilnadu,India

2 478 D. Pradeekannan and Dr. S. Sathiyamoorthy, 15 Australian Journal of Basic and Alied Sciences, 9(5) March 15, Pages: accetance in the last coule of decades. J Liouville made the study of fractional calculus in In 1867 A.K. Grunwaled worked on the fractional oerations. G.F.B. Riemann develoed the theory of fractional integration in Fractional order mathematical henomena allow us to describe and model a real object more accurately than the classical integer methods. Fractional order PID controllers are used in many control alications (Igor Podlubny, 1999). Schlegel Milos et.al (6), erformed a comarison between classical controller and fractional controller and summarized that the fractional order controller outerforms the classical controller. D Xue et.al(6), imlemented fractional order PID control in DC motor. Chuang Zhao, Xiangde Zhang, et.al (8), imlemented fractional order controller in osition servo mechanism. Varsha Bhambhani et.al (8) imlemented fractional order controller in water level control. Hyo-Sung Ahn et.al (8) imlemented fractional order integral derivative controller for temerature rofile control. Concecion A. Monje et.al (1), and Fabrizio Padula et.al (11), devised methods for tuning and auto tuning of fractional order controller for industry level control. Venu Kishore Kadiyala et.al (9) imlemented fractional order controller for aerofin control. Fabrizio Padula, Antonio Visioli et.al (11) devised the Tuning rules for otimal PID and fractional order PID controllers. A state sace design method based on feedback ole lacement can be viewed in (Dorcak, L., 1). The control of liquid level is a basic roblem in Process Industries such as Petro chemical lants, Chemical recovery of Fertilizer industry etc. It is essential for control system engineers to understand the behavior of non linear Sherical tank level control system and how the level control roblems are solved. Several real time works are being carried out to control the level of the sherical tank such as Design of self tuning Fuzzy controllers for non linear systems, by RajniJain, N.Sivakumaran, et.al (11). Model based Controller Design for a Sherical tank rocess by S.Nithya, N.Sivakumaran, et.al (8), Soft Comuting Based Controllers Imlementation for Non Linear Process in Real Time by S.Nithya, N.Sivakumaran et.al (1), Design of Controller using Simulated Annealing for a real time rocess by S.M.Girirajkumar,N.Anantharaman et.al (1), Exerimental study of Fractional Order Proortional Integral Controller for water level Control carried out by Varsha Bhambani and Y.Q.Chen (88), State Feedback with Intergal Controller for a Non-Linear sherical tank Process was done by PradeeKannan.D, S.Sathiyamoorthy (12) etc. Almost all the above works are focused on design of a controller for a nonlinear SISO system. The roblem of level control in a nonlinear couled sherical tank MIMO rocess with variable area is quite cumbersome. The PID controllers have been used for several decades in industries for rocess control alications..the erformance of PID controllers can be further imroved by aroriate settings of fractional-i and fractional-d actions. This aer attemts to study the behavior of fractional PI controllers. Finding [α,k, i,] as an otimal solution to a given rocess thus calls for otimization on a three dimensional sace. The erformance of the FOPI controllers is better than its conventional PI. Thus fractional order PI controller can be alied for couled nonlinear sherical tank rocess to control the level of the nonlinear tank by maniulating the inflow rate of the rocess tank by roviding otimal values of arameters such as k, i and α. so as to obtain a desired erformance characteristics. The roosed design will find extensive alication not only in non linear sherical tank rocess but also for other nonlinear rocess with simle fine tuning in the values of α. This aer is organized as follows. Section 2 exlains about the mathematical modeling of the non-linear couled sherical tank MIMO rocess. Section 3 describes the Exerimental set u. Section 4 illustrates the simulation of ZN tuned PI controller and Section 5 illustrates the simulation of FOPI controller. Section 6 describes the Results obtained for servo and regulatory oeration at various oerating oints of the tank for both the controllers. Finally the conclusion is given in section Mathematical modeling: Consider the couled Sherical tank rocess shown in Fig 1. The objective of the rocess is to control the level of the two tanks namely h a (t) and h b (t). The inlet water flow from the two ums f 1 (t) and f 2 (t) are used as maniulated variables so as to kee the control variable at the desired set oint. The level of the tank at any instant is measured by the combination of orifice and Differential ressure transmitters which are mounted on the resective tanks discharge line whose outut is (4 -)ma. This outut are comared with the desired set oint value of level one and level two which will be configured as (4 -)ma. The error signal is amlified based on the controller secification. The controller oututs is used to vary the inflow rates f 1 (t) and f 2 (t) of the sherical tank so as to maintain the set oint at desired level h a and h b of the tanks. Electro neumatic converters are used to convert the controller oututs of (4 -)ma in to a neumatic signal of (3-15) si so that the final control element will be able to throttle the inflow rates f 1 and f 2. Using the law of Conservation of mass, the non linear lant equations are obtained. For tank 1, f 1 - f 3 f 4 = (Ah) dh a /dt (1) For tank 2, f 3 +f 2 f 5 = (Ah) dh b /dt (2) f 3 = a 2g(h a h b ) (3)

3 479 D. Pradeekannan and Dr. S. Sathiyamoorthy, 15 Australian Journal of Basic and Alied Sciences, 9(5) March 15, Pages: f 4 = a 2g(h a - x ) (4) and f 5 = a 2g(h b - x ) (5) Where, f 1 and f 2 are in flow rates to tank 1 and tank 2 resectively in (m 3 /sec).f 4 and f 5 are outflow rate of tank 1 and tank 2 (m 3 /sec). f 3 is the flow rate between the tanks in m 3 /sec.radius on the surface of the fluid varies according to the surface level of fluid in the tank. Let this radius be known as r s. Therefore r s1 = 2r a h a h a and r s2 = 2r b h b h b Where r a = radius of tank 1 in metres. r b = radius of tank 2 in metres. r a = r b = r =.5metres h a = fluid level in tank 1 in metres. h b = fluid level in tank 2 in metres. a=π[x /2] 2 x = thickness of ie.4 in metres. h as - steady state water level of tank 1 =.m h bs - steady state water level of tank 2 =.21m. The linearised lant transfer function in S domain are given as s s. 794s. 8 (6) s s. 794s. 8 (7) s. 794s. 8 (8). 492 andg ( s ) s. 794s. 8 (9) Fig. 1: Schematic diagram of Couled Sherical Tank Process. 2.1 Black Box Modeling: The first order system with dead time td s ke reresented as a transfer function G( s ) s 1 (1) The outut resonse to a ste change in inut is given by, y( t ) k u( 1 ex( ( t ) / )) for t> (11) The measured outut is in deviation variable form. The three rocess arameters K,, can be estimated by erforming a single ste test on rocess inut. The rocess gain is found as simly the long term change in rocess outut to the change in rocess inut. The time delay is the amount of time, after the inut change, before a significant outut resonse is observed 2.2 Estimation of time constant by two oint method: Smith has obtained the arameters of FOPDT transverse function model by letting the resonse of actual system and that of the model to meet the two oints which describe the arameter & t. Here, time that required for the rocess outut to make d 28.3% and 63.2% resectively are measured. The time constant and time delay can be estimated from the equation given below for both the transfer function, ( 2 t / 3 ) 3 (t / ),andt t / d (12) Thus the obtained FOPDT models are given by s 11e G 11( s ) s 1 (13) 8. 79s Similarly e 7. 72s 1 (14) The arameters of PID and PI controllers as er Ziegler Nichols tuning method are determined. 2.3 Decouler design: The effect of interactions in a MIMO system is minimized with the introduction of decouler. Thus for the couled non linear interacting sherical tank system, the decouler are designed as given below D ( s ) s. 881 (15)

4 Height of the tank in cms 48 D. Pradeekannan and Dr. S. Sathiyamoorthy, 15 Australian Journal of Basic and Alied Sciences, 9(5) March 15, Pages: D ( s ) s. 612 (16) 2.4 Model validation: The FOPDT model obtained from two oint method is given by equations 13 and 14 and the derived transfer function on substituting the dimensions of the sherical tank is given by equations 5,7,8 and 9. The oen loo resonse for both the cases for a given ste change in set oint is obtained as follows, 8 Oen loo resonse of two interacting rocess foe a given unit ste changein set oint 6 oen loo resonse of rocess for tank1 oen loo resonse of rocess for tank 2 4 oen loo resonse of FOPDT model for tank1 oen loo resonse of FOPDT model for tank 2 Unit Ste inut Unit ste inut Fig. 2: oen loo resonses of rocesses and FOPDT models. It is evident from the figure 2 that both the resonses coincides and have similar time domain resonse. Hence FOPDT model aroximation can be used for tuning the PI controller to obtain otimal values of controller arameters. 3. Exerimental Set U Of Couled Interacting Sherical Tank Process: The exerimental set u of the Couled sherical tank system is shown in figure 3. And the corresonding schematic block diagram is shown in figure 4.The sherical tanks are made u of SS316 material which has high corrosion resistance roerty and has a maximum height, radius of.5 meter. Water from the reservoir tank whose size of 125 mm x 45 mm x 45 mm are umed through a Kirloskar make.5 HP ums having a discharge of 15 litres er hour that flows through a Teleline make rotameter having a range (4-44) LPH to the sherical tank. Fig. 3: Exerimental set u of couled sherical tank system. The levels of the tank 1 and tank 2 at any instant are measured by the Rose mount make Differential ressure transmitters having a measurement range of (-4) mm of water column corresonds to the outut range of (4 -)ma. These oututs are comared with the desired set value of levels in tank 1 and tank 2 resectively which will be scaled in the control law as (4 -)ma. The error signals are also in the range of (4-)mA which is then amlified based on the controller secifications. These outut are used to vary the inflow rate f 1 (t) and f 2 (t) of the sherical tank with the hel of an ABB make Electro neumatic converters which converts the outut of (4 -)ma in to a neumatic signal of (3-15) si so that the Equal ercentage control valve will be able to throttle the inflow rates f 1 and f 2 resectively. The controller arameters are determined for both ZN tuned PI Controller as well as FOPI controllers. The couled sherical tank set u is interface to the real time controller NI Comact RIO 924which is an 8 module chassis having an inbuilt FPGA real time controller with a data transfer baud rate of 4Mbs and with an accuracy of m.these values are alied to the PID controller block of LabVIEW rogram for a given ste change in inflow rates f 1 and f 2, and the corresonding steady state resonse are obtained. 4.Zn Tuned Pi Controller: The controller arameters are determined for both ZN tuned PI and PID Controllers. The values of

5 Height of the tank in cms Height of tank in cms Height of tank in cms Height of tank incms 481 D. Pradeekannan and Dr. S. Sathiyamoorthy, 15 Australian Journal of Basic and Alied Sciences, 9(5) March 15, Pages: k, ki, kd for ZN tuned PID controller G c1 are found to be.162,.31,.21and for ZN tuned PI controller G c1 are found to be.12,.137 resectively. Similarly the values of k, ki, kd for ZN tuned PID Controller G c2 are found to be.158,.64,.4372 resectively and for ZN tuned PI controller G c2 are found to be.793,.29 resectively. As dynamics of the rocess are large, changes in the control variable over a small interval of time are constant and the derivative term does not contribute more in the erformance of the controller outut hence, in this work the Conventional PI controller is chosen for the analysis against the FO PI controller. Fig. 4: Schematic block diagram of couled sherical tank system. 4 3 Servo resonse of ZN PI controller ZN servo resonse of tank1 Setoint in cms Fig. 5:Servo Resonse of ZN tuned PI controller for a set oint of 1,,36cms of water column of tank Servo resonse of ZN PI Controller for tank2 ZN servo resonse of tank2 Set oint in cms Fig. 6: Servo Resonse of ZN tuned PI controller for a set oint of 9, 21, 35cms of water column of tank Servo regulatory of ZN PI Controller Servoregulatory Resonse of tank1 Set oint in cms Fig. 7: Servo Regulatory resonse of ZN tuned PI controller for a set oint of cms of water column of tank Servo regulatory resonse of ZN PI Controller Servo regulatory resonse of tank 2 Setoint in cms Fig. 8: Servo Regulatory resonse of ZN tuned PI controller for a set oint of cms of water column of tank2. The figure 7 shows the servo regulatory resonse of ZN tuned PI Controller for a set oint of cms of water column and a disturbance is being alied after 1seconds.It is evident from the resonse that the controller effectively rejects the disturbance and track the set oint after 18seconds. The figure 8 shows the servo regulatory resonse of ZN tuned PI Controller for a set oint of

6 Height of the tanks in cms Height of the tanks in cms Height of tank 2 in cms Heightof tank 1 in cms Height of the in cms Height of the tank in cms 482 D. Pradeekannan and Dr. S. Sathiyamoorthy, 15 Australian Journal of Basic and Alied Sciences, 9(5) March 15, Pages: cms of water column and a disturbance is being alied after 1seconds. It is evident from the resonse that the controller effectively rejects the disturbance and tracks the set oint after 18seconds. Fractional Order Pi Controller: The fractional-order controller will be reresented by fractional-order PI α controller with transfer function given by the following exression. u(s) 1 Gfoi(s) K c[1 ] e(s) is (17) Where α is an arbitrary real numbers, K is amlification (gain), i is integration constant. Taking α =1, a classical PI controller is obtained. The PI α controller is more flexible and gives an oortunity to better adjust the dynamics of control system. It is comact and simle but the analog realization of fractional order system is very difficult and challenging. The fraction order PI, PID controller can be realized with FAMCON tool box, N integer tool box in matlab. Determination of otimal values of K, K i,, α, for a FOPI controller is done by a minimum search algorithm Keeing the objective function as minimization of integral square error. The values of k, ki, α for FOPI controller G c1 are found to be.8147,.958,.127 and similarly the values of k, ki, α for FOPI Controller G c2 are found to be.9134,.6324,.975 resectively. 4 3 Servo resonse of FOPI Controller Set oint incms Servo resonse of FOPI Controller of tank Fig. 9: Servo Resonse of FOPI controller for a set oint of 1,, 36cms of water column of tank 1. 4 Servo resonse of FOPI Controller 3 Set Point in cms Servo resonse of FOPI Controller for tank Fig. 1: ServoResonse of FOPI controller for a set oint of 9, 21, 35cms of water column of tank Regulatory resonse of FOPI Controller Set oint in cms FOPI Regulatory resonse for tank Fig. 11: Servo Regulatory resonse of FOPI controller for a set oint of cms of water column of tank Regulatory resonse of FOPI Controller.5 Set oint in cms Regulatory resonse of FOPI Controller for tank Fig. 12: Servo Regulatory resonse of FOPI controller for a set oint of 21cms of water column of tank 2. 3 Ste resonse of ZN PI Controller ZN PI Ste resonse of tank1 Set oint of tank1 incms ZN PI Ste resonse for tank2 Set oint of tank2 in cms Fig. 13: Ste Resonse of ZN PI controller for a set oint of, 21cms of water column of tank 1 and tank Ste resonse of FOPI Controller FOPI Ste resonse for tank1 FOPI Ste resonse of tank2 Set oint for tank1 in cms Set oint for tank2 i cms Fig. 14: Ste resonse of FOPI controller for a set oint of, 21cms of water column of tank 1 and tank2.

7 height of the tank in cms height of the tank incms 483 D. Pradeekannan and Dr. S. Sathiyamoorthy, 15 Australian Journal of Basic and Alied Sciences, 9(5) March 15, Pages: The figure 11 shows the servo regulatory resonse of FOPI Controller for a set oint of cms of water column and a disturbance is being alied after 1seconds.It is evident from the resonse that the controller effectively rejects the disturbance and track the set oint after 11seconds. The figure 12 shows the servo regulatory resonse of FOPI Controller for a set oint of 21cms of water column and a disturbance is being alied after 1seconds. It is evident from the resonse that the controller effectively rejects the disturbance and tracks the set oint after 11seconds. Further Robustness analysis has been done for both the ZN tuned PI controller as well as FOPI Controller. A 1 ercent change in rocess arameters such as k t d and t i are alied and the corresonding FOPDT model are determined as 4. 43s s 121e G 11( s ) and e s s 1 (12) 3 1 Robustness investigation for set oint changes FOPI controller resonse of tank1 FOPI Controller resonse of tank2 set oint for tank 1 set oint for tank timein seconds Fig. 15: Robust Resonse of FOPI controller for a set oint of,, 21cms of water column of tank 1 and tank Robustness investgation for ste change in set oint ZN resonse for tank1 Set oint for tank1 in cms ZN resonse for tank 2 Set oint for tank 2in cms time in seconds Fig. 16: Robust Resonse of ZNPI controller for a set oint of,, 21cms of water column of tank 1 and tank2. The figures 15 and 16 show that the robustness resonse of ZNPI controller as well as FOPI controller for a ste change in set oint of both the tanks 1and 2 resectively. It is evident that the FOPI controller is robust enough to track the set oint variation in site of rocess arameters variation. RESULTS AND DISCUSSION An ste resonse of ZN tuned PI controller and FOPI controller are obtained for servo roblem and servo regulatory roblem and their erformance characteristics are comared in terms of time domain secifications such as rise time, eak time, eak over shoot, steady state value etc and erformance indices such as ISE and IAE. The table shows the time domain secification and the corresonding erformance indices for both the designed controllers. It is evident from the table that the ZN tuned PI controller outut could track the set oint at an oerating oint of cms,21cms of water column for both tank 1 and tank2 with a settling time of 38.62and 69.54seconds and with 21.8% and 9. % overshoots. It is evident from the table that the FOPI controller outut could track the set oint at various oerating oints such as,1cmsfor tank 1 and 21, 9cms of water column for tank2 with settling time of 4.89 and 6.19 seconds. Further there exist a drastic reduction in erformance Indices ISE and IAE in FOPI Controller, maximum eak overshoot is nominal as that of ZN tuned PI controller. Table 1: shows the servo resonse at various oerating oints with time domain secification of FOPI controllers against conventional PI controller at various height of the sherical tank such as,21,and 1,9 cms. Tye of controller Set Point h a in cm Set Point h b in cm Rise time in sec Settling time in sec Max Peak over shoot in % Steady state values ZN PID ZN PID ZN PID ZN PID FOPI FOPI FOPI FOPI Conclusion: FOPI controller can coe u with tank nonlinear characteristics at various oerating oints such as, 21.1,9 centimeters of water column in the couled sherical tank. Conventional controller based on Ziegler Nichols tuning resonse is outerformed by Fractional order PI controller with less overshoot and lesser settling time, eak time, when subjected to servo and regulatory oerations. Further the FOPI controller roves itself that it is

8 484 D. Pradeekannan and Dr. S. Sathiyamoorthy, 15 Australian Journal of Basic and Alied Sciences, 9(5) March 15, Pages: robust enough for changes in rocess variables and kees track the set oints. Further the controller can be tuned by other soft comuting techniques and imlemented in real time so as to comare their erformances. Tuning FOPI controller can also be alied for other non linear rocesses such as continuous stirred tank reactor, fermentation rocess etc to obtain better controller erformance characteristics. Table 2: shows the servo resonse at various oerating oints with erformance indices such as ISE and IAE of FOPID controllers against conventional PID controllers at various height of the sherical tank such as,21, and 1,9 cms. Tye of controller Set Point Set Point h a in cm h b in cm ISE IAE ZN PID ZN PID ZN PID ZN PID FOPI FOPI FOPI FOPI ACKNOWLEDGMENT This work was suorted by deartment of electronics and Instrumentation engineering and research and develoment unit of K.L.N. College of Engineering, Pottaalayam, Sivagangai district, Tamilnadu, India. REFERENCES Astrom, K.J. and T. Hagglund, PID controllers, Theory, design and tuning, 2nd edition, Instrument Society of America. Astrom, K.J. and T. Hagglund, 1. The Future of PID Control, Control Engineering Practice, 9: Astrom, K.J. and T. Hagglund, Automatic Tuning of Simle regulators with secifications on Phase and Amlitude margins,automatica, (5): Astrom, K.J. and T. Hagglund, C.C. Hang, W.K. Ho, Automatic Control and Adatation for PID Controllers - A Survey, Control Engineering Practice, 1(4): Concecion, A., Monje, Blas, M. Vinagre, Vicente Feliu, YangQuan Chen, 8. Tuning and auto-tuning of fractional order controllers for industry alications, Control Engineering Practice, 16: Chuang Zhao, Xiangde Zhang, 8. The alication of fractional order PID controller to osition servomechanism, Proc. 7th World Congress Intelligent Control and Automation, Concecion, A., Monje, YangQuan Chen, Blas, M. Vinagre, Dingyu Xue, Vicente Feliu, 1. Fractional Order Systems and Controls, Sringer Publication. Deeyaman Maiti, Sagnik Biswas and Amit Konar, 8. Design of a fractional order PID controller using article swarm otimization technique, Proc. ReTIS 8. Dingyu Xue, Chunna Zhao, YangQuan Chen, 6. Fractional order PID control of a DC motor with elastic shaft: A case study, Proc. american control conference, Dorcak, L., I. Petras, I. Kostial and J. Terak, 1. State sace controller design for the fractional-order regulated system, Proc. of the International Carathian Control Conference, 15-. Fabrizio Padula, Antonio Visioli, 11. Tuning rules for otimal PID and fractional order PID controllers, Journal of Process Control, 21: Girirajkumar, S.M., BodlaRakesh, N. Anantharaman, 1. Design of Controller using Simulated Annealing for a real time rocess, International Journal of Comuter Alications, 6(2). Hagglund, T. and K.J. Astrom, Industrial Adative Controllers Based on Frequency Resonse Techniques, Automatica, 27(4): Hyo-Sung Ahn, Varsha Bhambhani and YangQuan Chen, 8. Fractional-order integral and derivative controller design for temerature rofile control, in Proc. CCDC-8, : Igor Podlubny, Fractional-order systems and PI α D β controllers, IEEE Transactions on Automatic Control, 44(1): Jun-Yi Cao and Bing-Gang Cao, 6. Design of fractional order controller based on article swarm otimization, Int. J. Control, Automation and Systems, 4(6): Majid Zamani, Masoud Karimi-Ghartemani, Naseer Sadati, 7. FOPID controller design for robust erformance using article swarm otimization, Fractional Calculus and Alied Analysis, 1(2): Nithya, S., N. Sivakumaran, T. Balasubramanian, N. Anantharaman, 8. Model based Controller Design for a Sherical tank rocess in Real Time IJSSST, 9(4): Nithya, S., N. Sivakumaran, T.K. Radhakrishnan, 1. Anantharaman.N, Soft Comuting Based Controllers Imlementation for Non Linear Process in Real Time,Proceedings of

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