J Control Theory Appl 2012 10 (3) 297–302DOI 10.1007/s11768-012-1044-4

Design of internal model control based fractionalorder PID controller

T. VINOPRABA 1, N. SIVAKUMARAN 1, S. NARAYANAN 1, T. K. RADHAKRISHNAN 2

1.Department of Instrumentation and Control Engineering, National Institute of Technology, Tiruchirappalli 620015, India;

2.Department of Chemical Engineering, National Institute of Technology, Tiruchirappalli 620015, India.

Abstract: This article presents a design of the internal model control (IMC) based single degree of freedom (SDF)fractional order (FO) PID controller with a desired bandwidth specification for a class of fractional order system (FOS).The drawbacks of the SDF FO-IMC are eliminated with the help of the two-degree of freedom (TDF) FO PID controller.The robust stability and robust performance of the designed controller are analyzed using an example.

Keywords: Fractional order PID controller; Fractional order systems; Model based control; Robust control

1 IntroductionIn recent years, the fractional order (FO) PID controller

has gained much attention in the control community be-cause it is more robust than the integer order (IO) controllerdue to the fractional powers of the integral and derivatives terms. Several tuning rules are available for FO PID con-troller for the IO process [1–6]. The optimization techniquessuch as genetic algorithm and the particle swarm optimiza-tion techniques are also used to obtain the FO PID parame-ters [7–8]. Real world processes are likely to be fractional,though the fractionality may be less [9]. Systems such asvoltage-current relation of a semi-infinite lossy RC line,the diffusion of heat into a semi-infinite solid [9], heat-ing furnace [10] and gas turbine [11] are of fractional or-der. For FOS, the FO controller parameters are tuned us-ing gain margin and phase margin specifications [12–13].Advanced FO controllers such as CRONE controller [14],fractional order lead compensator [15], self tuning regu-lator [16], model reference adaptive control [17], adaptivehigh gain controller [18], sliding mode controller [19], iter-ative learning control [20] have been implemented to im-prove the performance and robustness in the closed loopcontrol systems. It has been proved that, the stabilizing setof the fractional order PID controllers is wider than the inte-ger order PID controller [21–22]. If the stabilizing set of thecontroller parameters is wider, then the controller is morerobust i.e. it can accommodate more model uncertaintiescompared to integer order controller.

In the last decade, the internal model control (IMC) basedPID controller design has gained widespread acceptance inthe control community because the controller can be easilydesigned by taking inverse of the model with a single tuningparameter namely the IMC filter time constant. The optimalvalue of filter time constant is determined by a trade-off be-tween speed of response (small value of time constant) androbustness (large value of time constant). An IMC basedPID controller has been designed for the desired bandwidth

specification [23]. Increase in the bandwidth provides lessattenuation in reference signal and faster response. An IMCbased FO PID controller has been designed for the IO firstorder plus time delay process [24] and a class of FOS [25].In this article, an attempt is made to design IMC FO PIDcontroller with bandwidth specification. In SDF FO-IMC,both tracking performance and disturbance (output) rejec-tion performance cannot be achieved simultaneously whichhas been mathematically proved in Appendix B. Hence,TDF FO-IMC is designed which ensures good trackingperformance and satisfactory disturbance rejection perfor-mance. The designed TDF FO-IMC is more robust than theIO-IMC because of fractional powers of integral and deriva-tive s terms.

The paper is organized as follows. In Section 2, the prob-lem is formulated. The design of SDF FO-IMC and TDFFO-IMC are discussed in Sections 3 and 4. Simulation re-sults are presented in Section 5. Section 6 describes therobustness analysis of the designed controller. Conclusionsare drawn in Section 7.

2 Problem formulationThe basic structure of the IMC is shown in Fig. 1 where

Gp is the process, Gm is the model of the process, Gi isthe controller, r is the set point, d is the disturbance and yis the output of the process. Fig. 1 can be transformed intostandard feedback structure as shown in Fig. 2.

Gc is given by

Gc(s) =Gi(s)

1−Gm(s)Gi(s). (1)

The design of the IMC based IO-PID controller forthe desired bandwidth specification has been reported byMorari and Zafiriou [26] and the same has been briefly ex-plained in Appendix A. In this paper, an attempt is madeto design IMC based FO-PID controller with desired band-width specification.

Received 7 March 2011; revised 1 July 2011.

c© South China University of Technology and Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2012

298 T.Vinopraba et al. / J Control Theory Appl 2012 10 (3) 297–302

Fig. 1 Internal model control structure.

Fig. 2 Standard feedback controller structure.

3 SDF FO-IMCThe FOS is assumed to be of the form

Gp FO(s) =K

asα + bsβ + c, (2)

where α and β are real coefficients. Let the fractional modelof the process be

Gm FO(s) =K

asα + bsβ + c. (3)

Based on pole-zero cancellation, the controller Gi(s) is as-sumed to be

Gi(s) =asα + bsβ + c

K(η1 DF FOsλ + 1), (4)

where λ is of fractional order ranges from 0 <λ< 2 andη1 DF FO is the filter time constant of the FOC. Substitutingequations (3) and (4) in equation (1), Gc(s) is found to be

Gc(s) =asα + bsβ + c

Kη1 DF FOsλ. (5)

The general form of FO-PID controller is given by

GFOPID(s) = Kc(1 +1

Tisδ+ Tdsγ). (6)

Comparing equations (5) and (6), the controller parametersare obtained as follows

Kc =b

Kη1 DF FO, (7)

Ti =b

c, (8)

Td =a

b, (9)

δ = β, (10)γ = α− β. (11)

From Fig. 2, the closed loop transfer function with respectto disturbance rejection is obtained and is given by

y(s)d(s)

=1

1 + Gc(s)Gp(s)=

η1 DF FOsλ

η1 DF FOsλ + 1. (12)

The closed loop transfer function with respect to set pointtracking is obtained and is given by

y(s)r(s)

=Gc(s)Gp(s)

1 + Gc(s)Gp(s)=

1η1 DF FOsλ + 1

. (13)

The filter time constant for the disturbance rejection andtracking performance is determined from the bandwidthspecification.

4 TDF FO-IMCIn a SDF FO-IMC, the filter time constants obtained for

disturbance rejection performance and the tracking perfor-mance, with same bandwidth specification, are not same be-cause of fractional power in the s term (proof is shown inAppendix B). To eliminate this drawback, a TDF FO-IMCis designed.4.1 Design of TDF FO- IMC

The IMC structure based on TDF FO controller is shownin Fig. 3.

Fig. 3 Two degree of freedom controller.Here Gc1(s) is designed based on disturbance rejection

and Gc2(s) is designed to shape the servo response. ChooseGc1(s) to be

Gc1(s) =asα + bsβ + c

Kη1 DF FOsλ, (14)

where the filter time constant η1 DF FO is obtained fromequation (12). Choose Gc2(s) to be

Gc2(s) =1 + η1 DF FOsλ

1 + η2 DF FOsλ, (15)

where the filter time constant η2 DF FO is obtained fromequation (13) .4.2 Robust stability analysis

The control system design is usually based on the approx-imate mathematical model of the system to be controlled. Inreality, the system may behave differently than the model in-dicates, or the system parameters may vary with respect tooperating conditions. The closed loop system with the de-signed controller is robustly stable if the condition

|T (jω)||G∆(jω)| < 1, ∀ω (16)is satisfied [27] where

T (s) =Gp(s)Gc1(s)

1 + Gp(s)Gc1(s), (17)

and

G∆(s) =Gp1(s)−Gp(s)

Gp(s), (18)

where Gp(s) is the model of the process at an operatingcondition for which the controller is designed and is givenby

Gp(s) =K0

a0sα0 + b0sβ0 + c0. (19)

Hence, by equation (5),

Gc1(s) =a0s

α0 + b0sβ0 + c0

K0η1 DF FOsλ. (20)

Gp1(s) is the model of the process at a different operatingcondition and is given by

Gp1(s) =K1

a1sα1 + b1sβ1 + c1. (21)

As the prefilter Gc2(s) is not in feedback path, it has no ef-fect on the robust stability [26]. Substituting (19), (20) and

T.Vinopraba et al. / J Control Theory Appl 2012 10 (3) 297–302 299

(21) in equations (17) and (18),

T (s) =1

1 + η1 DF FOsλ, (22)

G∆(s) = (K1a0sα0 + K1b0s

β0 + K1c0 −K0a1sα1

−K0b1sβ1 −K0c1)/(K0a1s

α1 + K0b1sβ1

+ K0c1). (23)

4.3 Robust performance analysisThe closed loop system meets the robust performance

specification [26] if and only if

|T (jω)||G∆(jω)|+ |S(jω)||w(jω)| ¿ 1, ∀ω, (24)

where S(s) is the sensitivity function, which is given by

S(s) =e

rGc2(s)− d=

11 + Gc1(s)Gp(s)

. (25)

By substituting equations (19) and (20) in equation (25),

S(s) =η1 DF FOsλ

1 + η1 DF FOsλ. (26)

If the control system design is to be carried out to accom-modate a specific type of input such as step setpoint change,then the weighting function will be an integrator [26].

5 Simulation resultsFor simulation, consider the FOS plant given by [11]

Gp(s) =103.9705

0.0073s1.6807 + 0.1356s0.8421 + 1. (27)

The integer order model of the FOS [28] is given by

Gp(s) =68944.5109

s2 + 73.6206s + 663.7429. (28)

The frequency response of the fractional order plant and in-teger order plant is shown in Fig. 4.

Fig. 4 Frequency response of the plant.From Fig. 4, the corner frequency of the plant is found

to be 10 rad/s. The desired specification for the controllerdesign is open loop bandwidth is equal to the closed loopbandwidth. The filter time constant is chosen as 0.1 s for theconventional IO controller. The IO-IMC is obtained usingequations (a6)–(a8) given in Appendix A and is given by

Gc(s) =0.001ηIO

(1 +9.0157

s+ 0.0135s) (29)

Using equations (7)–(11), the FO-IMC for the plant de-scribed by the equation (28) is obtained and is given by

Gc(s) =0.007

η1 DF FO(1 +

7.3846s0.8421

+ 0.0534s0.8386). (30)

The filter time constant obtained for FO-IMC with respectto regulatory performance and tracking performance arefound and η1 DF FO is 0.1834 and η2 DF FO is 0.1128 re-spectively. The closed loop frequency response of the sys-tem with IO-IMC and FO-IMC are shown in Fig. 5. FromFig. 5, the bandwidth of the closed loop system with differ-ent controllers are found to be 10.

Fig. 5 Closed-loop frequency response of the system with differ-ent controllers.

The closed loop corner frequency of the process withdifferent controllers is shown in Table 1. The filter timeconstant tuned for conventional IO-IMC using disturbancerejection meets the desired specification of 10 rad/s usedfor set point tracking. In case of SDF FO-IMC, the filtertime constant η1 DF FO tuned with respect to regulatory per-formance provides poor tracking performance as shown inTable 1. Hence, TDF FO-IMC is attempted in which thecontroller tuned for disturbance rejection meets the desiredbandwidth specification for set point tracking.

Table 1 Closed-loop corner frequency of the systemdifferent controllers.

Disturbance rejection/ Set point tracking/Controller(rad·s−1) (rad·s−1)

IO-IMC 10 10SDF FO-IMC 10 5.5872TDF FO-IMC 10 10

6 Robustness issuesThe robustness of the designed controller is analysed with

the performance of the closed loop system at different op-erating regions. The model of the plant at second operatingcondition as given by Nataraj et al. [11] is

Gp(s) =110.9238

0.0130s1.6062 + 0.1818s0.7089 + 1(31)

and the corresponding IO model of the plant is found to be

Gp(s) =110.9238

0.0017s2 + 0.11695s + 1. (32)

The frequency responses of the FO and IO plant for differ-ent operating conditions are shown in Fig. 6.

300 T.Vinopraba et al. / J Control Theory Appl 2012 10 (3) 297–302

Fig. 6 Frequency response of the plant for different operatingcondition.

The closed loop frequency responses of the plant withdifferent controllers for two different operating conditionsare obtained and shown in Figs. 7–9.

Fig. 7 Closed-loop frequency response of the IO plant withIO-IMC.

Fig. 8 Closed-loop frequency response of FO plant with SDFFO-IMC.

Fig. 9 Closed-loop frequency response of FO plant with TDOFFO-IMC.

6.1 Robust stability analysisFor robustness analysis, assume Gp(s) to be the model

of the plant at the first operating condition and Gp1(s) to bethe model of the plant at second operating condition.6.1.1 IO controller

For IO controller, Gp(s) is given by equation (28) andGp1(s) is given by equation (32). From equation (a4),

Gc(s) =s2 + 73.6206s + 663.7429

68944.5109(0.1)s, (33)

Substituting Gp(s) and Gc(s) in equation (a12),

T (s) =1

0.1s + 1, (34)

Substituting Gp(s) and Gp1(s) in equation (a13),

G∆(s)=−6.2818s2 + 57.7374s + 4680.3737

117.2056s2+8063.0605s+68944.5109, (35)

The maximum value of |T (jω)||G∆(jω)| is found to be0.3951 and hence the closed loop system is robustly stable.6.1.2 FO controller

For FO controller, Gp(s) is given by equation (27) andGp1(s) is given by equation (31). Using equation (20),Gc1(s) is found to be

Gc1(s) =0.0073s1.6807 + 0.1356s0.8421 + 1

103.9705(0.1834)s0.8421. (36)

Hence, equation (22) and (23) becomes,

T (s) =1

0.1834s0.8421 + 1(37)

andG∆(s) = (0.8097s1.6807 − 1.3516s1.6062+15.0412s0.8421

−18.9018s0.7089 + 6.9533)/(1.3516s1.6062

+18.9018s0.7089+103.9705). (38)The maximum value of |T (jω)||G∆(jω)| is found to be 0.35and hence the closed loop system is robustly stable.6.2 Robust performance analysis6.2.1 IO controller

Substituting equations (28) and (33) in equation (a20),

S(s) =0.1s

0.1s + 1. (39)

The maximum value of |T (jω)||G∆(jω)| is found to be0.4335.6.2.2 FO controller

Substituting equations (27) and (36) in equation (25),

S(s) =0.1834s0.8421

0.1834s0.8421 + 1. (40)

The maximum value of |T (jω)||G∆(jω)| is found to be0.3905.

7 ConclusionsAn IMC based TDF fractional order controller is reported

for controlling a class of FO systems. When the power ofthe integral s term is decreased, the robustness of the sys-tem increases. However, in an SDF FO-IMC, the filter timeconstant tuned for disturbance rejection does not meet therequirement for the set point tracking. Hence, TDF FO-IMC has been designed, which eliminates the shortcomings

T.Vinopraba et al. / J Control Theory Appl 2012 10 (3) 297–302 301

of the SDF FO-IMC. The designed TDF FO-IMC is alsoshown to be robustly stable.

References[1] J. Cervera, A. Banos, C. A. Monje, et al. Tuning of fractional PID

using QFT. Proceedings of 32nd IEEE Conference on IndustrialElectronics, Paris: IEEE, 2006: 5402 – 5407.

[2] Y. Chen, T. Bhaskaran, D. Xue. Practical tuning rule developmentfor fractional order proportional and derivative controllers. Journalof Computational and Nonlinear Dynamics, 2008: 021403.1 –021403.8.

[3] H. Li, Y. Chen. A Fractional order proportional and derivative (FOPD)controller tuning algorithm. Proceedings of 47th IEEE Conference onControl and Decision, Mexico: IEEE, 2008: 4059 – 4063.

[4] G. Maione, P. Lino. New tuning rules for fractional PIα controllers.Nonlinear Dynamics, 2007, 49(1/2): 251 – 257.

[5] C. A. Monje, B. M. Vinagre, V. Feliu, et al. Tuning and auto tuningof fractional order controllers for industry applications. ControlEngineering Practice, 2008, 16(7): 798 – 812.

[6] D. Valerio, J. S. Da Costa. Tuning of fractional PID controllers withZiegler-Nichols-type rules. Signal Processing, 2006, 86(10): 2771 –2784.

[7] C. Yi, J. Liang, C. Gang. Optimization of fractional order PIDcontrollers based on genetic algorithms. Proceedings of 4th IEEEConference on Machine Learning and Cybernetics, Guangzhou:IEEE, 2005: 5686 – 5689.

[8] C. Yi, C. Gang. Design of fractional order controllers based onparticle swarm optimization. Proceedings of 1st IEEE Conference onIndustrial Electronics and Applications, Singapore: IEEE, 2006: 5402– 5407.

[9] D. Xue, Y. Chen. A comparative introduction of four fractional ordercontrollers. Proceedings of 4th World Congress on Intelligent Controland Automation, Shanghai, 2002: 3228 – 3235.

[10] I. Podlubny, L. Dorcak, I. Kostial. On fractional derivatives,fractional-order dynamic systems and PIλDµ controllers.Proceedings of the 36th IEEE Conference on Decision and ControlConference, California: IEEE, 1997: 4985 – 4990.

[11] P. S. V. Nataraj, R. Kalla, M. M. Deshpande. Computation of spectralsets for uncertain linear fractional order systems using intervalconstraint propagation. Proceedings of the 17th World Congressinternational Federation of Automatic Control, South Korea, 2008.

[12] Y. Luo, Y. Chen. Fractional order proportional derivative controllerfor a class of fractional order systems. Automatica, 2009, 45(10):2446 – 2450.

[13] C. Zhao, D. Xue, Y. Chen. A fractional order PID tuning algorithmfor a class of fractional order plants. Proceedings of IEEE Conferenceon Mechatronics and Automation, Canada: IEEE, 2005: 216 – 221.

[14] A. Oustaloup, M. Bansanol. First generation Crone control.Proceedings of IEEE Conference on Systems, Man and Cybernetics,France: IEEE, 1993: 130 – 135.

[15] L. A. Monje, V. Feliu. The fractional order Lead Compensator.Proceedings of 2nd IEEE Conference on Computational Cybernetics,Vienna, 2004: 347 – 352.

[16] D. Maiti, M. Chakraborty, A. Acharya, et al. Design of fractionalorder self tuning regulator using optimization algorithm. Proceedingsof 2nd IEEE Conference on Computer and Information Technology,Singapore: IEEE, 2008: 470 – 475.

[17] S. Ladaci, A. Charef. Model reference adaptive control withfractional derivative. Proceedings of International Conference onTele-communication systems, Medical electronics and Automation,Algeria, 2003.

[18] S. Ladaci, J. J. Loiseau, A. Charef. Fractional order adaptive highgain controllers for a class of linear systems. Communications inNonlinear Science and Numerical Simulation, 2008, 13(4): 707 – 714.

[19] H. Delvari, R. Ghaderi, A. Ranjbar, et al. Fuzzy fractional ordersliding mode controller for non linear systems. Communications inNonlinear Science and Numerical Simulation, 2010, 15(4): 963 – 978.

[20] Y. Chen, K. L. Moore. On Dα type iterative learning control.Proceedings of 40th IEEE Conference on Decision and Control,Orlando: IEEE, 2001: 4451 – 4456.

[21] S. E. Hamamci, M. Koksal. Calculation of all stabilizing fractional-order PD controllers for integrating time delay systems. Computersand Mathematics with Applications, 2010, 59(5): 1621 – 1629.

[22] T. Vino praba, N. Sivakumaran, N. Selvaganesan, et al. Stabilizationusing fractional order PIDα controllers for first order time delaysystem. Proceedings of International Conference on Advances inComputing Control and Telecommunication Technologies, Kerala:IEEE, 2009: 725 – 728.

[23] D. E. Rivera, M. Morari, S. Skogestad. Internal model control for PIDcontroller design. Industrial Engineering Chemical Process, 1986,25: 252 – 265.

[24] D. Li, W. Fan, Q. Jin, et al. An IMC PIλDµ controller designfor fractional calculus system. Proceedings of 29th Chinese ControlConference, Beijing: IEEE, 2010: 3581 – 3585.

[25] T. Vinopraba, N. Sivakumaran, S. Narayanan. IMC based fractionalorder PID controller. Proceedings of IEEE Conference on IndustrialTechnology, Auburn: IEEE, 2011: 71 – 76.

[26] M. Morrari, E. Zafiriou. Robust Process Control, Englewood Cliffs,New Jersy: Prentice Hall, 1989.

[27] G. C. Goodwin, S. F. Graebe, M. E. Salgad. Control system design,Valparaiso: Prentice Hall, 2000.

[28] S. Narayanan, N. Sivakumaran, T. Vinopraba, et al. IMC BasedPIλDδ controller design for gas turbine plant. Proceedings ofInternational Conference on Modeling and Simulation, Kerala, 2009:386 – 390.

Appendix AConsider the process Gp(s) to be

Gp(s) =K

as2 + bs + c, (a1)

where K is the gain of the process, a, b and c are the real coeffi-cients and the model Gm(s) is same as that of that of the processGp(s).

Gm(s) =K

as2 + bs + c. (a2)

Based on pole-zero cancellation; assume Gi(s) to be

Gi(s) =as2 + bs + c

K(ηIOs + 1), (a3)

where ηIO is the filter time constant. The filter time constant has tobe tuned according to the desired specification. Substituting Gi(s)and Gm(s) in equation (1), then

Gc(s) =as2 + bs + c

KηIOs. (a4)

The PID controller transfer function is given by

Gc(s) = Kc(1 +1

Tis+ Tds). (a5)

Based on [26], equating (a4) with (a5), the controller parametersare obtained to be

Kc =b

KηIO, (a6)

Ti =b

c, (a7)

Td =a

b. (a8)

The closed loop transfer function with respect to disturbance re-jection is given by

y(s)

d(s)=

ηIOs

ηIOs + 1. (a9)

302 T.Vinopraba et al. / J Control Theory Appl 2012 10 (3) 297–302

The corner frequency is determined from the bandwidth specifi-cation. The closed loop transfer function with respect to set pointtracking is given by

y(s)

r(s)=

1

ηIOs + 1. (a10)

In the above equation, the filter time constant is tuned accordingto the bandwidth specification. It is found that for the conventionalinteger order IMC, the filter time constants tuned for disturbancerejection and for tracking performance are same.

Robust stability analysis:For the closed loop system to be robustly stable, the following

condition must be satisfied:|T (jω)||G∆(jω)| < 1, ∀ω, (a11)

where

T (s) =Gp(s)Gc(s)

1 + Gp(s)Gc(s)(a12)

and

G∆(s) =Gp1(s)−Gp(s)

Gp(s). (a13)

Gp(s) is the model of the process at an operating condition forwhich the controller is designed.

Gp(s) =K0

a0s2 + b0s + c0. (a14)

Hence Gc(s) is given by

Gc(s) =a0s

2 + b0s + c0

K0ηIOs, (a15)

Gp1(s) is the model of the process at a different operating condi-tion.

Gp1(s) =K1

a1s2 + b1s + c1. (a16)

Substituting (a14), (a15) and (a16) in equations (a12) and (a13)

T (s) =1

1 + ηIOs, (a17)

G∆(s)=((K1a0 −K0a1)s2 + (K1b0 −K0b1)s

+(K1c0−K0c1)/(K0a1s2+K0b1s+K0c1). (a18)

Robust performance analysis:The closed loop system will meet the robust performance spec-

ification if and only if|T (jω)||G∆(jω)|+ |S(jω)||w(jω)| ¿ 1, ∀ω, (a19)

where S(s) is the sensitivity function, which is given by

S(s) =1

1 + Gc(s)Gp(s). (a20)

By substituting (a14) and (a15) in equation (a20),

S(s) =ηIOs

1 + ηIOs. (a21)

Appendix BFrom the simulation results, the filter time constant tuned for

the set point tracking is η1 = 0.1128. While applying the samefilter time constant to disturbance rejection, the transfer functionbecomes ˛̨

˛̨y(s)

d(s)

˛̨˛̨ =

˛̨˛̨ η1s

α

η1sα + 1

˛̨˛̨ (a22)

=

˛̨˛̨ 1

η1sα + 1

˛̨˛̨ ∗ |η1s

α|, (a23)˛̨˛̨ 1

η1sα + 1

˛̨˛̨ = 1√

2. (a24)

(Because η1 is tuned for the set point tracking)˛̨˛̨y(s)

d(s)

˛̨˛̨ = 1√

2∗ |η1s

α|. (a25)

The desired specification cannot be achieved for the SDF FO-IMCdue to fractional power of the s term.

T. VINOPRABA received the B.E. degree in Elec-tronics and Instrumentation Engineering from An-namalai University, Chidambaram, in 2006, M.E.degree in Process Control and Instrumentation En-gineering from Annamalai University in 2008, andcurrently she is pursuing her Ph.D. in National In-stitute of Technology, Trichy. Her research interestsinclude fractional order controller, controller de-sign for chemical and biomedical systems. E-mail:

vinopraba@gmail.com.

N. SIVAKUMARAN received the B.E degree inElectronics and Instrumentation Engineering fromBharathidasan University, Trichy, in 1999, M.E.degree in Process Control and InstrumentationEngineering from Annamalai University in 2002and Ph.D. from National Institute of Technology,Trichy, in 2007. His research interests include sys-tem identification, intelligent systems, controllerdesign for chemical and biomedical systems. He

is the recipient of the AICTE-National Doctoral Fellowship for the year2004–2006. He has research grant from DST, MHRD, CDAC, Governmentof India. He has teaching experience of 8 years. E-mail: nsk@nitt.edu.

S. NARAYANAN received the B.E. degree in Elec-tronics and Instrumentation Engineering from An-namalai University, Chidambaram, and M.E. de-gree in Instrumentation Engineering from MIT,Anna University, Chennai. He completed his Ph.D.from MIT, Anna University, Chennai. He is cur-rently working as Assistant Professor in the De-partment of Instrumentation and Control Engineer-ing, National Institute of Technology, Trichy. His

research interests include PID control design and control engineering. E-mail: narayanan@nitt.edu.

T. K. RADHAKRISHNAN received his B.E. de-gree in Chemical Engineering from AnnamalaiUniversity and M.Tech. degree from Indian Insti-tute of Technology, Chennai, India. After his grad-uate program he joined Indian Institute of Chemi-cal Technology, Hyderabad in the Simulation, Op-timization and Control Group. He later moved toRegional Engineering College, Tiruchirappalli andreceived Ph.D. He is currently working in National

Institute of Technology, Tiruchirappalli as Professor and Head of Chemi-cal Engineering Department. His interests include process control, processmodeling and soft computing. E-mail: radha@nitt.edu.