Analysis of Hybrid Temperature Control for Nonlinear Continuous Stirred Tank Reactor

Analysis of Hybrid TemperatureControl for Nonlinear ContinuousStirred Tank Reactor

Om Prakash Verma, Sonu Kumar and Gaurav Manik

Abstract Classical controllers usually require a prior knowledge of mathematicalmodeling of the process. The inaccuracy of mathematical modeling degrades thecontrol performance of the continuous stirred tank reactor (CSTR), which showsnonlinearity to some extent. It is very necessary to attain desired temperature withina specied period of time to avoid overshoot and absolute error, with better tem-perature tracking capability, else the process is disturbed in the nonlinear CSTRsystem. This paper studies the output (temperature) tracking and disturbancerejection problem of nonlinear CSTR control systems with uncertainties via clas-sical control PID, cascade control, and hybrid intelligent controller that includesFLC, adaptive control, and adaptive neuro-fuzzy inference system (ANFIS). Thispaper evaluates change in an adaptive controller response with varying adaptivegain. It has been observed that OLTF of CSTR is stable, and adaptive controller isbest suitable for temperature control for ISE, and also has much better temperaturetracking capability. Adaptive controller and ANFIS both have observed zeroovershoot.

Keywords CSTR Nonlinearity PID controller Cascade controller Adaptivecontroller MIT rule FLC ANFISNomenclature

Density of the material in the system lb/ft3

V Total volume of the system ft3

F Volumetric flow rate of the system ft3/hCA Molar concentration (moles/volume) of component A in the systemrA Reaction rate per unit volume component A in the system

O. Prakash Verma G. Manik (&)Department of Polymer and Process Engineering, Indian Instituteof Technology Roorkee, Saharanpur Campus, Saharanpur, Indiae-mail: [email protected]

S. KumarDepartment of Electrical and Electronics Engineering, Graphic Era University,Dehradun, India

Springer India 2015K.N. Das et al. (eds.), Proceedings of Fourth International Conference on SoftComputing for Problem Solving, Advances in Intelligent Systems and Computing 336,DOI 10.1007/978-81-322-2220-0_9

103

Q Amount of heat exchanged between the system and its surrounding perunit time

U Over all heat transfer coefcientTst, Tj Temperature of the steam and jacket, respectivelyAH Total area of heat transferDH Heat of reaction at temperature T

1 Introduction

Temperature control is one of the most critically limiting factors in the productionoperations of process industries, for example, production of propylene glycol formhydrolysis of propylene oxide is an exothermic reaction [1] requiring carefultemperature control, due to its high nonlinear dynamics, of continuous stirred tankreactor (CSTR), controlling its temperature has been a challenging task, for processautomation engineers. The overshoot and undershoot are undesired which badlyaffect the nal product, if the temperature is out of the given range. Therefore, it isnecessary for a control engineer to reach steady state at given desired set pointtemperature range quickly and also to minimize the overshoot. Since, the CSTRpossesses nonlinearity and its response changes in an unpredictable manner, it is noteasy to control the parameters accurately.

A design methodology is proposed for the analysis and synthesis of robust linearcontrollers for a nonlinear CSTR [2]. The achievement of robust stability and robustperformances is guaranteed when the operating regions are dened in phase plane.To overcome the difculty of achieving zero overshoot, zero absolute error, andbetter temperature tracking capability, the intelligent controllers using FLC andAdaptive Neuro-fuzzy Inference System (ANFIS) have been proposed for waterbath temperature control system [3]. As compared to conventional controller, FLCand ANFIS produce a stable control signal. It has been found to exhibit bettertemperature tracking capability with almost zero overshoot and minimum absoluteerror. Model reference adaptive control (MRAC) [47] has been designed previ-ously for second-order system using MIT rule scheme or gradient method toovercome the variation in process dynamics due to its nonlinear nature and changesin environmental condition with disturbances variation.

One of the major disadvantages of non-adaptive control is it cannot cope thevariation in the parameters of the process. When the plant undergoes transitions orexhibits nonlinear behavior and when the structure of the plant is not known, thenadaptive scheme has been found to show efcient control [8]. Adaptive trackingcontrol is considered for general nonlinear systems using multilayer neural network(MNN) [9] that is used to realize feedback linearization. This technique ensures thestability of closed-loop system, and the system output tracks a set point signal whiletracking error converges to neighborhood of zero.

104 O. Prakash Verma et al.

This paper demonstrates a comparative analysis of controller efciency amongconventional controller (PID), advanced controller (Cascade), and intelligent con-trollers (Fuzzy, MRAC, and ANFIS) for controlling the temperature of nonlinearCSTR and discusses each.

2 Mathematical Modeling

Chemical reactors often have signicant heat effects [10], so it is important to beable to add or remove heat from them. In a jacketed CSTR, the heat is added orremoved by virtue of the temperature difference between a jacket fluid and thereactor fluid. An irreversible exothermic reaction A ! B DH occurs in a CSTR.The heat of reaction is removed by the coolant medium that flows through a jacketaround the reactor as shown in Fig. 1. Consequently, when the CSTR is at steadystate, the heat produced by the reaction should be equal to the heat removed by thecoolant. The objective is to keep the effluent temperature T at a desired value Ts.The operation of CSTR is disturbed by external factor, such as changes in the feedflow rate and inlet temperature (Fi and Ti). At steady state, there is no need tosupervise and to control the system. But, this is not practically true, since Fi and Tiare frequently changing. And, therefore, some form of control action [11] will beneeded to alleviate the impact of the changing of the disturbance and keep thetemperature T at the desired value. During the process, (i) mixing in the reactor isperfect; liquid density (q) and the heat capacity Cp are constant (ii) To remove theexothermic heat, the coolant is introduced into jacket; the reactor is assumed to beperfectly insulated (iii) Coolant is perfectly mixed in the jacket (iv) volume ofreactor and jacket is to constant.

Total mass balance across reactor gives,

dVdt

Fi F 1

Coolant ( ) Product ( )

Reactant ( )

Fig. 1 Conguration of a perfectly mixed CSTR with a cooling jacket and the process parameters

Analysis of Hybrid Temperature Control for Nonlinear Continuous 105

Balance on component A yields,

CAdVdt

V dCAdt

FiCAi rA V FCA 2

Using Eq. (1),

dCAdt

FiVCAi CA rA 3

Since, rA = rate of disappearance of A and

rA K0eE=RTCA 4

Applying energy balance across the reactor,

dVqCpTdt

FiqCpTi FqCpT Q DH rAV 5

VdTdt

T dVdt

FiTi FT QqCp DH rAVqCp

6

From Eq. (1), we get

dTdt

FiVTi T QqVCp DH rA

1qCp

7

Now, using Eq. (4),

dTdt

FiVTi T QqVCp DH

K0eE=RTCAqCp

8

The state variable form that includes the effect of cooling jacket on CSTRresponse is given as,

dCAdt

f1 CA; T ; Tj Fi

VCAi CA K0eE=RTCA 9

dTdt

f1 CA; T ; Tj Fi

VTi T UA T TjVqCp DH

K0eE=RTCAqCp

10


Similarly, the equation of jacket temperature is given as

dTjdt

f3 CA; T ; Tj Fj

VjTj in Tj UAT Tj

VjqjCpj11

where,

Q UAT Tj 12

Since, the above sets of Eqs. (9)(10) are nonlinear, on linearizing [12],

dCAdt

1sCAi CA K0eE=RTCA; 13

where, s V=FidTdt

1sTi T QqVCp SK0e

E=RTCA 14

where, S DHqCp : The nonlinear term present in the modeling equation, eE=RTCA;is linearized close to the operating point, T0 and CA0 as

eE=RTCA eE=RT0CA0 @ eE=RTCA

@T

" #T0;CA0

T T0

@ eE=RTCA

@CA

" #T0;CA0

CA CA0 15

eE=RTCA eE=RT0CA0 E

RT20eE=RT0CA0

T T0 eE=RT0CA CA0

16

The linearized model,

dCAdt

1sCAi CA K0eE=RT0CA0

E

RT20eE=RT0CA0 T T0

eE=RT0CA CA0 17

dTdt

1sTi T QVqCp SK0e

E=RT0CA0 E

RT20eE=RT0 T T0

eE=RT0CA CA0 18


At steady state condition,

dCAdt

0 1sCAi0 CA0 K0eE=RT0CA0 19

dT0dt

0 1sTi0 T0 Q0VqCp SK0e

E=RT0CA0 20

Equations (19)(20) represent the modeling equation. Linearized model (interms of deviation variables for concentration) yields,

ddt

CA CA0 1s

CAi CAi0 CA CA0 K0E

RT20eE=RT0CA0 T T0

K0eE=RT0 CA CA0 21

ddtC0A

1s

C0Ai C0Ah i

K0 ERT20

eE=RT0CA0T0 K0eE=RT0C0A 22

where the deviation variables are given as,

C0Ai CAi CAi0 ; C0A CA CA0 ; T 0 T T0

Likewise, expressing the linearized model (in terms of deviation variable fortemperature) as

ddt

T T0 1s Ti Tio T T0 Q Q0VqCp

SK0 ERT20

eE=RT0CA0 T T0 eE=RT0 CA CA0

23

dT 0

dt 1

sT 0i T 0 Q

VqCp SK0 E

RT20eE=RT0CA0T

0 eE=RT0C0A

24

Therefore, steady-state solution is given as

f1 CA; T; Tj dCA

dt 0 Fi

VCAi CAi K0eE=RTCA 25

f2 CA; T; Tj dT

dt 0 Fi

VTi T UAT TjVqCp DH

K0eE=RTCAqCp

26


f3 CA; T; Tj dTj

dt 0 Fi

VTj in Tj UAT TjVjqjCpj

27

The above equations are solved and the matrices, A, B, C, and D of stateequation are found. The state and input variables represented in deviation variableform are as follows:

X X1X2

CA CAS

T Ts

; Y T Ts; U

U1U2U3U4

26664

37775

Tj TjsTi TisCAi CA isF Fs

26664

37775

A FiV K0eE=RT0 K0ERT20 e

E=RT0CA0

DHqCp K0 eE=RT0 FiV DHK0ERT20qCp

eE=RT0CA0 UAHVqCp

264

375;

B 0UAHVqCp

" #; C 0 1; D 0

From reactor parameters values used previously [1316] and shown in Table 1,the state matrices determined are given as:

A 7:991 0:01372922:9 4:5564

; B 0

1:4582

; C 0 1 ; D 0

Table 1 Parameters valuesof proposed design of CSTRsystem

Reactor parameters Parameter values

E (Btu/lb mol) 32,400

Ko (h1) 16.96 1012

DH (Btu/lb mol) 39,000

UAH (Btu/h F) 6,600

qcp (Btu/ft3 F) 53.25

R (Btu/lb mol F) 1.987

Fi/V (h1) 4

CAi (lb mol/ft3) 0.132

Ti (F) 60

CAo (lb mol/ft3) 0.066

To (F or R) 101.1 or 560.77

Tji (F) 80

Tji (F) 0

jCpj (Btu/ft3 F) 55.5


The transfer function Gps of the system based on above matrices obtained isfound as

Gp s TTj 1:458s 11:65

s2 3:434s 3:557 28

The evaluated Eigen values are as follows:

Y 1:7173 i0:8273 and 1:7173 i0:8273

Complex Eigen value with negative real part ensures the stability of CSTR.

3 Control Topologies

The controllers are classied as classical and intelligent. P, PI, PID, and Otto-Smithare examples of classical controllers that require a prior and accurate knowledge ofmathematical model of the process in order to design an efcient controller. Anyinaccuracy in mathematical modeling results in inaccurate calculation of controlparameters and hence poor controlling action. Intelligent controllers, overcome thisdisadvantage, by using a new approach to the controller design that does not requireknowledge of mathematical model of the process. FLC, MRAC, Articial NeuralNetwork (ANN), ANFIS, and Model Predictive Control (MPC) are some examplesof intelligent controllers.

3.1 PID Controller

A PID controller calculates an error value as the difference between a measuredprocess variable and a desired set point. The controller, as shown in Fig. 2, attemptsto minimize the error by adjusting the process control inputs. Control signal of PIDcontroller is given as follows.

Fig. 2 Conguration of a block diagram of a conventional PID controller


This may also be written as

u t Kpe t KiZ t0

e s ds Kd detdt 29

The transfer function, Gcs; of PID controller can be represented as

Gc s Kp 1 1sis sds

30

In discrete form, transfer function of PID controller may be represented as givenbelow

Uk K ek 1Ti ek ek 1 DT Td ek ek 1DT

31

The Eq. (29) is used for the realization in FLC.The selection of a controller type and its parameters Kp;Ki;Kd is related to the

model of process to be controlled. The adjustment and selection of controllerparameters to achieve satisfactory control is essentially an optimization problem.Ziegler and Nichols (Z-N) developed a closed-loop method for parameters tuning[17]. In this paper, the parameters of PID have been tuned by Z-N tuning methodsand are determined as, Kp 0:1; Ki 0:116 and Kd 0:020:

3.2 Cascade Controller

The response of simple feedback control has been improved by the changes in thecoolant temperature [18] by measuring Tj and taking control action before its effectcan be felt by the reacting mixture. If Tj rises, the flow rate of coolant is increased toremove the same amount of heat and vice versa. Therefore, two control loops havebeen involved using two different measurements, T and Tj, that share a commonvariable, Fj: This is illustrated in Fig. 3.

The state space model matrices for cascaded controller [19] reduce to

A 7:991 0:0137 02922:9 4:5564 1:45820 4:7482 5:8977

24

35; B 00

3:2558

24

35; C 0 1 0

0 0 1

;

D 00


The transfer function for primary controller, Gp1s; and secondary controller,Gp2s; are found as

Gp1s TTj 4:747s 37:937

s3 9:332s2 16:97s 33:9 32

Gp2s TjFj 3:256s2 11:18s 11:83s3 9:332s2 16:97s 33:9 33

The primary and secondary controllers have also been tuned using Z-N methodsand parameters determined as: Kp1 655:007; Ki1 4; 265:269; Kd1 20:197; forprimary loop, andKp2 0:092;Ki2 0:022;Kd2 0:006; for secondary loop.

3.3 Fuzzy Logic Controller

Fuzzy inference system (FIS) is proposed as a highly efcient method for con-trolling the settling time, delay time, and overshoot parameters for nonlinear CSTRsystems. Fuzzy logic is a way to make machines more intelligent, enabling them toreason in a fuzzy manner like humans [20].

The FLC makes a nonlinear mapping between the input and the output usingmembership functions and linguistic rules (normally in the form If_Then_). TheCSTR system uses two input variables error (e), change in error (de), and one outputvariable (Y). The computational structure of fuzzy logic control scheme is composedof fuzzication, inference engine, and de-fuzzication as shown in Fig. 4. Fuzzi-cation converts a crisp value (real value) into a member of fuzzy sets. FIS formu-lating the mapping from a given input to an output using fuzzy logic, while de-fuzzication converts the fuzzy output determined by the inference system to a crisp

Primary controller Secondary Controller

CSTR dynamics

TM 1

TM 2

Jacket Dynamics

TC 1 TC 2 +

Fig. 3 Generalized block diagram of a cascade controller


value. In FLC, the membership functions are utilized to nd the degree of mem-bership of the element in a given set. The fuzzy control rules have the form [21]:

R1 : If X is A1 and Y is B1; then Z is C1R2 : If X is A2 and Y is B2; then Z is C2... ..

. ... ..

. ... ..

.

Rn : If X is An and Y is Bn; then Z is Cn

where X, Y, and Z are linguistic variables that represent two process state variablesand one control variable, respectively;

Ai;Bi and Ci are linguistic values of the linguistic variable X, Y, and Z in theuniverse of discourse U, V, and W, respectively, with i = 1, 2, 3 n; ANDoperator, MAMDANI-type FIS and 11 rule base has been utilized here and shownin Fig. 5. Centroid method has been used for controlling the fuzzy inference controlaction to real value. The gain for error (e) and derivative of error (de) has beentuned to 0.5 and 0.5, and the gain for FLC controller taken as 150.

InputsFuzzifification Inference De-fuzzifification, denormalization

CSTR

Knowledge base

Rule base

Sensors Output-scaling factors, normalization

Scaling factors, normalization

Fig. 4 Block diagram of fuzzy logic control (FLC)

Fig. 5 FIS editor of fuzzy control model for a CSTR system


3.4 Adaptive Control

Adaptive control is a combination of a parameter estimator, which generatesparameter estimates online, with a control law in order to control classes of plantswhose parameters are completely unknown and/or could change with time in anunpredictable manner [22]. An adaptive control can be used when the plantundergoes the transitions and show nonlinearity and also plant structure is notknown exactly [23]. This control can adjust the parameter automatically to com-pensate for variations in the characteristics of the CSTR. An adaptive control forCSTR consists of two loops: a normal feedback loop and the parameter adjustmentloop as shown in Fig. 6.

3.4.1 Model Reference Adaptive Control (MRAC)

MRAC is also regarded as adaptive servo system [2426] in which, the desiredperformance is expressed in terms of a reference model, which gives the desiredresponse to a command signal. The parameters are changed on the basis of feedbackfrom the error, e Yp Ym; where Yp is the plant output and Ym; the model output.

The mechanism for adjusting the parameters in a MRAC can be obtained using agradient method.

3.4.2 MIT Rule

For a closed-loop system, the controller has one adjustable parameter, h; dependenton the minimized square of the prediction error, e. The desired closed-loop systemresponse is specied by a model whose output is Ym:

And,

e Yp Ym 34

CSTRController Control Signal

O/P

Controller Parameters

Command Signal

Adjustment Mechanism

Reference Model ( )

Fig. 6 Block diagram of MRAC applied to a CSTR


Adjusting the parameters in such a way that the loss function, Jh 12 e2 isminimized. To make J small, the parameter h is changed in the direction of thenegative gradient of J, i.e.,

dhdt

c @J@h

ce @e@h

; 35

where c is the adaptation gain and @e@h the sensitivity derivative of the system. It givesan idea about how the error is influenced by the adjustable parameters. The transferfunction of the process is then represented as given below

Ypu K

s2 a1s a2 36

where K, a1 and a2 are the process parameters and control signal given as

u h1uc h2Yp 37

where h1; h2 and uc are adjustable parameters and command signal, respectively.Using Eqs. (36) and (37),

Ypuc

Kh1s2 a1s a2 Kh2 38

Ymuc

Kms2 A1s A2 39

where Km; A1 and A2 are the reference model parameters. And, for a perfect model(Fig. 7),

s2 a1s a2 Kh2 s2 A1s A2; 40

and

@e@h1

Kucs2 A1s A2 and

@e@h2

KYps2 A1s A2 41

Therefore,

dh1dt

c @e@h1

e c Kucs2 A1s A2 e 42

dh2dt

c @e@h2

e c KYps2 A1s A2 e 43


Then,

h1 csKuc

s2 A1s A2 e

and h2 csKYp

s2 A1s A2 e

44

Second-order model may be represented as:

Gms x2n

s2 2exns x2n45

The transfer function model of the CSTR temperature process from state spacematrix values is determined to be

Gps TTj 1:458s 11:65

s2 3:434s 3:557 k

s2 3:434s 3:557 46

For the temperature control, a maximum overshoot (Mp) is 2 % and a settlingtime (ts) less than 3 min are selected (assuming tolerance band (TB) is 2 %) [27].For this second-order system,

n ln Mp=100 p

1

1 lnMp=100ph i2

vuut and xn 4=n ts 47

Fig. 7 Block diagram of a rst-order MRAC


where n is the damping ratio, and xn is the natural frequency of second-ordersystem. For optimum performance characteristics, n 0:707 and xn 1:885 rad/shas been chosen.

The transfer function of the model is given as

Gm s 3:55s2 2:66s 3:55 : 48

3.5 Adaptive Neuro-fuzzy Inference System (ANFIS)

A neuro-fuzzy (ANFIS) system [28] is a combination of neural network and fuzzysystems in such a way that neural network is used to determine the parameters offuzzy system. This is illustrated in Fig. 8.

The neuro-fuzzy system with the learning capability of neural network and withthe advantages of the rule-based fuzzy system can improve the performance sig-nicantly and can provide a mechanism to incorporate past observations into theclassication process. The fuzzy inference system under consideration has twoinputs x and y and one output z. For a rst-order Sugeno fuzzy model, a rule set isthe followed:

RULE 1: If x is A1 and y is B1, then f1 p1x q1y r1;RULE 2: If x is A2 and y is B2, then f2 p2x q2y r2;Figure 8 illustrates the reasoning mechanism for this Sugeno model with the

corresponding equivalent ANFIS architecture, where nodes of the same layer have

Fig. 8 Architecture of ANFIS


similar functions. First layer is the premise parameters, calculated by parameterizedmembership function. Output of second layer is the product of two incoming sig-nals, third layer output nds the ring strengths of each node, the output of layer 4is the product of normalized ring weight with node function, and layer 5 overalloutput of the ANFIS model can be written as follows:

f w1w1 w2 f1

w2w1 w2 f2 w1f1 w2f2

P2i1 wifiP2i1 wi

49

where w1 and w2 are normalized ring strengths.The overall output expressed in Eq. (49) is a linear combination of the consequent

parameters when the values of premises parameters at level 1 are xed. Hybridlearning algorithm combines the gradient descent method and the least squareestimator (LSE) method which used to rene these parameters. In implementing thetraining scheme, a sequence of random input signals in ANFIS limited between 0and 5 is injected directly to the CSTR and the gain for ANFIS controller is 4.95.

4 Results and Discussion

The outputs of PID, Cascade, FLC, ANFIS, and adaptive controller for a step changein set point are shown in Fig. 9 and their performances are presented in Table 2 forcomparison. The goal is to screen and design a controller that will control thetemperature of CSTR system most efciently and follow a reference prole.

Results show that adaptive and cascade controllers have comparatively smallerdelay time (td) of 21.4 and 19.0 min, while PID, Fuzzy, and ANFIS show muchhigher values of 141, 199.3, and 199.5 min. It means adaptive and cascade con-troller has faster response capabilities. The faster response is also exhibited throughrise times of cascade control exhibits the low rise time tr of 32.6 and 22.7 min,respectively, for adaptive and cascade controllers verses other controlling actions.Adaptive and cascade controlling actions also improve tracking of set point byshowing low-error ISE values of 0.000157 and 0.001686 compared to all othercontrollers. Cascade and PID, however, have been found to suffer from highovershoots of 29 and 87 % versus (which is not desirable for CSTR system) othercontrolling actions for which the overshoot was negligible or zero. The tracking ofset point temperature was found to be best with adaptive controller with lowest ISEof 0.000157 compared to relative higher values of 0.02279 for FLC. The temper-ature tracking capability of ANFIS was, however, found to be poor with highervalue of ISE *0.23. In view of faster response (rise, delay, and settling times)though both adaptive and cascade control perform better, however, due to higherovershoots with cascade control, adaptive controlling action is proposed as the mostefcient controlling actions among all control techniques considered.


Adaptation gain ensures the convergence rate and is illustrated in Fig. 9f whichshows the parameter estimates for different values of the adaptation gain, c: Theconvergence rate increases with increasing values of c: When c ranges between 1.8and 2.0, an optimum response is observed, however, for larger values of c[ 2:0;overshoot appears and below 1.8, the response becomes sluggish.

(a) (b)

(c) (d)

(d) (e)

0 200 400 600 800 1000 1200 1400 1600 18000

50

100

150

200

Time

Tem

pera

ture

Set-pointPID control response

0 200 400 600 800 1000 1200 1400 1600 18000

50

100

150

200

Time

Tem

pera

ture

Set-pointCascade control response

0 200 400 600 800 1000 1200 1400 1600 18000

50

100

150

200

Time

Tem

pera

ture

Set-pointFLC response

0 200 400 600 800 1000 1200 1400 1600 18000

50

100

150

200

Time

Tem

pera

ture

ANFIS responseSet-point

0 10 20 30 40 50 60 70 80 90 100

0

50

100

150

200

Time

Tem

pera

ture

Set-pointAdaptive control response

0 10 20 30 40 50 60 70-20

0

20

40

60

80

100

120

Time

Tem

pera

ture

=0.7=1.0

=1.8=2.0

=2.5

=3=2.7

Fig. 9 Illustration of output temperature response of a PID controller, b cascade controller,c fuzzy logic controller, d ANFIS controller, and e adaptive controller, f adaptive controller withvarying adaptation gain, c

Table 2 Comparisons of control parameters for different controlling actions

Controllingaction

td (delay timein min)

tr (rise timein min)

ts (settling timein min)

Mp (2 %TB)

ISE

PID 141 175.5 174 87 0.168

Cascade 19 22.7 22.4 29 0.001686

Fuzzy 199.3 429 372 0 0.02279

ANFIS 199.5 430 373 0 0.2262

Adaptive 21.4 32.6 30.2 0 0.0001568


5 Conclusion

The present study observes that for a nonlinear CSTR system, adaptive controllergives the best controlling performance among the set of controlling actions studied(PID, cascade, fuzzy, ANFIS, and adaptive). Adaptive controller exhibits a zeroovershoot, better temperature tracking capabilities (as shown by very low ISEvalues), and a much quicker response (very small rise, delay, and settling times)than other controllers.

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Analysis of Hybrid Temperature Control for Nonlinear Continuous Stirred Tank Reactor

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