Fault Tolerant Control Design Based on Takagi-Sugeno Fuzzy Logic:Application to a Three-Tank System

Himanshukumar R. Patela and Vipul A. Shahb

a Instrumentation & Control Department, Faculty of Technology, Dharmsinh Desai University, Nadiad, Gujarat,India,e-mail: himanshupatel.ic@ddu.ac.in

bInstrumentation & Control Department, Faculty of Technology, Dharmsinh Desai University, Nadiad, Gujarat,India,e-mail: vashah.ic@ddu.ac.in

Abstract

This paper deals with a novel Fault-TolerantControl (FTC) strategy for non-linear sys-tems without hardware redundancy in caseof actuator and system component failures.These failures correspond to blocking or lossof effectiveness of an actuator, leakage of tankbottom and pipes which could lead to a largedegradation in performances. The abruptand increasing nature faults are introducedinto the system, followed by the simulationresults. The proposed method is based ona conventional PID controller and T-S Fuzzycontroller in order to maintain the acceptableperformance subject to faults. The effective-ness of this approach is evaluated throughthe application to a non-linear pilot plant,a three-tank system. A simulation result isgiven with IAE and ISE error to illustrate theeffectiveness of the proposed approach.

Keywords: Abrupt fault, Actuator fault,Fault-tolerant control, Increasing fault, Non-linear system, System fault, T-S fuzzy con-trol.

1 Introduction

At the event of faults in actuator, system compo-nents or sensor faults, in conventional feedback con-trol system may result in unacceptable performances.To overcome the limitations of conventional feedbackcontrol system, new strategies have been developedsince last thirty years, which are proficient of tolerat-ing various faults, during the time still maintainingsome required properties of performances [8],[9],[12]and [36]. Research in Fault-Tolerant Control (FTC)seems have a large application domain but it still re-mains too largely motivated by the controlling of non-linear system [14],[28],[29],[30]. This fault tolerant op-

eration can be realized either passively through the useof robust control law insensitive to faults and activelythrough a fault detection and diagnosis (FDD) algo-rithm and the results from FDD controller parameterswill reconfigure [23],[25]. The strategy to implementand the level of achieved performance in the event offailures will differ according to the type of process,the allocated degree of freedom and the severity offaults. The FTC methods demonstrates their abilitiesand effectiveness subject to various faults which in-volve abrupt and discontinuous variations in the sys-tem dynamics. The prime motive of FTC strategyis minimize the loss of productivity (to produce withan acceptable quality) or/and to operate safe opera-tion without risky situation to human operators or toequipments [13],[21].

The paper deals with two serious fault scenarios, oneis that loss of effectiveness or partial blocking of ac-tuator. Second fault scenarios is one of the systemcomponent (leak n bottom of the tank) faults occur-ring in the system. It is difficult to deal with stuck orloss of effectiveness actuator, system component faultsbecause the remaining actuators must compensate forthe effects of the failed actuators in the overall system.The main contributions of this paper are as following:

• Proposed unique linearized mathematical modelof the three-tank level control process is derivedusing Takagi Sugeno fuzzy model approach.

• The three-tank level process is converted in piece-wise linearized using three different premise vari-able z1, z2, andz3, and the membership functionsfor the premise variable having only two linguis-tic variable and hence it will not adding addi-tional computational burden for controller alsothe membership function are not optimized us-ing Genetic Algorithm (GA) which are presentedin brief [5][16].

• For designing the proposed Passive FTC con-troller conventional PID controller and Type-1

11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019)

Copyright © 2019, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Atlantis Studies in Uncertainty Modelling, volume 1

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FLC are used, Type-1 FLC structure is easy toimplement as compared to Type-2 FLC, but atthe same time Type-1 FLC will not incorporatethe model uncertainty and noise [15][26].

• The proposed controller structure is simple andeffective to control nonlinear process even thoughthe fault occurs, the author of [6] proposed Type-2fuzzy control system for controlling the longitudeof the aircraft.

• The main advantage of the Type-1 FLC is, veryless computational burden and no need to applyadditional algorithm to convert Type-1 fuzzy setsfrom Type-2 fuzzy sets [2].

In recent years, there has been an ever increasingpush to optimize the controllers to help fulfill theever increasing demands for high quality products[2].Overviews on the development of FTCS have been pro-vided in survey articles by [32] and [38], as well asbooks by [11], [20], [19] and [10]. Most chemical plantsare multivariable processes and have to be controlledin order to perform well.The work in [35] suggests acontrol reconfiguration method based on system re-sponses to accommodate stuck actuators. In recentFTC has design for non-linear system subject to dif-ferent faults, in [1] and [14].The paper contributed by[17] and [33] has proposed FTC scheme using adaptivefuzzy logic for non-linear system subject to sensor andactuator faults.In [7] author has project Active FTCstrategy for three-tank system using analytical redun-dancy. Passive FTC strategy using artificial intelli-gence techniques has investigating for interacting andnon-interacting level process (single and multiple tanklevel system) subject to system component (leak) andactuator faults in [21],[22],[24],[25],[28],[29],[30],[31],and excellent results reported in simulation as well asfor real-time system.In [18] adaptive fuzzy logic con-trol structure is used to design fault-tolerant controlof MIMO nonlinear uncertain systems. The authorsof [27],[15] and [5] design Type-2 FLC for the non-linear level process (MIMO level) process, In [5] and[15] has done comparative results using Type-1 andType-2 FLC, while in [27] author design interval Type-2 TSK FLC for three interconnected conical tank levelprocess, and proved the superiority of the same strat-egy, however the complexity and computational timeis constrain for the controller.

The paper is organized as follows.In section II a generalformulation of the problem with mathematical modelis given.The proposed FTC approach in this paper isbased on the T-S Fuzzy logic control with conventionalPID controller described in section III. The simulationresults presented in section IV.Finally, a concludingremarks given in section V.

2 Process Description and Modeling

The plant dynamic considered in this paper is de-scribed by the following m-inputs, n-outputs non-linear system

∑:

(∑):

X = f(X(t)) +

∑mi=1 gi(X(t))ui(t)

y1(t) = h1(X(t))· · ·

yn(t) = hn(X(t))

(1)

Where, X ∈ Rn is the state vector, U =[u1 · · · um

]T ∈ Rm s the control vector, and

Y =[y1 · · · yn

]T ∈ Rn is the output vector tobe controlled.f(X), gi(X), i = 1, ·,m are smooth vec-tor fields, and hi(X), i = 1, ·,m are smooth functions,defined on an open set of Rn.

The physical constraints of the system (1) are definedby:

(Ψ)

Xmin ≤ X(t) ≤ Xmax

Ymin ≤ X(t) ≤ Ymax

Umin ≤ X(t) ≤ Umax

(2)

2.1 Modeling of Three-tank benchmarksystem

In this paper three-tank benchmark system is consid-ered to be controlled.The three-tank system laboratorymodel can be viewed as a prototype of many industrialapplications in process industry, such as chemical andpetrochemical plants, oil and gas systems.The typicalcontrol issue involved in the system is how to keep thedesired liquid level in tank.The principle scheme of themodel is shown in Figure 1.The basic apparatus con-sists of three plexiglass tanks numbered from left toright as 1, 2 and 3, with cross sectional area of A. Allthree tank is identical in size. The process under con-sideration is a three-tank benchmark system shown infigure 1.

Figure 1: Synoptic of the Three-tank system.

It is composed of three cylindrical tanks with identicalcross section A. The tanks are coupled by two con-

257

necting cylindrical pipes with a cross section A, andan outflow coefficient γ21 = γ32. The nominal out-flow is located at the tank 2, it also has a circularcross section A, and an outflow coefficient γ3. Twopumps driven by DC motors supply the tanks 1 and2. Flow meters measure the flows q1 and q2 providedby each pump. All three tanks are equipped with dif-ferential pressure type transducers for measuring theliquid level (h1, h2, h3). Using the Torricelli rule andthe mass balance equations, the system can be repre-sented conveniently by:

A ∗ dh1(t)

dt = q1(t)− q21(t)

A ∗ dh2(t)dt = q21(t)− q32(t)

A ∗ dh3(t)dt = q2(t) + q32(t)− q3(t)

(3)

where qij represents the water flow rate from tank tankj to i (i, j = 1, 2, 3 ∀i 6= j) ), with

qij(t) = γijAnsign(hj(t)−hi(t))√

2 ∗ g ∗ |hj(t)− hi(t)|(4)

And q3 represents the outflow rate with

q3 = γ3An

√2gh3(t) (5)

The system can be written under the non-linear from

X(t) =

− 1A ∗ q21(X(t))

− 1A {q21(X(t))− q32(X(t))}− 1

A {q32(X(t))− q3(X(t))}

+

1A 00 00 1

A

U(t)

(6)

With X(t) =[h1(t) h2(t) h3(t)

]T, U(t) =

[q1(t)

]T,

and Y (t) =[h3(t)

]T. The liquid level is given in meter

and the flows in m3/s. The set (Ψ) is defined by:

(Ψ)

[0 0 0

]T ≤ X(t) ≤[0.635 0.565 0.432

]T[0 0

]T ≤ Y (t) ≤ [0.635]T[

0 0]T ≤ X(t) ≤

[10−5 10−5

]T(7)

The main objective of the three-tank system is tomaintain tank 3 height h3 which is controlled variablewith manipulated variable inflow q1 and q2. The stan-dard operating parameters of the three-tank bench-mark system presented in table 1.

Tank area(m2)

γ21(m3/sec)

γ32(m3/sec)

γ3(m3/sec)

0.615 0.9 0.8 0.3

Table 1: Parameters of the Three-tank process.

3 FTC Strategy using Takagi-SugenoFuzzy Logic System

In order to minimizing the consequence of the actua-tor and system component faults on proposed three-tank benchmark system, we adopt Passive FTC strat-egy. The proposed controller design in this paper, usesTakagi-Sugeno like fuzzy model. Figure 2 illustratesthe overview of proposed robust controller design. Thecontroller consist of conventional PID controller andT-S Fuzzy logic based controller.

Figure 2: Proposed Passive FTC strategy for theThree-tank system.

3.1 Takagi-Sugeno fuzzy modeling

Consider the nonlinear system given in Eq. 3, Thegoal is to derive a T-S fuzzy model from the nonlin-ear system given in Eq. 3 by the sector nonlinearityapproach as if the response of the T-S fuzzy model inthe specified domain exactly match with the responseof the original system with the same input u. Hereh1, h2, and h3 are nonlinear terms in the Eq. 3 so wemake them as our fuzzy variables. Generally they aredenoted as z1, z2, z3 and are known as premise vari-ables that may be functions of state variables, inputvariables, external disturbances and/or time. There-fore z1 = x1, z2 = x2 and z3 = x3.

The first step for any kind of fuzzy modeling is to de-termine the fuzzy variables and fuzzy sets or so-calledmembership functions [37].It is assumed in this arti-cle that the premise variables are just functions of thestate variables for the sake of simplicity. This assump-tion is needed to avoid a complicated defuzzificationprocess of the fuzzy controllers [2][9].

To acquire membership functions, we calculate theminimum and maximum values of z1(t), z2(t) and z3(t)which under x1 ∈ [0.235, 0.635], x2 ∈ [0.217, 0.565]and x3 ∈ [0.147, 0.432], they are obviously obtainedas follows:

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max z1(t) = 0.635 min z1(t) = 0.236max z2(t) = 0.565 min z2(t) = 0.217max z3(t) = 0.432 min z3(t) = 0.147

Now, x1, x2 and x2 can be represented by for member-ship functions P1, P2, M1, M2, N1 and N2 as follows.as follows:

z1(t) = x1(t) = P1(z1(t)) · 0.635 + P2(z1(t)) · 0.236,z2(t) = x2(t) = M1(z2(t)) · 0.565 +M2(z2(t)) · 0.217,z3(t) = x3(t) = N1(z3(t)) · 0.432 +M3(z3(t)) · 0.147

and because P1, P2, M1, M2, N1 and N2 are actuallyfuzzy sets according to fuzzy mathematics

P1(z1(t)) + P2(z1(t)) = 1,M1(z1(t)) +M2(z1(t)) = 1,N1(z1(t)) +N2(z1(t)) = 1.

Figure 3: Membership functions of premise variablesz1(t), z2(t) and z3(t).

We define name of the membership functions ”Pos-itive”, ”Negative,” ”Big,” and ”Small,” respectively.Figure 3 shows these membership functions. Here, wecan generalize that the ith rule of the continuous T-Sfuzzy models are of the following forms:

Model Rule i:

IF z1(t) is Mi1 and · · · and zp(t) is Mip,

THEN

{x = Aix(t) +Biu(t)

y(t) = Cix(t)

(8)

Here, Mij is the fuzzy set and r is the number of modelrules; x(t) is the state vector, u(t) is the input vector,y(t) is the output vector, Ai is the square matrix withreal elements and z1(t), · · · , zp(t) are known premisevariables as mentioned before. Each linear consequentequation represented by Aix(t) + Biu(t) is called asubsystem.

Now, the nonlinear system (3) is modeled by the fol-lowing fuzzy rules (we don’t consider input u(t)):

Model Rule 1 to 8:

IF z1(t) is “Positive” and z2(t) is “Big, ”and z3(t) is “High, ” THEN x(t) = A1x(t).

IF z1(t) is “Positive” and z2(t) is “Big, ”and z3(t) is “Low, ” THEN x(t) = A1x(t).

IF z1(t) is “Positive” and z2(t) is “Small, ”and z3(t) is “High, ” THEN x(t) = A1x(t).

IF z1(t) is “Positive” and z2(t) is “Small, ”and z3(t) is “Low, ” THEN x(t) = A1x(t).

IF z1(t) is “Negative” and z2(t) is “Big, ”and z3(t) is “High, ” THEN x(t) = A1x(t).

IF z1(t) is “Negative” and z2(t) is “Big, ”and z3(t) is “Low, ” THEN x(t) = A1x(t).

IF z1(t) is “Negative” and z2(t) is “Small, ”and z3(t) is “High, ” THEN x(t) = A1x(t).

IF z1(t) is “Negative” and z2(t) is “Small, ”and z3(t) is “Low, ” THEN x(t) = A1x(t).

where the subsystems are determined as:

A1 =

0.0066 0

max z1z1 ∈ Positive

0.0114max z3

z3 ∈ High0

max z2z2 ∈ Big

0.05681 0.0132

...

A8 =

0.0066 0

max z1z1 ∈ Negative

0.0114max z3z3 ∈ Low

0

max z2z2 ∈ Small

0.05681 0.0132

(9)

which is

A1 =

0.0066 0 0.6350.0114 0.432 00.565 0.05681 0.0132

...

A8 =

0.0066 0 0.2350.0114 0.432 00.217 0.05681 0.0132

(10)

259

This T-S fuzzy model can exactly represents thenonlinear system in the region [0.235, 0.635] ×[0.217, 0.565] × [0.147, 0.432], on the z1, z2, and z3space.

3.2 FLC Design and Structure

In this work we adopt T-S type FLC for the simplic-ity of controller structure and easiness for encounterthe nonlinear behaviour of the system. To design theT-S type controller, the FLC considered here havingthree input taken, error (e(k)), rate of change of er-ror (e(k)) and residue (r(k)) respectively. The out-put of the FLC is u2(k) For each input we use sevenfuzzy labels, Positive Very High (PVH), Very High(VH), High (H), Moderate (M), Negative (N), Nega-tive High (NH), and Negative Very High (NVH), forfuzzification, The degree to which set they belong to isdetermined by membership function illustrated in Fig.3. There are in total 73 = 343 fuzzy rules because ofeach input having 7 linguistic variable.

Figure 4: Membership function used for FLC.

A built-in membership function in the Matlab tool-box, named as Gaussian and triangle member-

ship function are used to represent fuzzy set of(e(k)), (e(k)))and r(k).

There are three reasons to employ the Gaussian andTriangle membership functions. First, the Gaussianand Triangle membership functions are appropriate torepresent the concepts of positive and negative as wellas gradually increasing and decreasing value. Second,the Gaussian membership function is exponential andTriangle membership functions are single-order poly-nomials, which are suitable for the implementationof the FLC because of their easiness in computing.Third, the FLC using the Gaussian and Triangle mem-bership functions provides varying controller outputbased on the residua (r(k)) that are desirable for con-trol of the height for three-tank benchmark system.The input output parameter range is found with op-erating point of three-tank system and normalized.

Each rule contributes to the final FLC output accord-ing to matching for the IF part of the fuzzy rule.The T-S type fuzzy inference takes a weighted averageof the individual outputs for each rule. The outputϑi (i = 1 ∼ 343) for each rule is weighted by the firingstrength µRi , which is calculated as given by equation8. The structure of FLC is T-S type, which consists ofrules of the following form

Ri : If (e(k) is Ai1) AND (e(k) is Ai

2);

AND (r(k) is Ai3), THEN (u2(k) = ϑi)

(11)

The firing strength for the first rule is

µR2 = µA1(e(k))µA1

(e(k))µA1(r(k)) (12)

The final output of the fuzzy controller is calculatedby aggregating all sixteen rules in the weighted form

µflc =

∑343i=1 µRiu2(k)∑343

i=1 µRi

(13)

3.3 PID controller design

The most common and simple control sachem is PID,which is used widely in industries because of its ro-bustness and linear output[23].PID controller is an ap-propriate combination of proportional, integral andderivative terms to provide all the desired perfor-mances of a closed loop system.It also gives zerosteady state error and overshoot is also very less.PID controller are recommended for use in slow pro-cesses and which are free from noise.The PID con-troller can be realized as a controller that takes ac-count of the present, the past and the future of the

260

error [34].Mathematically, PID controller is expressedas

Gc(s) = Kc

(1 +

1

τis+ τds

)(14)

Where, Kc is proportional gain, τi id integral time andτd derivative time.

As PID controller has three parameters to be adjusted,so many different methods have been developed.Manyresearchers have proposed different tuning methods fortuning PID controller.In this article Ziegler & Nicholstuning methods are used which is described below.

Ziegler-Nichols Method

In 1942, Ziegler and Nichols explained simple math-ematical procedures for tuning PID controllers.Theseprocedures are now accepted as standard in controlsystems practice [3].They proposed a mathematical ta-ble for tuning each parameters of PID controller.Theyproposed different procedures for open loop and closedloop systems.

Ziegler-Nichols Open-Loop Method

In this method we have to obtain step response of openloop system, so it is also called process curve method.

Steps involved in tuning a process using this method[4] are

• Make an open-loop step test of process transferfunction.

• From the process reaction curve, determine deadtime (τdead), time constant (τ), ultimate valuethat the response reaches at steady state, (Mu)for a step change of (P0).

K0 =P0

Mu∗ τ

τdead(15)

• Obtain PID tuning parameters using Table 2

Kc τi taudPID 1.2P0 2τdead 0.5τdead

Table 2: Ziegler-Nichols Open-Loop Tuning Parame-ters [4].

Based on Ziegler-Nichols tuning parameters tabulatedin table 2, the PID controller parameters are found asfollows:

Kc = 1.5482, τi = 2.4616, andτd = 0.7812

Now, proposed Passive FTC output u(k) is combi-nation of PID output u1(k) and Type-1 FLC outputu2(k) which is given by eq. 15.

u(k) = u1(k) + u2(k) (16)

4 Simulation Results

The results shown in the following figures are step re-sponses obtained for specific operating points.

The application results are depicted for:

• System component fault (Tank bottom leak)(Abrupt in nature) at t = 4 sec with the PFTCcontrol (figure 4)

• System component fault (Tank bottom leak) (In-creasing in nature) at t = 4 sec with the PFTCcontrol (figure 5)

• Pump fault (blocked or loss of effectiveness)(Abrupt in nature) at t = 4 sec with the PFTCcontrol (figure 6)

• Pump fault (blocked or loss of effectiveness) (In-creasing in nature) at t = 4 sec with the PFTCcontrol (figure 7)

• System component (Tank bottom leak) and pumpfault (blocked or loss of effectiveness) simultane-ously occurs,the fault having in different in nature(abrupt and increasing) at t = 4 sec and t = 12sec with the PFTC control (figure 8)

4.1 PFTC in case of system component fault:

On figure 5, it can be seen that the system componentfault (tank bottom leak) introduced at tank 3 at t = 4sec. The different magnitude of leak fault introducedin to tank 3 with abrupt in nature. The result fig-ures clearly shown the effects of leak fault on steadystate. At the instant system faults occurs the con-troller law u(k) given by T-S fuzzy logic control plusPID control which preserve the system performancesat acceptable level.The control performance of the Pas-sive FTC subject to system component fault (Abruptnature) measured using IAE and ISE errors, the errorresults illustrated in table 3.

On figure 6, it can be seen that the system componentfault (tank bottom leak) introduced at tank 3 at t = 4sec.The different magnitude of leak fault introduced into tank 3 with increasing in nature.The result figuresclearly shown the effects of leak fault on steady state.At the instant system faults occurs the controller lawu(k) given by T-S fuzzy logic control plus PID control

261

Figure 5: PFTC control response of system componentfault abrupt in nature.

Sr. No. Controller f1 IAE ISE1.

PassiveFTC

M=1 0.1606 0.06232. M=2 0.2142 0.11153. M=3 0.2445 0.15614. M=4 0.2698 0.2092

Table 3: Integral error results of Passive FTC for sys-tem component fault abrupt in nature.

Sr. No. Controller f1 IAE ISE1.

PassiveFTC

S=1 0.1213 0.046392. S=2 0.1356 0.047823. S=3 0.152 0.05064. S=4 0.1675 0.05435

∗S denotes the slope value for increasing fault nature.

Table 4: Integral error results of Passive FTC for sys-tem component fault increasing in nature.

Figure 6: PFTC control response of system componentfault increasing in nature.

which preserve the system performances at acceptablelevel.The control performance of the Passive FTC sub-ject to system component faults with different magni-tudes (increasing nature) illustrated in table 4.

4.2 PFTC in case of actuator fault

On figure 7, it can be seen that the actuator fault(block or loss of effectiveness) introduced for pump1 at t = 4 sec. The different magnitude of actua-tor faults introduced in to pump 1 with abrupt in

nature.The Passive FTC response clearly shows theeffectiveness of the strategy. The controller law u(k)smoothly maintain the reference point with all mostzero steady state error.The control performance of thePassive FTC subject to actuator faults with differentmagnitudes (abrupt nature) illustrated in table 5 interms of integral errors.

Figure 7: PFTC control response of actuator faultabrupt in nature.

Sr.No. Controller f2 IAE ISE1.

PassiveFTC

M=5 % 0.1213 0.046392. M=10 % 0.1356 0.047823. M=15 % 0.152 0.05064. M=20 % 0.1675 0.05435

Table 5: Integral error results of Passive FTC errorresult for actuator fault abrupt in nature.

Sr. No. Controller f2 IAE ISE1.

PassiveFTC

S=1 0.3291 0.11492. S=2 0.5514 0.32123. S=3 0.7737 0.66994. S=4 0.996 1.144

Table 6: Integral error results of Passive FTC for ac-tuator fault increasing in nature.

On figure 8, it can be seen that the actuator fault(block or loss of effectiveness) introduced for pump 1at t = 4 sec.The different magnitude of actuator faultsintroduced in to pump 1 with increasing in nature.ThePassive FTC response clearly shows the effectivenessof the strategy. The control performance of the PassiveFTC subject to actuator faults with different magni-tudes (increasing nature) illustrated in table 6 in termsof integral errors.

4.3 PFTC in case of actuator and systemcomponent faults simultaneously

On figure 9, it can be seen that the system component(tank bottom leak) and actuator fault (block or lossof effectiveness) introduced simultaneously with dif-ferent time. Also fault is introduce into system with

262

Figure 8: PFTC control response of actuator fault in-creasing in nature.

Figure 9: PFTC control response of system compo-nent and actuator fault simultaneously (abrupt andincreasing in nature).

two different nature, one is abrupt and second is in-creasing.The system component (leak in tank 3 bot-tom) faults (increasing nature) introduced at t = 16sec and actuator faults introduced at t= 6 sec.At theother side to check response subject same faults butabrupt in nature introduced into the process systemcomponent fault at t= 16 sec and actuator faults at t=6 sec.The critical observation and error results showsthat, same magnitude actuator faults is degrade con-trol performance drastically compared to same magni-tude of system component faults for both the abruptand increasing nature.Also from the responses we cameto know, abrupt nature actuator and system compo-nent faults effects is more vulnerable compare to in-creasing nature.The comparative control performanceof the Passive FTC subject to actuator faults withdifferent magnitudes (increasing and abrupt nature)illustrated in table 7 in terms of integral errors.

Sr.

No.

Con

trol

ler

f 1f 2

IAE

ISE

1.P

assi

veF

TC

M=

10M

=10\%

5.004

49.6

32.

S=

4S

=4

1.048

1.1

49

Table 7: Integral error results of Passive FTC resultcomparison for simultaneous system component andactuator fault (abrupt and increasing in nature).

5 Conclusion

The method developed in this paper allows to increasethe application field of Fault Tolerant control law: theindustrial processes without hardware redundancy, inthe event of actuator or system component failures.Asignificant actuator failure (blocked or loss of effective-ness), system component fault (tank bottom or pipeleak) on a process without hardware redundancy canbe considered as a critical failure.Its application to anon-linear process, a three-tank system, emphasizesthe importance and usefulness of such a fault toler-ance.The objective of this Fault Tolerant control isdifferent from that usually met.Indeed, in the pres-ence of critical faults on such process,it is impossi-ble to maintain the damaged system at some accept-able level of performances, whatever the applied con-trol strategy.The objective is so to operate safely andto minimize the loss of productivity.The abrupt andincreasing nature of actuator and system componentfaults are taken to check the efficacy of the proposedPassive FTC scheme.It is realized from the simulationresponses and error results T-S Fuzzy plus PID con-troller based Passive FTC is an efficient strategy for anon-linear three-tank level process.

In addition to this proposed work, Type-2 FLC will beuse full in the case of process having modeling uncer-

263

tainty and unexpected noise is a major future scope ofwork.Also one o the key part of future work is to mini-mize computation time of Type-2 FLC.Future work isextended to optimization of Type-1 ant Type-2 fuzzysets using Genetic Algorithm (GA) and design FLCusing this membership functions, this approach waswell defined in [16].

Acknowledgement

This research was carried out in Simulation lab ,De-partment of Instrumentation & Control Engineer-ing, Dharmsinh Desai University, Nadiad-Gujarat, In-dia.We thank Dr.Jalesh Purohit, Professor in Chem-ical Engineering Department, Dharmsinh Desai Uni-versity, Nadiad-Gujarat, India] for comments thatgreatly improved the manuscript. We would also liketo thank “anonymous” reviewers for their so-calledinsights and constructive suggestions to enhance thequality of manuscript.We would also like to thank“anonymous” reviewers for their so-called insights andconstructive suggestions to improve the quality of thepaper.

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