ISAP 2011 SEPTEMBER 25-28, 2011, HERSONISSOS, CRETE, GREECE 1

Fault Tolerant Control Scheme with PIDsMarino Sanchez-Parra,Senior Member, IEEE,Dionisio A. Suarez,Member, IEEE,and C. Verde,Member, IEEE

Abstract—This paper proposes a fault active tolerant controlswitching scheme with a PID’s set and switching functions tomanage the faults conditions. The family of PIDs which stabilizesthe model in each fault condition is off-line computed followinga procedure based on the signature of the closed loop rationalfunction. To guarantee the closed loop stability between switchingand reduce the number of PID’s sets in the scheme a switchinglogic function for the controllers is selected using the LMI theory.The scheme is applied to the case of critical faults of a gasturbo generator of an electric plant, assuming the existence of afault reconstruction system and known the multiple frequencyresponses of the gas turbine with four fault conditions. Thecomparison of a classic controller and the new scheme is shownby simulation results using real parameter of a Mexican electricplant.

Index Terms—Fault tolerant control, stabilizing PID’s family,switching scheme, gas turbines

I. I NTRODUCTION

A UTOMATED processes are vulnerable to faults and theconsequences of such faults may be a complete failure,

or a disaster. Actuator faults, erroneous sensor readings, andmechanical/thermal wear in components affects the profitableperformance, the process and human security, and increaseslevels of pollutant emissions. For such reasons Fault TolerantControl (FTC), as it has been described by [1], is a crucialdeveloping area in automatic control where several disciplinesand system-theoretic issues are combined to obtain a uniquefunctionality.

Along control evolution, some schemes involving multiplebreakdown plant models and multiple controllers have beenproposed, as one authored by [2]. Such scheme is an adaptableerror identification scheme having N plants matched withN controllers where a switching for controller selection iscoordinated by error models. When a deviation has occurred,control reconfiguration can be initiated for that particularcase. This approach using multiple models, switching, andtuning has been extended to nonlinear systems. The controlreconfiguration scheme from [3], is based in a continuallyadapting nonlinear model in contrast to multiple models andconsiders the fault cases. Also, a FTC should include a deci-sion element that recognizes when a particular fault occurs andactivates reconfiguration. The initial model is based on priorinformation concerning system structure and parameters, whilethe system model and corresponding control are adjusted asnew information is received at the decision element. AnotherFTC scheme by [4] defines the decision element as a Fault

M. Sanchez-Parra and D. Suarez are with the Control Systems Division,Instituto de Investigaciones Electricas, Cuernavaca, Morelos, 62490 Mexicoe-mail: msanchez@iie.org.mx

C. Verde is with Instituto de Ingenieria, Universidad Nacional Autonomade Mexico, Coyoacan, DF 04510 Mexico

Manuscript received February 26, 2011.

Detection and Diagnosis (FDD) system who orders adaptableReconfigurable Control (RC) actions that can react to theoccurrence of system faults on-line in real-time in an attemptto maintain the overall system stability and performance.

On the other hand the PID’s has been resurgence recently [5]and the stabilizing family for a given plant can be obtained ifthe relative degree of the plant and number of poles and zerosin the right half plane are known [6].

In the framework of fault tolerant control few approachesconsider the PID controller as an option to solve the issue;nevertheless the industry demans the design of controllerswith few parameters to adjust. Furthermore, from systemstheory one knows that a fault in any physical process generatesswitching from nominal plant to faulty plant. Then the FTCrequirements have to be focused to diagnosis closed loop sta-bility under switching. In this sense, Polytopic Linear Models(PLM) structures have been introduced as an approximate andalternative description of nonlinear dynamical systems [7]. Theabove facts motivated this work in which a switching schemewith stabilizing family od PID’S is suggested to manage thefault tolerant control of a gas turbine.

Due to its technical relevance, the selected case study inthis paper is a generic Gas Turbine (GT) for electric powergeneration. Because GT’s need to be highly automatized forguarantee profitable performance, less pollutant emissions andsecurity.

The paper is organized of the following structure: Section1 is the introduction, section 2 describes the Fault TolerantPIDs Scheme, section 3 corresponds to GT description, themechanical faults and fault diagnosis and isolation (FDI)system. Section 4 introduces the selection of PIDs for the GTand simulation tests results. Section 5 is for conclusions andfinally the references section.

A. Fault Tolerant PID’s Scheme

This paper proposes the scheme given in Fig. 1 to design aFTC system for some classes of parameterized faults, assum-ing that faulty plants are described by linear models. Other ele-ments which appear in proposed structure are: Fault Detectionand Isolation subsystem (FDI), Reconfiguration Logic (RL),and families of PID stabilizing controllers. The FDI subsystemrealizes the fault diagnosis and identifies the model of thefaulty plant. Additionally activates a reconfiguration logicwhich selects the appropriate PID - i stabilizing controllerby means of a switching mechanism. PID’s are tuning off-line applying a state of the art technique from robust control,which guaranties loop stability after fault accommodation. Thefollowing subsections describe with more detail how the PIDand the FTC scheme are adjusted.

ISAP 2011 SEPTEMBER 25-28, 2011, HERSONISSOS, CRETE, GREECE 2

Fig. 1. Fault Tolerant Control scheme with PID’s

1) PID’s design: To obtain controllers which stabilize aplant the technique given by [8] which use LTI systems isused in this paper. Over this line of research [6] developed amethod to calculate the whole family of industrial PID con-trollers whom stabilizes a physical process based in frequencyresponseP (jω), ωε [0,∞) models. So, with this technique afamily of stabilizing PID controllers can be determined off-line for each failure plant.

Consider that both controller PID and plant are character-ized by sets of transfer functions. Let a set of m linear timeinvariant failure plants

P = {Pf1, Pf2, ..., Pfm} (1)

wherePfi = P (s, fi), i = 1, ..., m denotes the plant transferfunction with faultfi, and the nominal plant is denoted by thetransfer functionP0. Let

Ci := PIDi(kp, ki, kd) (2)

the transfer functions of the family of stabilizing controllersPID’s for the plantPfi wherekp corresponds to the propor-tional gain interval,ki is the integral gain interval andkd isthe derivative gain interval.

This framework allows to associate a family of stabilizingcontrollersCi for each failure plantPfi

C1 → Pf1 C2 → Pf2 , ..., Cm → Pfm (3)

In this matching one has the freedom to select the controllerC∗i from the familyCi according to specific performances foreachPfi. Since, this association of plants and PID’s generatesa high number of controllers for multiple faults, a reductionin the number of PID’s could be looking for.

Since each familyCi defines a region in the parametersspace<3, an intersection of regions means a set of controllerswhich stabilizes more than one faulty plant. So,

if Ci

⋂Cj 6= ∅ ∃ Cij (4)

whereCij is an overlapped family which stabilizesPfi andPfj

simultaneously and then any selection of a controllerCi∗ =Cj∗ inside the overlapped region guarantees the stability ofboth plants. This condition is shown in Fig. 2 for a fictitiouscontroller with two overlapped regions andkp constant.

A recursive use of the overlapped condition (4) reduces thenumber of the controllers in the FTC scheme. The limit case

Fig. 2. Intersection of two families of controllers for the integral andderivative actions and proporcional gainkp constant

could be if a overlapped region exists for all the set of faultyplantsP.

Using condition (4) one can determine the family of PID’sdenotedC∧Pi which stabilizes simultaneosly all the subset offaulty plants

∧Pi = {Pfi, Pfj , ...} ⊂ P (5)

Then the set{C∧P1, C∧P2, · · · , C∧Pk} characterizes the minimalnumber of controllersk which stabilize allP. One can selectany Ca∧Pi

⊂ C∧Pi without any additional stability condition forthe subset of plants∧Pi.

2) Performance Adjustment:Following the method previ-ous described, one selects the set of stabilizing controllersCa∧Pito cover the family∧Pi. The next step should be a performanceevaluation first verifying the step response of the controlledvariable and after that the responses with non linear models iswell satisfactory. One suggests as performance index the set{Mp, tr, ts}, whereMp means overshoot,tr is the rise time,and ts the settling time.

If the selected controllers have poor performance for somemembers of the plants∧Pi, an adjustment of the controllerCa∧Pi

is required. As the adopted stabilizing PIDs design for afinite dimensional linear time-invariant plant is calculated fromthe frequency response data, it is suggested to use firstly thegain and phase margins (GM andPM ) as initial performanceparameters. The overlapped region with these specifications isdenoted

SGM,PM (ki, kd)|kp ⊂ S(ki, kd)|kp (6)

for a givenkp. On the base of set{Mp, tr, ts}, we proposedthe following adjustment steps to obtain a controllerC∗∧Pi

witha satisfactory response for each subset∧Pi. In particular, tominimize the frequency interval in which the controller has alow gain, it is proposed a PID structure with multiple zerosadjusting the value to achieve the settling timets. As graphicstools the software [8] is used.

1) Select the controller gains{kp, ki, kd} inside the stabi-lizing PID regions for the plants subset∧Pi such thatthe

C∧Pi =kd

s

(s2 +

kp

kds +

ki

kd

)= kd

s2 + 2zs + z2

s(7)

satisfies with an arbitrary zero valuez.2) Generate step response of the closed loop with the linear

and non linear plant model for the set{Ca∧Pi, Pfk} with

ISAP 2011 SEPTEMBER 25-28, 2011, HERSONISSOS, CRETE, GREECE 3

Pfk ⊂ ∧Pi. If the pair {tr, ts} is satisfactory for allthe set of plants, got to step 3, otherwise adjust thezero valuez taking into account the overlapped stabilityregions ofC∧Pi and that high values ofz reduce the timeresponse for a fixedkd. Then, at this step the controlleris characterized by the parametersk = kd andα = z

C∧Pi|step1 = k(s + α)2

s(8)

3) Adjust the derivative gainkd of C∧Pi|step1 holding thevalue α of the zeros to reduce the overshoot of thestep response for the linear and nonlinear case. At thisstage, if the response satisfy the performance the PIDcontroller is fixed toC∗∧Pi

for all the subset∧Pi resultingthe open loop gainC∗∧Pi

∧Pi. Otherwise, readjust the PIDwith small deviation of{k, α}, going to step 1.

This procedure can be used for all the subsets∧Pi withunsatisfactory performance.

3) Reconfiguration and Stability Test:Assuming the exis-tence of a FDI system which identifies the faulty plantPfi,the RL task consists to switch the particular controllerC∗iaccording to the failure plantPfi holding the stability ofthe closed loop system. The stability test switching betweencontrollers and plants is a key action in the FTC scheme. Then,the RL has to switch the particular controllerC∗∧Pi

according tothe faulty plants∧Pi from the nominal case holding the stabilityof the closed loop system during the transient of switchingaction. This means, the closed loop system switched from(C∗0 , P0) to (C∗∧Pi

, ∧Pi) for any i has to be stable. Since theset of controllers{C∧P1, C∧P2, · · · , C∧Pk} are known a priori, thestability test can be made off-line.

To test the stability of the switching system the result takenfrom [9] is used. Given any matricesAi and Aj associatedto state space description of linear systems(Ak, Bk, Ck, Dk),with k = i, j the system is asymptotically stable for aswitching fromAi to Aj or viceversa, if all eigenvaluesλ(Ak)have a strictly negative real part, and if the linear matrixinequality

AkT P + PAk < 0 (9)

satisfies fork = i, j with P a common positive symmetricmatrix.This condition can be easily verified for the FTCscheme generating the matricesAi and Aj from the transferfunctions of the sets of closed loop systems

Ti =C∗∧Pi

∧Pi

1 + C∗∧Pi∧Pi

Tj =C∗∧Pj

∧Pj

1 + C∗∧Pj∧Pj

(10)

and generating the inequality (9) by LMI-PLM Toolbox from[?]. Note that this condition does not guarantee that thestability of the switching action hold for the nonlinear plantsassociated to the linear cases.

B. Gas Turbine Description

GT thermodynamic cycle is best known as Bryton’s Cycle[10] and its functionality depends of the main equipments(components) shown in Fig. 3: air compressor, combustionchamber (CC), gas turbine heat recovery (HSRG) and theelectric generator. Besides the inlet guide vanes actuator

ExciterStartMotor

Generator

MW

CompressorCombustion

ChamberGas

TurbineHRSG

Stack

AfterBurnersGas Control

Valve ABGas Control

Valve GT

Inlet Guide VanesActuator (IGV’s)

Bleed Valve

k16

k9

k18

k6

x15

x12

k11

x18

k14

k10 x

23

x25

x17

x16

x6

k5

k17

x8 x

10

k8

k9

k19 x

26

x1

x14

k15

k2

x11

Vel

k13 x

3

k3

k4

k7

x9

k1

k12

Fig. 3. Gas turbine components

(IGVA’s), two gas fuel control valves, one for CC and theother for after-burners, and the compressor bleed valve.

GT dynamical model was developed based in physical lawsof thermodynamics and heat transfer, with the criteria oflumped parameters. The most relevant simplifications adoptedfor its design were: isentropic compression and gas expansion,combustion gases behavior as ideal gases and linear charac-teristic for control throttle valves. This model emulates GTdynamical behavior from startup to base load in stationarystate, based in non linear static and dynamical equations. GTmodel is composed with 28 non-linear equations (19 static and9 derivatives), 3 control inputs and 3 actuators. The calculatedprocess variables are flow (air, fuel, gas), pressure, temperature(gas, turbine blades), gas enthalpy and gas density, energy(electrical, mechanical), rotor speed and position of actuators.

1) Gas Turbine Operation and Control:Fully automaticoperation of GT is going up from startup, with acceleratingrotor unit up to reach nominal speed (60RPS), and syn-chronizing to the electric network taking minimum load of4000KW . Then the automatic power generation, based in amegawatt control (MW) loop is initiated. The operation iscommanded by a human operator who selects the parameters,MW demand and MW rate, by a Human Machine Interface(HMI). With such scheme is possible to get increasingly valuesof the controlled variablek13, the electric power generated,[11].

2) Control strategy.:The control strategy commonly usedis based on classic proportional and integral PI controllers. Itconsists in regulating the fuel gas and air flow accordinglyto the operation stage while keeping surge, acceleration andtemperature under safe and efficient conditions. Fig. 4 showsthe basic fuel controller which is formed by two PI industrialcontrollers, which form a dual speed/loadk2/k13 closed-loopcontrol circuit for fuel flow regulationx12. Speed/load control.The control circuit has two complementary paths of operationto develop the fuel valve control signal and thus scaling it toform the fuel valve demand signalk18. During startup andacceleration to nominal speed value, the right PI of the figureis active, thus providing a control signal from the position-PI algorithm acting on the speed deviation calculation from aspecific acceleration pattern minus the rotor speedk2. Whenthe electric generator is synchronized to the electric network,the left PI path of the figure starts functioning. In this case

ISAP 2011 SEPTEMBER 25-28, 2011, HERSONISSOS, CRETE, GREECE 4

Fig. 4. Conventional control scheme for the GT

the control signal is obtained in a feedback mode of thecalled load, or electric power generated, minus the megawattsreference signal MWRef generated by means of the HMI.Then the output of the position load PI is added to the outputof the speed PI and modifies the control signalk18, starting theelectric power generationk13 to a secure minimum value of4000 KW . While the output of the speed PI is kept as a biasto the load path fuel valve demand. To increase the electricpower generated to the base-load value of47000 KW and getthe best operational efficiency of the GT, the control systemuses the HMI. In this case study one defines the base-loadvalue at stationary state as the equilibrium point.

Air flow regulation to IGV’s is obtained in base of anopen loop control with a programmed reference [12], withthe control signalk17. As the reference signal is constantwhen GT is generating electric power,k17 is constant too, thenfor analysis purposes is possible to take avoiding action overactuator dynamics, and consequently the order of the modelis reduced. With respect to after-burners control gas valve, itremains out of operation, because in this operating scenerysteam is not required for combined cycle process. Then, asin previous case, the control signalk19 is constant and ispossible to take avoiding action over this actuator dynamics.The controlled outputs arey1 = k13 andy2 = k2

3) Fault Scenario for the GT:The critical fault consideredin this paper is a mechanical fault in rotor-turbine/generatorcoupling, which affects the value of the electric power gen-erated (EPG)k13. This fault can be emulated by means of aparameter’s variation named ”friction coefficient of GT rotor”θ11, which is an element of the parameter vector of thestructured model [13]. So, the new value isθf

11 = θ11∆11

where∆11 represents a fault intensity factor. At fault instantenergy loses by friction increases suddenly, and produces aspeed transient, which affects the value of the generator’selectric power angle and this immediately reduces the electricpower generatedk13. Fig. 5 shows the effect of this fault inopen loop. However GT speedk2 remains constant becauseGT unit is coupled to the electric net. According to previousdescription, at the faulty scenery the electric power value

0 5 10 15 20 25 30

4.45

4.5

4.55

4.6

4.65

4.7

x 104 GT Mechanical friction fault (base−load eq. point)

Time (sec)

Ele

ctric

Pow

er G

ener

ated

k13

(K

Wat

ts)

44.49 KWatt

Fig. 5. Electric power reduction for a fault with factor∆11 = 2

Fig. 6. Residuals by mechanical fault

changes and gets a new value, less than the previous nominalvalue. If the new value is too small, it means the energyloses by friction are too big, then GT protection system couldgenerate a shutdown signal.

4) Redundant Relations:To study fault detectability andaislability properties of the FDI system for the GT model, astructural analysis study focused to analytical redundancy wasrealized. The canonical decomposition of the incidence matrixgot two subsystems: one over-constrainedS+ od dimension30× 20 and the other just-constrainedS0 of dimension7× 7.[13] describe how the whole system based in 10 analytical re-dundant relations (ARR) resulted completely monitorable butnot completely detectable in presence of faults. The analysisshowed that the structure is not capable to detect mechanicalfailures at rotor-generator coupling, nor speed rotor changesk2, nor changes of friction parameterθ11. Another deeperstudy [14] concerning GT analytical redundancy showed thatadding a new sensor, the structure over-constrainedS+ ofdimension37 × 26 resulted with11 ARR, with the systemcompletely monitorable and detectable. To verify the analysisresults the residual were programmed and the GT model withthe FDI system were simulated in Matlab platform in nominaland fault conditions. In nominal condition of the model atbase-load state, residual shown to be zero, as it was expected.While at fault condition, the intensity factor is selected in theset∆11 = {1, 2, 5, 8, 10}. Theni = 1 is the nominal condition.This fault produces,k13 changes to a less value, whilek2

recovers the nominal value. From the analytical redundancyrelation given in [14] the fault signature

Fault ARR6 ARR8 ARR11

∆11 0 0 1 (11)

is taken and the residuals by simulation test for a fault at6200sis shown in Fig. 6.

ISAP 2011 SEPTEMBER 25-28, 2011, HERSONISSOS, CRETE, GREECE 5

−100

−50

0

50

100

150Falla mecánica por fricción del rotor de la Turbina de Gas

Mag

nitu

d (d

B)

10−2

10−1

100

101

102

103

−270

−225

−180

−135

−90

−45

0

Frecuencia (rad/seg)

Fas

e (°

)P0 (teta11x1)Pf1 (teta11x2)Pf2(teta11x5)Pf3 (teta11x8)Pf4 (teta11x10)

Fig. 7. Bode diagram ofP in normal and fault conditions

Kp=0.02

(0,0)

(300,500)(0,500)

PID Triangle for Pf1 [Sólo lectu1 1PID Triangle for Pf1 [Sólo lectu1 1 11/06/2009 07:37:56 p.m.11/06/2009 07:37:56 p.m.

Fig. 8. Surface withkp=0.02 withGM = 5 andPM = 200

C. PID’s Selection for the GT

Considering the transfer functions of the GT at base-load value, called nominal condition, and the set of faultsconditions described in Section 3. At selected operating pointis possible to reduce the model’s order to seven state variables,two controlled outputs and one input. Such conditions avoiddesigning a PID for a distributed MIMO system [15]. Fig. 7shows the frequency response ofP (s, fi) in failure conditionsand nominal case.

1) Stabilizing PID in normal and faulty conditions:Follow-ing the algorithmic procedure by [6] implemented in Lab ViewNI Program from Texas University, giving the coefficientsof the open loop transfer function of the plantPfi and aproportional gain rangekp = c, one can get graphically thefamily of PID’s for such gain. This family corresponds to asurface in<2 denotedS(ki, kd)|kp=c.

Case 1. For the GT with the nominal modelP0 and set ofmodel with a faultP with the stabilized PID’s family withgainkp = 0.02 is given for all the cases by the rectangle withki ε[0, 500] andkd ε[0, 500]. This means the family of PID’sfor all faults conditions is overlapped and any parameters setinside of the surface can be used.

Case 2. RequiringGM = 5 and PM = 200 for the plantPf1 with the samekp = 0.02 the surface is given in Fig.8. This surface with performances requirements is inside thestability rectangle of case 1, i.e.

SGM,PM (ki, kd)|kp=0.02 ⊂ S(ki, kd)|kp=0.02 (12)

Taking inside of the surface of Fig. 8, the set of parameters

Fig. 9. Powerk13 response for the linear model

0 5 10 15 20 25 30 35 40 450

0.2

0.4

0.6

0.8

1

1.2

1.4Step response to mechanical friction fault Pf1

Step Response

Time (sec)

Am

plitu

de

PID*: kp=0.0714, Ki=0.0714, kd=0.01785

Fig. 10. Response with linear modelPf1 andC∗p1

of the PID

kp = 0.02, ki = 0.01, kd = 230 (13)

the step response of the closed loop system for the linear GTmodel is simulated and is oscillating as, one can see in Fig.9. Since the stability is guaranteed with the linear model, theevolution of the GT withf1 from the starting point to theoccurrence of the faulttf = 5000s has been analyzed with thenonlinear model. In this case the standard PIkp = 0.02, ki =0.01, kd = 0 is switched to (13) attf andk13 oscillated.

2) Stabilizing PID with performance:Case 3. Accordingto section 2.2 the performance of a PID has been improvedusing negative real multiple-zeros and a selected value ofkd,following the next steps:

1) Adjust a PID with eachz = 0.5, 1, 2 and kd = 1 forplant Pf1 and get the response for each case of theclosed loop system. Comparing the results the betterresponse corresponds toz = 2.

2) Adjust the derivative gain, starting withkd = 1, holdingz = −2 and evaluating the step response of the closedloop system in each case. After a strong reduction ofkd

and analyzing the linear model response given in Fig.11, the parameters set is selectedk∗p = 0.0714, k∗i =0.0714, k∗d = 0.01785.

Fig. 11 shows the non linear responses of the faulty plantPf1 and alsoPf2, Pf3, Pf4. It means the obtained PID con-troller C∗p1 was applied for all cases since the begining of theelectric power generationk13. One appreciates forPf1 thatrising timetr is almost equal to settling timets, (20s) withoutovershoot. Other cases are similar and the overshoots are lessthan1%.

ISAP 2011 SEPTEMBER 25-28, 2011, HERSONISSOS, CRETE, GREECE 6

4980 4990 5000 5010 5020 5030 5040 5050 50602

2.5

3

3.5

4

4.5

5x 10

4

Time (SEC)

Ele

ctric

Pow

er k

13 (

KW

att)

Mechanical friction faults responses

PID: kp=0.0714, ki=0.0714, kd=0.01785

Pf1

Pf2

Pf3

Pf4

Fig. 11. Response of the non linear model with faults

With respect to stability of the switched process, it has beenfind a common Lyapunov function to the closed loop systemswith nominal modelP0 and the modelPfi, and the singlecontroller C∗p1. Then, the system is asymptotically stable fora switching fromP0 to Pfi, because all eigenvalues of theclosed loop dynamix matrix are in the RHCP, and the LMI(4) satisfies with P a common positive symmetric matrix.

II. CONCLUSION

This paper complements Rauch and Zhangs proposals forFTC and Keel’s method for the stabilizing PID controller,because one uses multiple models of failure plants, linearizedat each operating point and includes a FDI subsystem whichactivates the reconfiguration logic. The calculation of the PID’sfamily which stabilizes a given linear time invariant plant indiverse conditions is used and the search of fixed stabilizingPID controllers with a reduced number of switching functionsis achieved using stability LMI tools. The proposal with twocommutative PID’s has been tested by simulation with a gasturbine.

REFERENCES

[1] M. Blanke, M. Kinnaert, J. Lunze, and M. Staroswiecki,Diagnosis andFault Tolerant Control. Berlin: Springer, 2003.

[2] K. S. Narendra, J. Balakkrishan, and M. Kemal, “Adaptation andlearning using multiple models, switching and tuning,”IEEE ControlSystems Magazine, vol. 15, no. 3, pp. 37–51, 1995.

[3] H. E. Rauch, “Autonomous control reconfiguration,”IEEE ControlSystems Magazine, vol. 15, no. 6, pp. 37–48, 1995.

[4] Y. Zhang and J. Jiang, “Issues on integration of fault diagnosis andreconfigurable control in active fault tolerant control systems,” inSAFEPROCESS’06-IFAC, Beijing, China, 2006, pp. 1513–1524.

[5] IEEE, “Special issues on pid,”Control and Systems Magazines, vol.February, pp. 30–50?, 2006.

[6] L. H. Keel and S. P. Bhattacharyya, “Controller synthesis free ofanalytical models: Three term controllers,”IEEE-TAC, vol. 53, no. 6,pp. 1341–1352, July 2008.

[7] G. Z. Angelis, “System, modelling and control with polytopic linearmodels,” Ph.D. dissertation, Technische Universiteit Einhoven, TheNetherlands, 2001.

[8] A. Datta, M. Ho, and S. Bhattacharyya,Advances in Industrial ControlStructyures and Synthesis of PID Controller. New York: Springer, 2000.

[9] D. Liberzon,Switching in systems and control. Birkhaeuser, 2003.[10] T. Giampaolo,The gas turbine handbook: principles and practice. The

Fairmont Press, 2003.[11] R. Garduno and M. Sanchez-Parra, “Control system modernization:

turbogas unit case study,” inIFAC Symposium on Control of PowerPlants and Power Systems, Cancun, Mexico, vol. 2, 1995, pp. 245–250.

[12] M. Sanchez-Parra and Y. Rudecino-Mendoza, “Control and dynamicsimulation for a combined cycle power plant,” inProc. IFAC Symp. ofPower Plants and Power Sytems, Seoul, Korea, 2003, pp. 774–779.

[13] C. Verde and M. Sanchez-Parra, “Monitoreability analysis for a gasturbine using structural analysis,” in6th IFAC Symposium on FaultDetection, Supervision and Safety of Technical Process, August 2006,pp. 721–726.

[14] J. Mina, C. Verde, M. Sanchez-Parra, and F. Ortega, “Fault isolation withprincipal components structural models for a gas turbine,” inACC-08,Seattle, 2008.

[15] A. N. Guendes and A. B.Osguler, “PID stabilization of mimo plants,”IEEE- Trans. Automatic Control, vol. 526-(8), pp. 1502–1508, 2007.

Marino Sanchez-Parra received the B.S. Degree inElectronic and Communication from National Poly-technic, Mexico in 1975, and M.Eng. and Dr. Eng.Degrees in Control from National University fromMexico (UNAM) in 1984 and 2010. Dr. Sanchez-Parra joined the Instituto de Investigaciones Elec-tricas in 1988 where he is a full time researcherand head project engineer. Since 1990, he has been

involved with development of real time digital control systems for gas turbines,steam turbines and HRSG of Combined Cycle Power Plants. His main topicsof research include automatic robust fault detection and fault tolerant controlof industrial process. He’s a senior member of IEEE.

Dionisio A. Suarez received the B.S. Degree inElectrical Engineering from Universidad Michoa-cana de San Nicolas de Hidalgo, Mexico in 1980,the M.Sc. Degree in Electrical Engineering fromCINVESTAV Mexico in 1989, and the Ph.D. Degreein Control of Systems from the University of Tech-nology of Compiegne, France, in 1996. Currently heis working at Instituto de Investigaciones Electricas,

where he is a full time researcher. His research interests include IntelligentControl, Adaptive Control, System Identification and their applications toimprove the operation of Electrical Fossil Power Plants. He is a memberof the National Research System of Mexico.

C. Verde received the B.S. and M.Sc. Degrees inElectronic and Communication and Electrical Eng.from National Polytechnic, Mexico and the PhDDegree in Electrical Eng. from Duisburg Universityin 1983. Prof. Verde joined the National Universityfrom Mexico and is author and co-author of over150 papers published in congress and journals. Hermain topics of research include automatic robust

fault detection of industrial process. She is a member of the IEEE, the MexicanNational Academy of Engineering, the Germany Society of Engineering, theMexican National Academy of Sciences and got the Prize 2005 Sor JuanaInes de la Cruz given by the National University to the outstanding women.