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Vol. 15, No. 1 (2016) 275-290Revista Mexicana de Ingeniería Química

CONTENIDO

Volumen 8, número 3, 2009 / Volume 8, number 3, 2009

213 Derivation and application of the Stefan-Maxwell equations

(Desarrollo y aplicación de las ecuaciones de Stefan-Maxwell)

Stephen Whitaker

Biotecnología / Biotechnology

245 Modelado de la biodegradación en biorreactores de lodos de hidrocarburos totales del petróleo

intemperizados en suelos y sedimentos

(Biodegradation modeling of sludge bioreactors of total petroleum hydrocarbons weathering in soil

and sediments)

S.A. Medina-Moreno, S. Huerta-Ochoa, C.A. Lucho-Constantino, L. Aguilera-Vázquez, A. Jiménez-

González y M. Gutiérrez-Rojas

259 Crecimiento, sobrevivencia y adaptación de Bifidobacterium infantis a condiciones ácidas

(Growth, survival and adaptation of Bifidobacterium infantis to acidic conditions)

L. Mayorga-Reyes, P. Bustamante-Camilo, A. Gutiérrez-Nava, E. Barranco-Florido y A. Azaola-

Espinosa

265 Statistical approach to optimization of ethanol fermentation by Saccharomyces cerevisiae in the

presence of Valfor® zeolite NaA

(Optimización estadística de la fermentación etanólica de Saccharomyces cerevisiae en presencia de

zeolita Valfor® zeolite NaA)

G. Inei-Shizukawa, H. A. Velasco-Bedrán, G. F. Gutiérrez-López and H. Hernández-Sánchez

Ingeniería de procesos / Process engineering

271 Localización de una planta industrial: Revisión crítica y adecuación de los criterios empleados en

esta decisión

(Plant site selection: Critical review and adequation criteria used in this decision)

J.R. Medina, R.L. Romero y G.A. Pérez

CONTINUOUS-DISCRETE OBSERVER-BASED FAULT DETECTION ANDISOLATION SYSTEM FOR DISTILLATION COLUMNS USING A BINARY

MIXTURE

SISTEMA DE DETECCION Y AISLAMIENTO DE FALLAS BASADO EN UNOBSERVADOR CONTINUO-DISCRETO PARA COLUMNAS DE DESTILACION

EMPLEANDO UNA MEZCLA BINARIAA.C. Tellez-Anguiano1, C.M. Astorga-Zaragoza 2, R. F. Escobar2, E. Alcorta-Garcıa3, D. Juarez-Romero4*

1Instituto Tecnologico de Morelia, Av. Tecnologico No. 1500, Col. Lomas de Santiaguito, C.P. 58120, Morelia, Mich., Mexico2Centro Nacional de Investigacion y Desarrollo Tecnologico, Int. Internado Palmira S/N, Palmira C.P.62490, Cuernavaca,

Morelos, Mexico.3FIME, Universidad Autonoma de Nuevo Leon, Avenida Universidad s/n, Cd. Universitaria, San Nicolas de los Garza, N.L.,

66450, Mexico.4Centro de Investigacion en Ingenierıa y Ciencias Aplicadas-Universidad Autonoma del Estado de Morelos, Av. Universidad

1001, Col. Chamilpa, C.P. 62209, Cuernavaca, Morelos.Received July 31, 2014; Accepted February 17, 2016

AbstractIn this work a Fault Detection and Isolation (FDI) system is presented. The FDI system detects simultaneous failuresin the temperature sensors placed in a distillation column. The distillation column is used to separate an Ethanol-Water binary mixture. The estimated temperature is used as the reference variable in the FDI system. This system isbased on a continuous-discrete high-gain observer. This observer is an extension of the continuous-time constant-gainobserver developed for systems having a triangular form, such as distillation columns. The continuous-discrete observeris selected to deal with the problem of performing a continuous estimation of the system without exceeding the availablecomputational capabilities. The proposed FDI system has a dynamic behavior that allows detecting transitory failures aswell as determining their magnitude. The developed FDI system was experimentally validated on-line, providing usefulinformation that allows the user to make early decisions when a failure occurs.Keywords: nonlinear system, continuous-discrete observer, fault detection and isolation system, distillation column.

ResumenEn este trabajo se presenta un sistema de deteccion y aislamiento de fallas (FDI, por sus siglas en ingles). El sistemapropuesto detecta fallas simultaneas en los sensores de temperatura situados en una columna de destilacion, la cual operacon una mezcla binaria de etanol-agua. La temperatura estimada se utiliza como variable de referencia en el sistemade deteccion y aislamiento de fallas. El sistema FDI se basa en un observador de alta ganancia continuo-discreto. Esteobservador es una extension del observador de ganancia constante de tiempo continuo desarrollado para los sistemascon forma triangular, como las columnas de destilacion. El observador continuo discreto se selecciona para tratar conel problema de estimar continuamente el sistema sin exceder las capacidades computacionales disponibles. El sistemade deteccion y aislamiento de fallas propuesto tiene un comportamiento dinamico que permite la deteccion de fallastransitorias, ası como la determinacion de su magnitud. El sistema se valida experimentalmente en lınea, proporcionandoinformacion util que permite al usuario tomar decisiones tempranas cuando se produce una falla.Palabras clave: Sistemas no lineales, observador continuo-discreto, sistema de deteccion y aislamiento de fallas, columnade destilacion.

*Corresponding author. E-mail: [email protected]. +52 7777 329-79-84, Fax +52 7777 329-70-84

Publicado por la Academia Mexicana de Investigacion y Docencia en Ingenierıa Quımica A.C. 275

Tellez-Anguiano et al./ Revista Mexicana de Ingenierıa Quımica Vol. 15, No. 1 (2016) 275-290

1 Introduction

A failure can be defined as any malfunction in adynamic system that leads to an unacceptable anomalyin its behavior. Failures can occur in sensors, actuatorsor components of the process. The early detection ofthese failures can prevent an undesirable behavior ofthe plant or catastrophic events such as damages to theplant or its operator (Frank, 1990).

FDI systems are used to estimate failures incomplex industrial systems. FDI systems are basedon physical or analytical redundancy. Analyticalredundancy has been widely used in industrialprocesses because, being based on models, doesnot require additional hardware that can increasemaintenance costs in the plant (Chetouani, 2013;Escobar et al., 2014).

FDI systems based on analytical redundancy use amathematical model of the process under analysis; themodel must represent adequately the behavior of theprocess under the selected operation range.

Observers are widely used in FDI systems becausethey can estimate variables not directly measurable inthe plant due to nonexistent or high-cost sensors. Inorder to perform adequately the FDI tasks the valueof the state variables is required (Pierri et al., 2008;Manuja et al., 2009; Velardi et al., 2009; Tian et al.,2013; Shen et al., 2012).

FDI systems used for linear systems have beenwidely studied, however, not many papers dealingwith the problem of designing FDI systems to isolatesimultaneous failures (Garcia-Morales et al., 2015)nor based on nonlinear observers can be found inliterature (Rusinov et al., 2013; Ahmed et al., 2009;Ben 1997).

Diverse interesting problems arise when the on-line implementation of FDI systems is required, suchas how to deal with the problem of performing acontinuous estimation of the system without exceedingthe available computational capabilities. A solution todeal with this problem consists in using continuous-discrete observer-based FDI system for state-affinesystems (Deza et al., 1992; Nadri et al., 2004).Continuous-discrete observers are an alternative ofsolution when relatively long-time sampling periodsare available (Goffaux et al., 2009; Astorga et al.,2002; Ibrir, 2007; Frogerais et al., 2012). In the cited

papers, the gains of the continuous-discrete observersneed to be computed after a variation of coordinates ofthe original nonlinear system. The selected observerfor the FDI system developed in this work is thecontinuous-discrete constant-gain observer, presentedin Hammouri et al., (2002).

The main objective of this paper is to implementan FDI system based on a continuous-discrete high-gain observer to detect on-line sensor faults in adistillation column. The FDI system is based on theestimation of molar fractions and temperatures of thelight component of a binary mixture; the effectivenessof the FDI system is proved by inducing failures indifferent temperature sensors of the plant.

2 Continuous-discrete observerHigh-gain observers have been suggested foruniformly-observable non-linear systems, one of theadvantages of high-gain observers is their robustness.Choosing a high enough gain can lead to an arbitrarilysmall observer error. Besides, the observer gainscannot depend on the system inputs if a canonical(triangular) form of the system is used (Hammouri etal.,, 2002).

An extension of a continuous-discrete form of thecontinuous high-gain observer described in Nadri etal., (2004); Goffaux et al., (2009); Escobar et al.,(2011) is presented in Tellez et al., (2012).

A continuous-discrete observer is suitable whenmeasurements are available in relatively long samplingperiods. A continuous-discrete observer consistsof (i) a mathematical model of the process in theprediction step and (ii) a correction term composed ofthe observer gain and the error of the measured processoutput (with respect to the estimated output) in thecorrection step. Considering this fact, the followingproposition is stated.

Proposition. Given the continuous-time systemwith discrete measurements given by:

ζ1(t) = f1(ζ(t),u(t)) + ε1(t)ζ2(t) = f2(ζ(t),u(t)) + ε2(t)

%(tk) =[%1(tk) %2(tk)

]T =[Cn1ζ

1(tk) Cn2ζ2(tk)

]T

(1)

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where the states ζ j(t), the input vector u(t), thedisturbance vectors ε(t) j, the vector fields f j(·) andCn j = [ 1 0 . . . 0 ], (n = dimension of stateand j = 1,2) are defined as the continuous case, andthe output vector % is defined in a discrete time tk; acontinuous-discrete observer is described in two steps:

Step 1: A prediction step in the semi-open timeinterval t ∈ [tk, tk+1):

˙ζ1(t) = f1(ζ(t),u(t))˙ζ2(t) = f2(ζ(t),u(t))

(2)

Step 2: A correction step at time t = tk+1:

ζ1(tk+1) = ζ1(t−k+1)−Q1θ[Cn1 ζ

1(t−k+1)− %1(tk+1)]

ζ2(tk+1) = ζ2(t−k+1)−Q2θ[Cn2 ζ

2(t−k+1)− %2(tk+1)] (3)

where the observer gains Q jθ are given byQ jθ = r j∆θδ jS−1

n j CTn j for

j = 1,2where∆θδ j = diag(θδ j , θ2δ j , ..., θn jδ j )

and

Sn j =

s11 s12 0 · · · 0

s12 s22. . . · · ·

...

0. . . · · ·

. . . 0... · · · · · ·

. . . s(n j−1)n j

0 . . . 0 s(n j−1)n j sn jn j

The tuning parameters of the proposed observer

are r j ( j = 1,2) and θ. S n j is a symmetric positivedefinite (SPD) matrix. The system is shown in Eq.(2) fulfills the existence conditions of the observerpresented in Deza et al., (1992). The constant gainis obtained because the structure of the system in Eq.(2) satisfies the conditions given in Hammouri et al.,(2002). The convergence properties of the continuousobserver are theoretically verified in Hammouri et al.,(2002). The convergence properties of the continuous-discrete observer are experimentally verified in Tellezet al., (2012).

3 Application to a distillationcolumn

Distillation columns have been widely used inchemical industries to perform the separation process

for liquid chemical mixtures. Currently, they are usedto produce biofuels (such as ethanol); there are severaldistillation column designs (Meski and Morari, 1995).

The distillation process involves not onlyflammable chemical mixtures but also hightemperatures and pressures that may provoke thatthe system under failure is dangerous for both, theprocess, and its users. This is the main reason toperform an early on-line failure detection, in orderto ensure the safe and proper operation of industrialdistillation systems (Skogestad, 2004).

In this work, molar compositions and temperaturesof the components of an ethanol-water mixture arerequired to perform FDI tasks. Authors as Olsenet al., (2002); Quintero-Marmol et al., (1991);Han and Clough, (2006) propose estimating molarcompositions by using secondary measurements suchas temperature and pressure because the equipmentrequired to perform this measurement can be veryexpensive.

3.1 Distillation column model

A distillation column consists of a condenser, ntrays, and a boiler (see Fig. 1). The condenser islabeled with number 1, the boiler with number n andthe intermediate trays are numbered ascending fromthe condenser to the boiler. The feeding mixture isdeposited in tray number f , named the feeding tray.

The heating power is provided by an elementlocated in the boiler, which causes the evaporationof the liquid stored into it. The condenser is locatedat the top of the column; its function is to cool andto condense the vapor that arrives from the body ofthe column until it becomes liquid. In this part of thecolumn the reflux is performed, where all or a fractionof the condensed liquid returns to the column allowingthe equilibrium phase.

There are several approaches for distillationcolumn models in the literature. Since distillationis a process used to separate chemical mixtures, itneeds to perform the balance of vapor and liquidphases depending on the mixture into the process.By definition: If a vapor and a liquid are in contact fora long time the equilibrium between the two phasesis achieved, i.e. there is no flow of heat, mass, andmomentum between the two phases.

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Fig. 1. Distillation column schematic diagram

A mathematical model of the system is requiredto design a state observer; this model provides thestructure on which the observer is based.

The following assumptions are considered tomodel the distillation column:

• Binary mixture (Ethanol-Water).

• Constant pressure inside the column.

• Insignificant vapor molar mass compared to theliquid molar mass.

• Constant process enthalpy in every tray.

• Constant molar mass retention in every tray.

• Known feed stream molar flow F and liquidcomposition x f .

• Total condenser.

Under the above considerations, the followingsimplified model is obtained:

M1 x1 = VR(y2 − x1)Mp xp = VR(yp+1 − yp) + LR(xp−1 − xp), p = 2, ..., f − 1M f x f = VS y f +1 −VRy f + LRx f−1 − LS x f + Fx fMp xp = VS (yp+1 − yp) + LS (xp−1 − xp), p = f + 1, ...,n− 1Mn xn = VS (xn − yn) + LS (xn−1 − xn)

(4)

where xp and yp are, respectively, the liquid and vapormolar fractions of the light component in tray p.VR, VS and LR, LS are the vapor and liquid molarflows of the system; subindex R and S correspond tothe rectifying and stripping sections of the column,respectively.

Temperature and molar composition are relatedinversely by the vapor-liquid equilibrium phenomenain distillation columns, this equilibrium is consideredin the presented model, which makes possibleto determine trays temperatures from molarcompositions and vice versa.

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3.2 State-Space Model

The state-space model of the distillation columnpresented in this section is derived from themathematical model described in subsection 3.1. Thetriangular form of the distillation column modelguarantees the uniform observability of the system(Hammouri et al., 2002). The states of the model arethe liquid compositions xi (i = 1, . . . ,n), where n isassociated to the number of trays in the column. Theyare represented in one vector:

x1(t) =

x1x2...

x f−1...

xn−1xn

∈ Rn

Physically, the elements of the vector x1(t)represent the liquid compositions in both, therectifying and the stripping section.

The two control variables are u(t) =

[u1(t) u2(t)]T = [V L]T . These input variables canbe manipulated by varying the heating power appliedon the boiler, Qb(t), and the opening period of thereflux valve, rv(t), respectively.

If the bottom product composition x12 can bemeasured, the measured output is %12(t) = x12(t)T .

These notations allow to obtain the followingcompact representation of the dynamical mathematicalmodel of the distillation column, considering discrete-time measurements:

x1(t) = f1(x(t),u(t))

%(tk) =[Cx1(tk)

]T (5)

where x(t) =[x1(t)

]T∈ Rn,

f1(x,u) =

f 11 (x1

1, x12,u)

f 12 (x1

1, x12, x

13,u)

...

f 1n−1(x1,u)f 1n1(x,u)

and

C = [0 0 0 . . . 0 1]

Considering the distillation column model givenin Eq. (5) the following assumptions are physicallyverified:

• A1. Flow rates physically bounded.

• A2. Liquid compositions xp ∈ [0,1].

According to the Proposition given in Section 2,the continuous-discrete observer given by Eqs. (2)and (3) allows estimating the molar compositionsx1 . . . x12, based on the measurement of the bottommolar composition, x12(t) = %(t).

4 FDI SystemThe continuous-discrete observer described in section2 is used in the FDI system developed for a distillationcolumn. The FDI system performance is validated,on-line, in a distillation column pilot plant (Figure2) which is located at the Centro Nacional deInvestigacion y Desarrollo Tecnologico (CENIDET).The plant has 12 plates, including the boiler (tray 12)and the condenser (tray 1), 8 temperature sensors,located in plates 1, 2, 4, 6, 7, 9, 11 and 12.The temperature measurements obtained by thesesensors are the secondary measurements used toestimate molar compositions and temperatures ofthe components in the distillation column using anazeotropic binary mixture (Ethanol-Water).

The FDI system detects additive failures at the (8)RTD Pt-100 temperature sensors located in the bodyof the column. The failure detection is performed byusing a bank composed of continuous-discrete high-gain observers.

This work is based on the Dedicated ObserverScheme (DOS) (Chen y Patton, (2012); Frank, (1990),as shown in Figure 3. The DOS configuration allowsdetecting and locating simultaneous faults in thesystem by using a relatively simple procedure, easyto be implemented on-line.

Figure 3 shows that every observer estimatestemperatures and compositions for the 12 trays,using the manipulable variables of the system (reflux,feeding mixture and heating power) as well as thereference signal (measured temperature) used toobtain the estimation error.

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Fig. 2. Distillation column pilot plant.

Fig. 3. Dedicated Observer Scheme (DOS).

Every reference temperature is measured by onetemperature sensor, so the DOS bank has 8 observers.Because the observers used in the DOS bank requireone temperature measurement, the bank can detectonly 6 simultaneous failures in the temperaturesensors.

4.1 Residual generation

The residual generation stage of the FDI systemcompares the estimated temperatures by the DOSbank.

Because the estimation error is small in the traywhose measurement is taken as reference (less than1%) (Tellez et al.,, 2012) the estimated value for thistray is considered as the measured value (withoutlosing reliability). Table 1 presents the numberassigned to every observer and the corresponding traynumber.

Residual generation is based on comparing thetemperature value estimated by the reference observerwith the temperature value estimated by the rest of thebank observers for this particular tray, i.e.:

rO,k = TO − Tk (6)

where O = 1, ...,8 is the number of theobserver considered as the measured value andk = {1, ...,8} 3 {O} is the number of the observer towhich it is compared.

By Eq. (6) it is possible to determine that

rO,k

{= 0 i f TO = Tk consistent measurement-estimation, 0 other case

Figure 4 shows the actual temperature behavior intray 12, estimated by observers 8 and 7. As can be seenin Figure 3, the estimated measurements deviate fromeach other at t = 116 min due to the input conditions.

4.2 Failure signature generation

The main objective of the failure signature generationstage is determining if a failure exists in any sensorof the system. The signature generation is obtainedby comparing the residual calculated in Eq. (6) to areference threshold ξ.

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Fig. 4. Estimated temperatures comparison.

Fig. 5. Relative residual, r8,7.

Fig. 6. Symptom generation stage.

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Fig. 7. Generated symptom.

The signal obtained by comparing twosimultaneously-evaluated related residuals is calleda symptom (Figure 6).

i.e.

S O,z =

{1 if |rO,k| > ξ OR |rk,O| > ξ0 in other case (7)

where ξ is the detection threshold, O = 0, ...,7 is thenumber of the observer that represents the measuredsignal and z = (O + 1), ...,8 is the number of theobserver used to compare the measured signal.

The FDI detection threshold is empiricallydetermined to generate binary symptoms. Astatistical analysis was performed over more than 50experiments to obtain the minimum threshold.

Figure 7 shows the binary behavior of thesymptom corresponding to the residual shown inFigure 5. The residual is compared to a thresholdset at 0.5oC, as can be seen, the symptom changesfrom 0 to 1 when the residual value is higher than thethreshold value.

Fig. 8. Sensor 1 failure tree.

The 8 observers generate 28 symptoms (Eq. 7),allowing determining the failure signatures of thesystem. In the decision block, in order to locate thefaulty sensor, a failure tree is designed for every sensor(Figure 8). The failure tree compares the signaturegenerated by the obtained symptoms to the referencefailure signatures to determine if a sensor failureoccurs.

The FDI system can detect and locatesimultaneous failures in 6 sensors. It can even detecttransitory failures due to the dynamic characteristicsof the system.

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Table 1. Thermodynamic proprieties of the ethanoland water.

Parameter Ethanol Water UnitsDensity (ρi) 0.789 1 g/cm3

Molecular weight (Wi) 46.069 18.015 gNormal Boiling Temperature (Tbi ) 78.400 100 oC

Specific heat (Cp j ) 0.112 0.076 kJ/mol oC

Table 2. Initial operating conditions.Parameter Value Units

Ethanol volume in the boiler 3700 mlWater volume in the boiler 300 ml

Boiler heating power 1250 wattsCooling liquid flow 250 l/h

Pressure 84.92 kPa

Table 3. Process inputs and perturbations.Input Value Execution time (min)

Qb 1250 watts 0 < t ≤ 54rv Total 0 < t ≤ 26rv Pulse(ton = 6s, to f f = 6s) 26 < t ≤ 41rv Total t > 41Qb 1750 watts t > 54

5 FDI experimental validationThe FDI system is validated, on-line, by usingexperimental data from the distillation column pilotplant. In both cases, the detection threshold was fixedin 3.5oC, considering that the temperature deviationselected to simulate a failure was 4oC (values under3oC are considered as uncalibrated sensor, not asa failure, according to the sensor manufacturerspecifications).

Two different experiments were performed: failurein one sensor and simultaneous failures in multiplesensors. An Ethanol-Water mixture is used in thisexperiment. The mixture characteristics are shown inTable 1, the initial operating conditions are shown inTable 2 and the process inputs in Table3.

5.1 Failure in one sensor

In this experiment, a failure occurs when thetemperature deviation in one sensor is induced tobe equal or higher than 4oC. There are 8 availabletemperature measurements in the pilot plant, obtainedby 8 RTD Pt-100 temperature sensors, which arelocated in plates: 1, 2, 4,6, 7, 9, 11 y 12.

In order to simulate a failure in tray 7, theselected deviation is induced in this sensor tray by

adding an offset to the temperature measured by thecorresponding sensor.

Every observer estimates, on-line, thecompositions and temperatures in the 12 plates ofthe plant, based on the measured temperature used asthe reference input. The experimental validation isperformed considering the plant in steady-state.

5.2 Simultaneous failures in multiplesensors

In this experiment a failure occurs when a temperaturedeviation is induced to be equal or higher than 4oC,simultaneously, in multiple sensors of the distillationpilot plant.

In order to simulate simultaneous failures in plates1, 4 and 9 the selected deviation is induced in thesetrays by adding an offset to the temperatures measuredby the corresponding sensors.

6 Results and discussionThe obtained results are presented graphically tofacilitate their interpretation.

Obtained results - Failure in one sensor

Figure 9 presents the temperature estimated by the8 observers for the tray 7, where the failure occurs.

As can be seen in Figure 9, the estimatedtemperature by the observer corresponding to tray7 has the 4oC deviation induced as failure, whilethe rest of the observers estimate the temperaturescorresponding to sensors without failures.

Figure 10 shows the residuals obtained bycomparing the temperatures between the observerthat present the deviation and the rest of the bankobservers. The obtained results have a 4oC value,which implies the failure is adequately detected.

The reference threshold (ξ) is set at ±3.5oC toget the symptoms. Figure 11 shows the 28 obtainedsymptoms, as can be seen, the residuals involvingobserver 5 (S 1,5, S 2,5, S 3,5, S 4,5, S 5,6, S 5,7 and S 5,8)are equal to 1, indicating the sensor located in tray 7fails.

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Fig. 9. Tray 7 Measured and estimated temperatures.

Fig. 10. Tray 7 relative residuals.

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Fig. 11. One failing sensor - Obtained symptoms.


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Obtained results - Simultaneous failures inmultiple sensors

Figures 12 to 14 show the estimated temperaturesfor plates 1, 4 and 9, respectively, by the 8 observersof the DOS bank.

As can be seen in Figs. 12 to 14, the estimatedtemperatures in plates 1,4 and 9 by the corresponding

observers have important differences compared to therest of the observers without sensor failures.

Clearly, modifying the reference input signal of theobserver implies a visible variation of the estimatedtemperatures in the 12 plates of the column.

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Fig. 15. Estimated residuals for multiple failures.

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Fig. 16. Three failing sensors - Obtained symptoms.

Figure 15 shows the residuals obtained bycomparing the estimated temperatures. As can beseen, residuals corresponding to sensors where failuresoccur have a higher deviation (r > 3oC) compared toresiduals corresponding to sensors without failures(r < 1oC).

The reference threshold is set at ±3oC to get thecorresponding symptoms. Figure 15 shows the 28obtained symptoms, as can be seen, the residualsinvolving observers 1, 3 and 6 are equal to 1, indicatingfailures in the sensors located in plates 1, 4 and 9.

DiscussionAs can be seen in the obtained results, the FDI

system detects adequately the sensor induced failuresin both cases, single and multiple and simultaneous.

Although the distillation column model selectedin this work is simple and considers severalsimplification assumptions, the observer estimates theplates temperatures with a maximum estimation errorlower than 2% (Tellez et al., 2012), which makesmodel and observer suitable to perform FDI tasks.

The noise measured by the sensors located atthe body column is less than 0.05oC, due to the

analog/digital converter included in the distillationpilot plant, which is lower than the minimum detectionthreshold determined for the FDI system, so it does notaffect the failure detection.

Perturbations due to reflux, feeding flow, andheating power are common inputs for every observer,modifying every observer response. Although theeffect for each observer has a different magnitude dueto the selected model, this difference is small enoughto be eliminated through an adequate sensor failuretree, meaning these perturbations do not affect the FDIresults.

Conclusion

In this work, the development and on-lineimplementation of an FDI system based oncontinuous-discrete high-gain observers for a classof nonlinear systems having a triangular structureare presented. Due to the slow dynamics of thetemperature in distillation columns it is possible toacquire the corresponding measurements neglectingthe delayed effects.

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The FDI system is designed by using a DOS bankand it was experimentally validated in a distillationpilot plant. The obtained results demonstrate thatthe FDI system detects, adequately, if a failureoccurs in one or several sensors located in the pilotplant. The FDI system allows not only to detectsimultaneous but also transitory failures due to thedynamic characteristics of the system.

By setting the reference threshold the system iscapable of determining the magnitude of the failures,so it can provide valuable information to the user.Early detection of failures avoids damages in the plant.It also prevents high repair investment, if a failureoccurs.

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