observer-based fault detection and moisture estimating in coal mills

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Control Engineering Practice 16 (2008) 909–921

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Observer-based fault detection and moisture estimating in coal mills

Peter Fogh Odgaarda,�,1, Babak Matajib

aKK-Electronic a/s, Jens Juhl Vej 40, DK-8260 Viby J, DenmarkbDong Energy A/S, Kraftværksvej 53, DK-7000 Fredericia, Denmark

Received 6 February 2006; accepted 23 October 2007

Available online 26 November 2007

Abstract

In this paper an observer-based method for detecting faults and estimating moisture content in the coal in coal mills is presented.

Handling of faults and operation under special conditions, such as high moisture content in the coal, are of growing importance due to

the increasing requirements to the general performance of power plants. Detection of faults and moisture content estimation are

consequently of high interest in the handling of the problems caused by faults and moisture content. The coal flow out of the mill is the

obvious variable to monitor, when detecting non-intended drops in the coal flow out of the coal mill. However, this variable is not

measurable. Another estimated variable is the moisture content, which is only ‘‘measurable’’ during steady-state operations of the coal

mill. Instead, this paper suggests a method where these unknown variables are estimated based on a simple energy balance model of the

coal mill. In the proposed scheme an optimal unknown input observer is designed based on the energy balance model. The designed

observer is applied on two data sets covering variating moisture content as well as a data set including a fault in the coal mill. From these

experiments it can be concluded that the moisture content is successfully estimated and that the fault is detected as soon as it emerges.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Fault detection; Disturbance estimation; Optimal unknown input observers; Energy balance models; Power plants; Coal mills

1. Introduction

In the recent years the requirements to the production atDanish power plants have been forced in the direction of amore dynamical production. Meaning that the load at thepower plants is constantly varying and not set to fixed(steady state) production, which the plants originally weredesigned for. The required load of the plants varies due to anumber of factors. One of these factors is the large relativepower production from wind turbines in Denmark. Thepower delivered from wind turbines is almost non-controllable, as the production is dependent on the windi.e. the power plant production must compensate for thefluctuations in the wind power production. Anotherimportant factor is the trading of electrical power withDenmark’s neighboring countries, depending on prices in

e front matter r 2007 Elsevier Ltd. All rights reserved.

nengprac.2007.10.008

ing author. Tel.: +4521744963; fax: +4597211431.

ess: [email protected] (P.F. Odgaard).

was at Department of Electronic Systems, Aalborg

drik Bajers Vej 7C, DK-9220 Aalborg East, Denmark,

rch for this paper.

the various countries, electrical power is either imported orexported. The last reason for the varying production is thedemand of electrical power from the consumers, whichvaries during the day and throughout the year.A consequence of these increased requirements to the

power plants regarding dynamical production, is a growingfocus on the dynamic performance of the plants. In orderto increase the performance of the power plants, it is clearlyvery important to control the fuel fed to the furnace in theplant. The difficulty of this control task is highly dependedon the fuel used. Coal is a relatively problematic fuel, as itis pulverized in a coal mill before it is blown into thefurnace. It is difficult to control the coal flow into thefurnace mainly due to the fact that the coal flow intothe coal mill and the coal flow from the coal mill into thefurnace are not measured, the flow into the mill is given asa requested coal flow. In addition to this problem coal millsare relatively complicated dynamic systems.As a consequence of these problems with controlling

coal mills, modeling and control of coal mills have been themain focus in many research activities. Some examples of

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ARTICLE IN PRESSP.F. Odgaard, B. Mataji / Control Engineering Practice 16 (2008) 909–921910

publications in the field are as follows. Examples dealingwith modeling of coal mills are: Rees and Fan (2003) andZhang et al. (2002). High order dynamic models andobserver design for coal mills are the topics in Fukayama,Hirasawa, Shimohira, and Kanemoto (2004). Differentcontroller types have been applied in the coal mill, someexamples are: An advanced PID-controller is designed inRees and Fan (2003) designs and compares differentadvanced controller strategies, Jankowski, Domanski,and Swirski (2003) and Palizban, O’Kelly, and Rees(1995) have designed model predictive controllers for thecoal mill, Jun, Dezheng, and Pingyang (1998) introduces afuzzy PID controller.

The growing requirements to the general performance ofthe plants imply a strict requirement to prevent unneces-sary close downs of the power plants, meaning that faultand malfunction detections and accommodation schemesare of interest. En example on this interest can be seen inLi, Thompson, and Peng (2004). It should also be notedthat due to the dynamical production at the plant thedetection schemes are required to take plant dynamics intoaccount, i.e. static detection methods are not suitable. Onething is to guarantee good performance of the coal milloperating under normal and fault free conditions. It is,however, a different thing to handle faults and malfunc-tions in the coal mill in an effective way, i.e. in a way thatprevents unnecessary stops of the power plant. It isimportant that these faults are detected in time, so thatthe operator can prevent the plant stop, if possible. A non-detected fault in a coal mill results in problems controllingthe coal flow to the furnace, under unfortunately operating

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conditions, it can result in too much coal to the furnaceresulting in an overheating of the furnace and thereby theplant. To detect faults in a system such as the coal mill, anumber of different approaches can be followed. Someexamples are: Parity relations, observer based, expertsystems, see Chen and Patton (1999) and Gertler (1998).The interest has been poor in regard to monitoring of the

coal mills with the purpose of detecting any eventual faultsor malfunctions as they emerge. However, one example inthis condition is the publication (Fan & Rees, 1997) inwhich an expert system is designed to supervise the coalmill in order to detect faults and other malfunctions. Theproblem with such an expert system is that data and/orknowledge of the entire normal operational set is needed todefine the normal operations, thus faults and malfunctionsof the coal mill can be distinguished from normaloperations. However, this information can be difficult toobtain in practice.Another approach to take is an observer-based scheme

for detecting faults in the coal mill, an example of thisapproach is the publication (Odgaard & Mataji, 2005b),which deals with detection of a fault in terms of a blockedcoal inlet pipe. The occurrence of this fault is illustratedby data obtained from the coal mill, when the faultoccurs. In Fig. 1 the coal flow demand as well as theclassifier temperature are plotted. When the fault occurs,the temperature increases as the coal flow into the millhas stopped. After a certain period of time a problem inthe plant is detected and the plant has been closed downin order to locate and accommodate the cause of theproblem.

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P.F. Odgaard, B. Mataji / Control Engineering Practice 16 (2008) 909–921 911

Another interesting parameter to monitor in the coalmill is the coal moisture content. Information of the coalmoisture content can be valuable for the plant operator,since it is an essential variable of the coal mill. Measure-ments can be performed using laboratory test, but thesecannot be provided in real time, and last but not the least,an estimate provided using existing sensor signals arecheaper than additional measurement equipment to mea-sure the moisture content. Data from a relevant case can beseen in Fig. 2, where the coal flow demand as well as thetemperature in the mill (measured at the classifiers) areillustrated. The temperature drop to below 100 �C is aconsequence of an accumulation of coal in the mill. It isimportant to know the moisture content, as it influencesthe maximal possible load and load gradient of the coalmill. In detail this means that after the coal is pulverized inthe mill, it is dried and lifted up to the furnace by theprimary air flow. However, if an extensive load change isrequired with a relatively high load and moisture content, itis not possible to deliver sufficient energy through theprimary air, for the coal to be dried adequately. Highmoisture content in the coal will lead an accumulation ofcoal in the mill, and consequently less coal flow to thefurnace. This means in that the coal will be accumulatedinside the mill until it is dried sufficiently. This will lead to adrop in the power production and the power plant mastercontroller will consequently increase the coal flow set point,which eventually will result in an even larger problem.However, if the moisture content can be estimated before-hand, this can be used to limit the maximal load gradientdepending on the moisture content, (Odgaard, Stoustrup,

& Mataji, 2007). In Odgaard and Mataji (2005a) anoptimal unknown input observer is designed to estimatethe moisture content of the coal fed into the coal mill.In this paper a scheme based on the optimal unknown

input observer is designed for detecting faults in the coalmill (exemplified with a blocked coal inlet pipe as well asestimating the moisture content of the coal simulta-neously). This is done by assuming a frequency domainseparation of faults and changes in the moisture content,this separation can be validated by experiments.The outline of this paper is as follows. The coal mill is

introduced in Section 2, this leads to the energy balancemodel of the coal mill, also introducing models of the faultsand the moisture content, see Sections 3–3.2. The optimalunknown input observer is subsequently introduced inSection 4, followed by the observer design in Section 4.1,the fault detection scheme in Section 4.2, the scheme’susability in a fault isolation scheme in Section 4.3, andmoisture estimation scheme in Section 4.4. In Section 5 thedesigned scheme is applied to data containing faults andchanging moisture content. In Section 6 the overallconclusion is given.

2. The coal mill

The work presented in this paper, is based on a BabcockMPS 212 coal mill used at Elsam’s NordjyllandsværktetUnit 3 (rated capacity 411MW). However, the methodproposed in the paper is so generic, that it can be applied toother types of coal mills. The coal mill is illustrated inprinciples in Fig. 3. The coal is fed to the coal mill through

ARTICLE IN PRESS

RotatingClassifier

Primary Air

Grinding table

Pulverized coal

Raw coalInlet

RollerRoller

Fig. 3. An illustration of the coal mill.

Fig. 4. An illustration of energy balance in the coal mill, where mm is the

mass of the coal mill, TðtÞ is the temperature in the mill measured at the

classifier, QairðtÞ is the energy flow in the primary air flow, PmotorðtÞ

denotes the power delivered by the roller motors, QcoalðtÞ is the energy flow

in the coal flow, and QmðtÞ is the energy flow in the coal moisture.

P.F. Odgaard, B. Mataji / Control Engineering Practice 16 (2008) 909–921912

the central inlet pipe. Hereafter the coal is pulverized onthe rotating grinding table by the rollers. The pulverizedcoal is subsequently blown up and the hot primary airevaporates the moisture content. The primary air is amixture of cold air and air heated by the preheater. Theratio of these air flows is used to control the temperatureand the flow of the primary air. Coal particles that duringthe pulverizing process have been ground fine andsufficiently dried will pass through the classifier and outthrough the outlet pipes into the furnace. Larger andheavier particles fall back on the grinding table and willpass the rollers once more.

2.1. Control and measurements

References to the coal flow and primary air flow aregiven by the master controller. The objective of the mastercontroller is to follow the required power production byadjusting the coal flow and primary air flow among overvariables. The power plant is monitored by a simplesupervisory control scheme with the purpose of identifyingeventually faults by monitoring certain measurements. Ifthese measurements get out of the allowed range, thescheme either notifies the operator via alarms or in somerare cases, trips the plant. The temperatures of the primaryair and pulverized coal flow are used to control thetemperature in the coal mill at the classifier. Thetemperature controller is required to keep the temperatureat 100 �C in the mill in order to ensure that the moisture inthe coal evaporates. A coal mill is a harsh environment toperform measurements in, which means that not all thevariables are measurable e.g. the actual coal flow in and outof the coal mill is not measurable. However, the primaryair flow and temperature are measurable, as well as the

temperature at the classifier. The coal flow in and out of themill is assumed to be represented well by the flow demandunder normal operational conditions of the mill, butvariates from the flow demand during faults, high moisturecontent, etc.

2.2. Faults and problems

A number of different faults can occur in the coal mill,and if the fault leads to a decrease in the output coal flowfrom the coal mill, this can result in a trip of the entirepower plant unit. Some examples of critical faults are:blocking of the raw coal inlet pipe, faults in the primary airsupply both the fan and the temperature controller, andfinally failures in the sensors, etc. It is very important thatthese faults are detected as early as possible.As described in the Introduction, the coal moisture

content is of high importance, if the maximal possible millload is to be computed in terms of the coal flow demand.The moisture content of the coal fed into the mill variatesslowly with high time constants. Even though the coalmoisture content is highly depending on the coal batch aswell as, to a small degree, precipitation during the outsidestorage at the plant, it is also influenced by the fact that thecoal is stored in a silo, before it is fed to the coal mills,which leads to a low pass filtering effect of the coalmoisture content resulting in the slowly variating effect.

3. Model of the energy balance in a coal mill

A simple energy balance model of the coal mill is basedon Rees and Fan (2003). In this model the coal mill is seenas one body with the mass mm, as illustrated in Fig. 4, inwhich TðtÞ is the temperature in the mill measured at theclassifier, QairðtÞ is the energy flow in the primary air flow,PmotorðtÞ denotes the power delivered by the grinding table,QcoalðtÞ is the energy flow in the coal flow, and QmðtÞ is theenergy flow in the coal moisture. It is also assumed that theinput and output coal flows are equal. Even though thisassumption is only entirely true for steady state operations,this assumption has been made in this paper in order tosimplify the model. A more detailed model, which takesdifferent coal flows into account, might produce betterresults with respect to even earlier detection of the faults.

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non-linear modelmeasurementslinear model

Fig. 6. A plot of the non-linear and linear model response compared with

measurements of a step response on the coal mill.


The energy balance is given by

mm � Cm � _TðtÞ ¼ QairðtÞ �QcoalðtÞ �QmðtÞ þ PmotorðtÞ. (1)

The heating and evaporation of the moisture in the coal aremodeled by a combined heating coefficient. It is theobjective of the primary air temperature controller to keepthe classifier temperature at 100 �C. The latent energy ofthe evaporation dominates the energy required for theheating of the moisture. The combined heat coefficient,Hst, is defined as Hst ¼ Cw þ Lsteam=100, where Cw is thespecific heat of the water, and Lsteam is the latent heat. Thiscombined heat coefficient does also deal with the fact thatthe specific heat of water and steam is different. However,the temperature model output is a couple of degrees above100 �C which is clearly negligible in this context.

The dynamic non-linear model is subsequently given by

mmCm_TðtÞ ¼ _mpaðtÞCairðTPAðtÞ � TðtÞÞ

þ _mcðtÞCc � ðT s � TðtÞÞ þ gðtÞ _mcðtÞCw � T s

� gðtÞ _mcðtÞHst � TðtÞ þ PmotorðtÞ, ð2Þ

where Cm is the specific heat of the mill, TðtÞ is the milltemperature measured at the classifier, _mpaðtÞ is the primaryair mass flow in and out of the mill, Cair is the specific heatof air, TPAðtÞ is the temperature of the inlet primary air,_mcðtÞ is the coal mass flow, Cc is the specific heat of thecoal, T s is the outside temperature, and thereby thetemperature of the coal entering the mill, gðtÞ is the ratioof moisture in the coal, Cw is the specific heat of themoisture, Hst is the parameter combining the latent heat ofthe steam and specific heat of the water, and PmotorðtÞ is thepower delivered by the mill motor.

The non-linear model (2) is subsequently linearizedand transformed into a state space representation, see (3).The motor power is also removed from this state spacemodel, as it is much smaller than the other powers in theequation.

_TðtÞ ¼ ATðtÞ þ B �

_mPAðtÞ

TPAðtÞ

_mcðtÞ

gðtÞ

266664

377775þ qðtÞ, (3)

TmðtÞ ¼ CTðtÞ þ rðtÞ, (4)

where a given signal � is linearized by � ¼ � � �o, �o is theoperation point of �, qðtÞ is the normal distributed processdisturbances, rðtÞ is the normal distributed measurementnoises, TmðtÞ is the measured classifier temperaturerepresenting the mill temperature and

A ¼ð� _mPA;o � Cair � _mc;o � ðCc þ go �HstÞÞ

mm � Cm

� �, (5)

B ¼

Cair � ðTPA;o � ToÞ

mm � Cm

Cair � _mPA;o

mm � Cm

Cc � ðT s � ToÞ þ go � ðCw � T s �Hst � ToÞ

mm � Cm

_mc;o � ðCw � T s �Hst � ToÞ

mm � Cm

2666666666664

3777777777775

T

, (6)

C ¼ I. (7)

All parameters in the non-linear and the linear models arefound in data sheets except mm � Cm which is identified onthe basis of measurements of a step response of the coalflow demand of the coal mill, see Fig. 5. The modelresponses are compared with measurements in Fig. 6.


From this figure, it can be seen that the responses fromboth models are quite similar to the large dynamicalchanges as the measurements show. However, it isdifficult to validate the response details due to the waythe signals are sampled. A dead band of some percentage ofthe measurement range is applied to these measurementsmeaning that the signals must have changes of a given sizebefore the signal value is sampled. The dead band isapplied to the data for limited the data storage demands.However, if the scheme is applied on-line to the coal mill,no dead bands will be present on the measurements.

3.1. Fault and moisture model

The model given in (2) has uncertain inputs, _mcðtÞ andgðtÞ. The question is how to deal with these. The coal flow,_mcðtÞ, can under normal fault free conditions be assumed tobe flow demand. On the other hand, the moisture content isnot measurable. It is estimated by a static estimate, which isonly valid during static operation of the mill, meaning thatthis input is really unknown, but it can be used to obtainthe steady state moisture content, or can be viewed as anoisy measurement. Faults causing imbalances in theenergy balance model, (2), can also be viewed as anunknown input. These could be described as two energyflows, QfaultðtÞ denotes the energy flow to the possiblefaults, and QmðtÞ denotes the energy flow relating to themoisture content of the coal. These two signals areseparated in frequencies, as the moisture content changesslowly, but on the other hand the faults in the mill occurfaster and are consequently located in higher frequencies.This is illustrated in Fig. 7.

This means that if the unknown input is denoted, QunðtÞ,QfaultðtÞ and QmðtÞ can be seen as filtered versions of QunðtÞ.A low pass filter can represent the moisture and a high passfilter can represent the faults. In order to simplify themodel, first order models are subsequently used. QmðtÞ isscaled to get the moisture content, gðtÞ.

gðsÞ ¼ kmois �QmðsÞ ¼ kmoispm

sþ pm

QunðsÞ, (8)

Am

plitu

de

Frequency

FaultsMoisture content

Fig. 7. An illustration of the separation of moisture and faults in the

frequency domain.

where kmois is the moisture gain, pm is the pole of themoisture model. The fault model is given by

QfaultðsÞ ¼sþ zf

sþ pf

QunðsÞ, (9)

where zf is the zero of the fault model and pf is the pole ofthe fault model. In order to make separations in thefrequency domain, these poles and the zero are related as:pm5zf5pf . Since faults and moisture content changes canbe separated in frequencies, a low and high pass filter couldin principle be used to estimate the moisture content andthe fault residual. The advantage using the proposedobserver is that it takes all the inputs into account, andintroduces some robustness towards model uncertainties.These models are subsequently combined with the small

signal model of the coal mill given in (3)–(7).

3.2. Combined model

The moisture content as well as the fault energy flow areintroduced in the linear small signal model (3)–(7), by twoadditional states. In addition an unknown input signal isintroduced in the model. Since an uncertain static estimateof the moisture content is available, it is included forimproving the estimate of steady state value of the moisturecontent.

_xmðtÞ ¼ Am � xmðtÞ þ Bm � umðtÞ þ EmQunðtÞ þ qðtÞ, (10)

ymðtÞ ¼ Cm � xmðtÞ þ rðtÞ, (11)

where qðtÞ is the independent normal distributed processdisturbances with zero mean and covariance matrix Q, rðtÞis the normal distributed measurement noises with zeromean and covariance matrix R, and

xmðtÞ ¼

TðtÞ

gmoisðtÞ

QfaultðtÞ

2664

3775; umðtÞ ¼

_mPAðtÞ

TPAðtÞ

_mcðtÞ

2664

3775,

ymðtÞ ¼TmðtÞ

gmðtÞ

" #, ð12Þ

Am ¼

ð� _mPA;o � Cair � _mc;o � ðCc þ go �HstÞÞ

mm � Cm1 zf � pf

0 �pm 0

0 0 �pf

26664

37775,

(13)

Bm ¼

Cair � ðTPA;o � ToÞ

mm � Cm0 0

Cair � _mPA;o

mm � Cm0 0

Cc � ðT s � ToÞ þ go � ðCw � T s �Hst � ToÞ

mm � Cm0 0

266666664

377777775

T

,

(14)

ARTICLE IN PRESSP.F. Odgaard, B. Mataji / Control Engineering Practice 16 (2008) 909–921 915

Em ¼

1

kmois

pfault

264

375, (15)

Cm ¼1 0 0

0 1 0

� �. (16)

The moisture gain can be computed as a factor relating themoisture content to the energy flow due to the moisture,meaning that

kmois ¼ð _mc;o � ðCwater � T s �Hwater � ToÞÞ � pm

mm � Cm. (17)

The three remaining parameters have been found empiri-cally to: pf ¼ 1:5� 10�3, pm ¼ 5:4� 10�8, zf ¼ 1� 10�4.These parameters are found so that the two correspondingfilters separates the energy flows according to moisturecontent and faults, such that the moisture content estimatedo not respond on load changes or faults, and so that thefault residual do not depend on the moisture content.

The model represented by (10)–(16) is discretized beforean observer is designed to estimate the states in the model,including the fault residual and moisture content, see(18)–(19).

xm½nþ 1� ¼ Ad � xm½n� þ Bd � um½n� þ EdQun½n� þ r½n�, (18)

ym½n� ¼ Cd � xm½n� þ r½n�, (19)

where ðAd;Bd;Cd;EdÞ are the discretized representations ofðAm;Bm;Cm;EmÞ. This model is a system with an unknowninput, disturbances and measurement noises, which in-dicate that an optimal unknown input observer would bean obvious observer to use for estimating the residual.

4. Optimal unknown input observer

The optimal unknown input observer is described inChen and Patton (1999). It is normally used to estimatestates in systems with unknown inputs and disturbancesand measurement noises. However, in this case theobjective is to estimate the unknown inputs, meaning thatthe model has been modified to include the states of theunknown inputs as seen below. Given discrete time systemswith unknown inputs and disturbances as represented by

xm½nþ 1� ¼ Anxm½n� þ Bnum½n� þ End½n� þ q½n�, (20)

ym½n� ¼ Cnxm½n� þ r½n�, (21)

an optimal unknown input observer of the following formcan be derived.

z½nþ 1� ¼ Fnþ1z½n� þ Tnþ1Bnum½n� þ Knþ1ym½n�, (22)

x½nþ 1� ¼ z½nþ 1� þHnþ1ym½nþ 1�. (23)

The basic idea behind this observer is to eliminate thedependency of the unknown input from the estimationerror by matrix transformations. A Kalman estimator issubsequently designed for the transformed system. A

positive side effect of this is that the estimator gain isrecomputed at each sample, meaning that the model can bechanged so that the linear model matrices can be updatedcorresponding to current state values. The schemes forcomputing the matrices in the optimal unknown inputobserver can be seen in Appendix A.

4.1. Observer design

The design of the observer is given directly by AppendixA, if the two variance matrices q½n� and r½n� are known.However, these two variance matrices are unknown, butcan be used to tune the observer to give the ‘‘right’’estimates. Still some elements are known concerning thesedisturbances and measurement noises. Regarding theprocess disturbances, the temperature is more influencedby process disturbances than the moisture content andfault energy flow, as these two are unknown inputs. On theother hand, when regarding the measurement noises, it isalso known that temperature measurement is relativelyreliable, while the static moisture estimate can be viewedas a highly non-reliable measurement, (only its DC-component is reliable) meaning that this measurementcontains a measurement noise with a large variance. Thevariance matrices are subsequently found empirical theknowledge of the variance matrices are taken into account.Only the first state is subject to disturbances, as the twoother states the unknown inputs, and the first measurementis much more reliable than the second. Subsequently thesetwo parameters are adjusted until the expected responsesare seen from the observer applied to the data shown inSection 5. The parameters are found to be

Q ¼

55:8 0 0

0 1 0

0 0 1

264

375, (24)

R ¼1 0

0 6:9� 103

� �. (25)

4.2. Fault detection

Experiments have shown that the filter describing thefaults does not separate faults enough from the moisturecontent. One solution could be to increase the order of thefilter modeling the fault, so that it has lower gain at thelow frequencies. However, experiments have given amuch simpler solution. First of all assume that themoisture model does not support the faults, whilethese are occurring consequently it is simple to removethe moisture dependency of the fault residual by subtract-ing the moisture energy flow from the fault residual. Thenew clean residual is denoted, Qfault½n�, and is defined asin (26).

Qfault½n� ¼ Qfault½n� �g½n�

kmois. (26)


This transformation almost entirely clears the moisturedependency from the fault residuals, which can be seenfrom the experiments work in Section 5.

Subsequently two methods for detecting the faults basedon the residual are described. The first method is to use asimple threshold b, and compare the absolute value ofQfault½n� with a threshold b as in (27). This means that afault is detected based on this rule if kQfault½n�k is largerthan the threshold b. In the following f d½n� denotes a signalwhich is equal 1 in case of a fault and 0 elsewhere.

f d ¼1 if Qfault½n�4b;

0 elsewhere:

((27)

The second method partly removes the influence by thecoal moisture content from Qfault½n� by dividing it by theenergy flow contribution from the coal, before the thresh-old is applied, this residual is multiplied with a factor 1�106 in order to keep the value in a normal range, see (28).

f d ¼1 if

Qfault½n� � 106

_mc½n� � Cc � ðT s � T ½n�Þ4b;

0 elsewhere:

8><>: (28)

In theory the differences between these two methods arethat the first method reacts faster on a variation in Qfault½n�.However, a detection based on (28) is more certain toactually detect a fault, and not due to a variation in thecoal flow. In practice both methods seem equally effective,as seen in Section 5. For both methods the threshold b arefound, such that it gives a detection of the beginning of thefault as early as possible, with the constraint that falsedetection of faults are avoided.

4.3. Fault isolation

The sign of the energy balance can be used to separatethe possible faults in combination with e.g. logical schemes.A negative energy imbalance means that more energy isneeded to heat the coal than is being delivered by theprimary air flow. This can either be caused by too muchcoal or too low primary air flow or primary airtemperature. A positive imbalance on the other hand isdue to more energy is being delivered by the primary airflow than is required to heat up the delivered coal flow.Again this situation can be caused by the coal flow or theprimary air flow.

4.4. Moisture estimation

The moisture content is estimated directly by the optimalunknown input observer, meaning that no additionalcomputation is needed in order to get this estimate. Theestimated moisture content will, however, also describe anyfaults with low frequency response.

5. Experiments and results

The designed estimator is subsequently applied on threedifferent sets of data, sampled at the coal mill described inSection 3.2. All data are sampled with a sample time of60 s, two data sets with varying moisture contents but nofaults (subsequently denoted data set A and data set B) andin the last data set: the coal inlet pipe to the coal mill isblocked by the raw coal (a fault). Resulting in a stop in thecoal flow into the coal mill, this data set is denoted data set

C. All data is obtained from the measurement database onthe power plant.

5.1. Data set A

In the first data set, the moisture content increases in thebeginning and decreases eventually. In addition to thesevariations in the moisture content a step up and down inthe required coal flow of the coal mill are present, see Fig.2, meaning that the dynamics of the system are excited bythis change in the coal flow demand. In Fig. 8 the estimatedmoisture content is compared with the static estimate of themoisture content. The static estimate, has however, beenvalidated by comparing the static estimated values with labanalyzed samples of coal taken at the conveyor belt beforethe entrance to the coal mill, these samples were taken fordifferent kinds of coal as well at different plant loads. Thestatic estimate of the moisture content respond to the loadchange demands by some large decreasing peaks, which donot correspond to the real moisture content. From thisfigure, it can be seen that all dynamical estimated moisturecontent do not react on the load changes, while it followsthe static moisture content estimate outside the loadchanges, (where these can be considered reliable). Thismeans that the designed optimal unknown input observerestimates the moisture content quite successfully. The nextstep is to test how much these changes in moisture contentinfluences the fault energy flow/fault residual.Fig. 9 shows the non-normalized residual computed

using (26) and (27) and Fig. 10 shows the normalizedresidual computed using (28).From these it can be seen that both signals variate

following the moisture content, this is due to modeluncertainties, especially those originating from lineariza-tion of the model, as the largest signal components areachieved when the operation conditions are farthest awayfrom the operating point of the linear model. This pointhas not been changed during this experiment, since thesignal values are still much smaller than those achievedduring the fault in the mill. A threshold can be set muchhigher than these variations.

5.2. Data set B

In the next data set, data set B, the moisture content isslowly increasing, as it appears from Fig. 11. The figurecompares the observer estimate with the static moisture

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0 5 10 15 20

12

13

14

15

16

Samples [n]

Ob

se

rve

d C

oa

l

mo

istu

re [

%]

0 5 10 15 20 25

12

13

14

15

16

Time [hours]

Sta

tic E

stim

ate

d C

oa

l

mo

istu

re [

%]

Fig. 8. Illustration of the moisture content estimate compared with the static estimate, for data set A.

0 5 10 15 20 25−6

−4

−2

0

2

4

6

Time [hours]

Resid

ual – e

nerg

y [

J/s

]

x 10−3

Fig. 9. The non-normalized residual computed for data set A.

0 5 10 15 20 25−6

−4

−2

0

2

4

6

8x 10−3

Time [hours]

Resid

ual – e

nerg

y [

J/s

]

Fig. 10. The normalized residual computed for data set A.


content estimate, and since this data set does not containany changes in the coal flow demand, the static estimatecan be considered relatively reliable. I.e. the observerestimate should be close to the static estimate, which can beseen from Fig. 11.

Fig. 12 shows the non-normalized residual and Fig. 13shows the normalized residual.

From these figures it is evident that both signals varyconsiderably due to model uncertainties, especially thoseoriginating from linearization of the model, in this examplethe operating point is chosen at the end value of variables.

The operational point has not been changed during thisexperiment, as the signal values are still much smaller thanthe values achieved during the fault in the mill.

5.3. Data set C

The last data set contains a decreasing moisture content,and a fault starting approximately at 18.58 h. The moisturecontent estimated by the observer is compared with thestatic estimate in Fig. 14, from which it can be seen that theobserver estimated moisture content follows the static

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0 4 62 8 10 1612 1412

13

14

15

16

17

Time [hours]

Ob

se

rve

d C

oa

l

mo

istu

re [

%]

0 42 6 8 10 12 14 16 1812

13

14

15

16

17

Time [hours]

Sta

tic E

stim

ate

d C

oa

l

mo

istu

re [

%]

Fig. 11. Illustration of the moisture content estimate compared with the static estimate, for data set B.

0 2 4 6 8 10 12 14 16 18−8

−7.5

−7

−6.5

−6

−5.5

−5

−4.5

−4

−3.5x 10−3

Time [hours]

Resid

ual – e

nerg

y [

J/s

]

Fig. 12. The non-normalized residual computed for data set B.

0 2 4 6 8 10 12 14 16 18−10

−9

−8

−7

−6

−5

−4x 10−3

Time [hours]

Resid

ual – e

nerg

y [

J/s

]

Fig. 13. The normalized residual computed for data set B.


estimated moisture content, except during the fault, wherethe static estimate responds to the fault and even goes intonegative values. On the other hand is the dynamic estimatenot influenced by the presence of the fault.

The non-normalized residual can be seen in Fig. 15, thisfigure shows that a fault results in an evident increase in thevalue of the residual to levels much higher than thoseobtained from fault free data with changing moisturecontent, meaning it should be possible to separate moisturecontent variations from faults.

In Fig. 16 a zoom view of the fault in Fig. 15 is shown.Having the residual values of fault free data in mind, athreshold can be set to 0.04. Using this specific thresholdwill result in detection of the fault at time 18.58 h in thisspecific case, a visual inspection of the measurementsturned up with the same conclusion.The normalized residual can be seen in Fig. 17, this

figure shows that the fault results in a clear increase in thevalue of the residual to levels much higher than thoseobtained from fault free data with changing moisture

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0 5 10 15 20 2516

16.5

17

17.5

18

18.5

19.5

19

Time [hours]

Observ

ed C

oal

mois

ture

[%

]

0 5 10 15 20 250

5

10

15

20

Time [hours]

Sta

tic E

stim

ate

d C

oal

mois

ture

[%

]

Fig. 14. Illustration of the moisture content estimate compared with the static estimate, for data set C.

0 5 10 15 20 25−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Time [hours]

Resid

ual – e

nerg

y [

J/s

]

Fig. 15. The non-normalized residual computed for data set C.

18.3 18.35 18.4 18.45 18.5 18.55 18.6 18.65 18.7 18.75 18.8

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.11

0.1

Time [hours]

Resid

ual – e

nerg

y [

J/s

]

Residual

Threshold

Fig. 16. A zoom on the fault in the non-normalized residual computed for

data set C.


content, meaning that the fault residual is usable for faultdetection.

In Fig. 18 a zoom view of the fault in Fig. 17 is shown.Having the residual values of fault free data in mind, athreshold can be set to 0.04. Using this specific thresholdwill result in a detection of the fault at time 18.6 h in thisspecific case, which is identical to the case with visualinspection and the non-normalized residual detection.

5.4. Summary of experiments

These experiments show that the moisture content in thecoal is estimated correctly both for moisture content

variations as well as occurring faults. This is as wellsupported by approximately 10 other experiments withdifferent coals, all showing the same results of theestimator estimating the moisture content well. It shouldalso be noted that the static estimate responds to the fault.Based on the estimated fault residuals, the fault (blockedcoal inlet pipe) can be detected at time 18.58 for the non-normalized and 18.6 h for the normalized scheme, at whichtime sample the fault can be determined to start. In this testexample the two defection schemes have shown verysimilar performances. However, in theory the normalizedresidual would be less sensitive to other system inputs and

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0 5 10 15 20 25−10

60

50

40

30

20

10

0

Time [hours]

Resid

ual – e

nerg

y [

J/s

]

Fig. 17. The normalized residual computed for data set C.

18.3 18.35 18.4 18.45 18.5 18.55 18.6 18.65 18.7 18.75 18.8

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Time [hours]

Resid

ual – e

nerg

y [

J/s

]

Residual

Threshold

Fig. 18. A zoom view of the fault in the normalized residual computed for

data set C.


disturbances, meaning less false detections, but it can reactslower on the fault.

6. Conclusion

In this paper an observer based method for detection offaults and estimating the moisture content of coal in a coalmill is presented. The obvious variable to monitor in orderto detect problems in the coal mill is the coal flow in andout of the mill. However, these coal flows are notmeasurable, and the coal moisture content is not measur-able, either. The existing control system provides a staticestimate of the coal moisture content. Instead this papersuggests a method where these unknowns are estimatedbased on simple energy balance model of the coal mill,including an optimal unknown input observer. Moreover,two different fault residuals and detection schemes are

suggested. The designed observer is applied on three datasets covering variating moisture content as well as faults inthe coal mill. From these experiments it can be concludedthat the moisture content is successfully estimated, and thatthe fault is detected in the sample, as soon as the faultemerges.

Acknowledgments

The authors acknowledge the Danish Ministry ofScience Technology and Innovation, for support to theresearch program CMBC (Center for Model BasedControl), Grant no. 2002-603/4001-93.

Appendix A. Optimal unknown input observer

A necessary and sufficient condition for the existenceof a solution to the given observer problem is in Chenand Patton (1999) given as: an optimal unknown inputobserver solution exists if and only if: rankðCnþ1EnÞ ¼

rankðEnÞ.The computation of the matrices in the observer is also

given in Chen and Patton (1999) as

(1)
Set initial values: P0 ¼ Pð0Þ, z0 ¼ x0 � C0E0ðC0E0Þþy0,
H0 ¼ 0.
(2) Compute Hnþ1 ¼ EnðCnþ1EnÞ
þ.
(3) Compute K1
nþ1¼A1nþ1PnC

Tn ðCnPnC

TnþRnÞ

�1, and P0nþ1¼

Pn � K1nþ1CnPnðA

1nþ1Þ

T.

(4)
Compute Tnþ1 ¼ I�Hnþ1Cnþ1, Fnþ1 ¼ An �Hnþ1
Cnþ1An � K1nþ1Cn, K

2nþ1 ¼ Fnþ1Hn, and Knþ1 ¼ K1

nþ1þ

K2nþ1.

(5)
Now compute z½nþ 1� ¼ Fnþ1z½n� þ Tnþ1Bnu½n� þ
Knþ1y½n� and x½nþ 1� ¼ z½nþ 1� þHnþ1y½nþ 1�.
(6) Compute P0nþ1 ¼ Pn � K1
nþ1CnPnðA1nþ1Þ

T, and follow-

ing Pnþ1 ¼ A1nþ1P

0nþ1ðA

1nþ1Þ

Tþ Tnþ1QnT

Tnþ1 þHnþ1

Rnþ1HTnþ1.

(7)
Set n ¼ nþ 1 and jump to step 2.
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