*Corresponding author. Tel.: #39-02-2399-3542; fax: #39-02-2399-3412.E-mail address: savaresi@elet.polimi.it (S.M. Savaresi).

Control Engineering Practice 9 (2001) 249}266

On modelling and control of a rotary sugar dryer

Sergio M. Savaresi��*, Robert R. Bitmead�, Robert Peirce��Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza L. da Vinci, 32, 20133, Milan, Italy

�Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA�CSR Ltd, Herbert River Mills, Post Ozce Mail Box 4, Ingham Qld, 4850, Queensland, Australia

Received 5 November 1999; accepted 25 September 2000

Abstract

This paper deals with the problem of "tting a set of data collected on a rotary sugar dryer, by means of a "rst-principlesmathematical model. Owing to the highly constrained structure of the model, it was discovered that the sugar dryer is characterised bytwo di!erent working conditions: the `standard-modea (characterised by a non-zero sugar moisture content), and the `overdried-modea (namely a condition where the sugar moisture content is almost nil, and the evaporative phenomenon becomes negligible). Onthe basis of this two-stage behaviour, an accurate "t between the model and the measured data can be achieved, and an innovativecontrol strategy can be drawn. � 2001 Elsevier Science ¸td. All rights reserved.

Keywords: Sugar dryer; Model identi"cation; Non-linear model; Plant regulation

1. Introduction

The aim of this paper is to analyse and discuss theproblem of "tting a set of real data collected on a rotarysugar dryer (at the CSR Ltd. plant of Plane Creek* Queensland, Australia) with a "rst-principles model,and to propose an innovative regulation scheme, basedon a posteriori model analysis.

The problem of regulating the characteristics (temper-ature and moisture content) of the sugar collected at thedryer outlet is a standard problem in sugar plants. Spe-ci"cally, the goal of a sugar dryer (which is the last stageof the plant) is two-fold:

� cooling the sugar to a temperature of about 30}313C orlower, in order to avoid the discolouring phenomena,which inherently reduces the commercial value of thesugar;

� regulating the moisture content of the sugar, in order toavoid sticking (caused by high-moisture content) andthe dispersion of sugar dust in the environment(caused by low-moisture content). Sugar moisture con-tent also has an immediate impact on price, with

excessive moisture attracting a penalty. The targetmoisture content is typically about 0.2%.

The regulation of the dryer is a crucial issue in a sugarplant; however, this problem is usually dealt with withoutresorting to mathematical modelling tools and automaticcontrol: plant personnel manually change the controlvariables, according to accumulated experience of theplant behaviour. However, due to the comparativelylarge number of input/output variables and the complic-ated relationships among them, it is expected that replac-ing human operators with automatic controllers couldremarkably improve the quality and the evenness of theoutput sugar characteristics.

It is interesting to point out that, at a "rst glance, thedesign of a feedback controller for the regulation ofoutput sugar moisture and temperature seems to berather simple and straightforward. As a matter of fact, therequired bandwidth of the regulation loop is very small(if compared to the main time constants of the plantdynamics) since only the average value of the outputvariables really matters; moreover, many input variablesare available for control purposes. However, unfortu-nately, additional constraints make this control problemdi$cult and tricky, namely:

� the on-line measurement of input/output variables isvery di$cult; this is especially true for moisturemeasurements;

0967-0661/01/$ - see front matter � 2001 Elsevier Science Ltd. All rights reserved.PII: S 0 9 6 7 - 0 6 6 1 ( 0 1 ) 0 0 0 0 4 - 1

� even collecting an o!-line set of input/output data ofa plant is di$cult and takes a lot of time: this makesthe validation of physical models rather di$cult, andblack-box modelling hardly or not practicable;

� the plant is a!ected by large and unpredictable distur-bances; therefore, an automatic control strategy mustbe simple and robust;

� the environmental conditions are extremely hard dueto humidity, dust, and vibrations; as a consequence,only simple sensors and electronic equipment can beemployed;

In the literature, the problem of controlling numeroustypes of dryers (rotary, solar, cross-#ow, mixed-#ow,#uidised or "xed bed, drum, etc.) used for the desiccationof many di!erent materials (fertilisers, pharmaceuticals,mineral concentrates, agricultural products, cereals,cement, etc.) has been treated extensively, both froma theoretical and from a practical point of view (seeSection 6 at the end of this paper for a brief overview ofthe literature on the topic). However, it is worth noticingthat (to the best of the authors' knowledge) very fewworks have been published on the problem of modellingand control of rotary sugar dryers.

The purpose of building a dynamical model of a rotarysugar dryer is primarily for conducting `what ifa simula-tion experiments. These must be su$ciently faithful tothe real process to yield quantitative guidelines for con"-dent decision-making on capital expenditure. Addition-ally, operating guidelines and feedback control principlescan be derived from the model.

A relevant feature of the modelling proposed here isthat it takes place using sampled data from an operatingproduction dryer. This process operates in continuousmode, rather than in batch, with a counter-#ow ofhot/moist sugar and cool/dry air. The data collected onthe dryer are of two types: highly aliased `full-stateasamples of sugar temperature and moisture content fromwithin the dryer at Macknade mill; corroborated andextended by more frequently sampled input}output datafrom the Plane Creek mill (the plant this paper mainlyfocuses on). The quantity of data is low, and the measure-ment of each sample's moisture content requires laborat-ory analysis. The variability of the data also is large.

Given the model's purpose, and the nature of the data,a discrete-time model was constructed that focuses on thedetermination of the dominant physical processes at playand the coarse quanti"cation of their e!ects. What distin-guishes this study from earlier ones is the material beingdried, which does not exhibit a signi"cant transitionbetween drying phases, the continuous mode of opera-tion using an industrial plant in use, and the couplingbetween model properties and its ultimate purpose.

Among the few recent papers on rotary sugar dryers,the most closely related to the present work is Douglas,Kwade, Lee, and Mallick (1993), which is mainly devoted

to the development of a "rst-principles dynamicalmodel of a rotary sugar dryer. A sequence of data col-lected on two Australian sugar plants has been used forvalidation.

The present work di!ers from Douglas et al. (1993) inthat a purpose-directed model is "tted by determiningthe dominant physical processes capable of describingthe data rather than developing a complete "rst-prin-ciples model. Like Douglas et al. (1993), the purpose is toprovide a useful simulation system to aid capital deci-sions; here the use of the model is also extended tocontrol strategy development. The models are construc-ted in discrete time and use internal state measurementsin addition to input}output data to discriminate betweenphenomena and to "t parameters. Thus, this paper can beregarded as extending Douglas et al. (1993). The maincontribution and novelty of this work can be summarisedas follows:

� The "rst-principles model proposed in Douglas et al.(1993) has been slightly modi"ed and re"ned. Speci"-cally, in the model presented herein the time andspatial discretisation is optimised to deal with the two(clearly separated) dynamics of vapour/air andsugar/moisture velocities.

� The analysis of the model has been extended to low-moisture ranges. This analysis reveals that the modelcannot be used for an accurate prediction of moisturecontent, when the sugar moisture is very low (below0.1%); however, it can be e!ectively used to predict thesugar temperature, and the working region of thesugar dryer.

� The data paucity (in terms of number of available dataand signal-to-noise ratio) and the use of only in-put/output data means that `grey-boxa ideas have hadto play a central function. Therefore, the validation-phase of a "xed "rst-principles model has been re-placed by the selection of a small number of freeparameters, and their subsequent tuning using a set ofmeasured data.

� Using the grey-box model, it has been shown that thesugar dryer is characterised by two main workingconditions, according to the sugar moisture content:the `standard-modea (characterised by a non-zerosugar moisture content), and the `overdried-modea(namely a condition where the sugar moisture contentis almost nil, and the evaporative phenomenon be-comes negligible). Even if this classi"cation is simple, itcaptures the main non-linearity of the system.

� The estimated grey-box model and the `two-stageabehaviour of the dryer has been used to generateoperating guidelines akin to feedback control solu-tions, making possible a considerable improvement inthe plant control strategy.

The outline of this paper is the following: inSection 2 the sugar dryer is brie#y described, and its

250 S.M. Savaresi et al. / Control Engineering Practice 9 (2001) 249}266

Fig. 1. Diagram of a standard rotary drum dryer.

Fig. 2. Internal surface of a sugar dryer in working condition (detail oftwo `#ightsa).

mathematical model is given, while in Section 3 the set ofdata collected on the Plane Creek dryer is presented anddiscussed. Section 4 is entirely devoted to the problem of"tting the model with the measured data; in Section 5 theproblem of controlling the sugar dryer is considered, andan innovative control strategy is proposed. Finally, inSection 6 the literature related to this work is brie#youtlined.

2. A rotary sugar dryer: model and description

The CSR Ltd Plane Creek sugar mill uses rotary drumdryers as the last stage in the sugar milling process. Thedryer operates in continuous mode. A basic diagram ofsuch a dryer is in Fig. 1.

It consists of a large drum (about 9 m long and withan internal diameter of about 2.5 m), set at a slightangle (about 33) in order to let the sugar moveslowly under gravity from the inlet to the outlet. Theaverage residence time of the sugar in the dryer is about7 min. The drum slowly rotates around its longitudinalaxis (about 6 revolutions per minute), in order toexpose the sugar to the air continuously, and to mixthe sugar. To this end, the internal surface of the drum isentirely covered with small `hand-shapeda plates(usually called `#ightsa* see Fig. 2), which lift the sugarin the drum. The inlet `wet/hota sugar passes throughthe dryer, moving counter-current to the air #ow, andout the lower end where it is dropped onto a conveyorwhich takes the `dried/cooleda sugar to the sugarhopper, from where it is transported to the customer.A fan is enclosed at the end of the dryer, which drawsthe air in through a duct and air conditioner. A fan in theair conditioner also provides forcing. When the air exitsthe dryer it passes through a scrubber to remove sugardust.

The Plane Creek Mill has actually two parallel dryersthat operate all year round as the "nishing stage of verylow colour (VLC) sugar production.

A simple model of the dryer can be derived by "rstprinciples. Speci"cally, the following main phenomenahave to be taken into account:

� the evaporation (removing both water and excess en-ergy from sugar to the air);

� the convection (removing excess energy from sugar tothe air);

� the transport of sugar and air along the drum incounter-#ow.

The description of these main e!ects can be comp-lemented * when necessary * with the following phe-nomena:

� the physical process of the wet sugar crystals stickingtogether;

� di!usion e!ects a!ecting the retention of water by thedrying sugar due to the hygroscopic properties of thedry sugar;

� impurity levels in the water layer, raising the boilingpoint;

� spontaneous crystallisation in the water layer.

The model presented herein (originally described inBitmead, Kammer, Jones, & Connolly, 1997; Tait, Schin-kel, & Grieg, 1997; Wright & Shardlow, 1997, and recal-led here for the sake of the consistency of this work)represents a slightly modi"ed version of the model pro-posed and validated in Douglas et al. (1993). Speci"cally,the time and spatial discretisation is optimised here todeal with the two clearly separated dynamics of va-pour/air and sugar/moisture velocities.

Following a typical approach used to model drumscharacterised by high length-to-diameter ratio, a `"nite-elementa approach is used: the length of the dryer issubdivided into a number N of equal-length `slicesa, soreducing an in"nite-dimensional model (the dynamic be-haviour of the dryer is rigorously described by a set ofpartial di!erential equations) into a "nite-dimensionalone. The dryer is therefore assumed to be completelydescribed by 4N state variables, given by (The subscript

S.M. Savaresi et al. / Control Engineering Practice 9 (2001) 249}266 251

index `ia indicates the actual slice.):

�M�

�(t) M�

�(t) 2 M�

�(t) 2 M�

�(t)

M��(t) M�

�(t) 2 M�

�(t) 2 M�

�(t)

¹��(t) ¹�

�(t) 2 ¹�

�(t) 2 ¹�

�(t)

¹��(t) ¹�

�(t) 2 ¹�

�(t) 2 ¹�

�(t) �,

where M��(t) is the mass of moisture in the sugar (liquid

water), M��(t) is the mass of vapour (gaseous water) in

the air, ¹��(t) and ¹�

�(t) are the temperatures of sugar/

moisture and air/vapour, respectively. It is assumed thatthe moisture has the same temperature as the sugar, andthe vapour has the same temperature as the air. Noticethat the sugar and air masses (which will be indicatedwith the symbols M�

�(t) and M�

�(t)) are modelled as being

constant and the same for each slice.Discretisation in time is a somewhat more di$cult task

than spatial discretisation, since the air/vapour velocity isdramatically higher (around 100 times) than that of thesugar/moisture. A suitable choice for the sampling rate� is given by the residence time of air in each slice, namely:

�"

length of dryer (m)

number of slices)

1

velocity of air (m s��).

Given the above de"nitions, the model equations are thefollowing:Evaporative mass transfer: This paper concentrates

only on evaporation as the vehicle of mass transfer. Theextent of evaporation depends upon the di!erence be-tween the partial pressure of moisture in the "lm sur-rounding the sugar crystal and the partial pressure ofvapour in the air. It is given by

E�(k�)"m

�A

��(P

������((k!1)�)!P

������((k!1)�)),

(1a)

where m�

is the mass transfer coe$cient, A�

is the avail-able sugar surface area, while P

������and P

������are the

partial pressure of water in the sugar and in the air,respectively, within slice i. They are given by

P������

(k�)"exp�16.31!

3829.48

¹��(k�)#227.51�,

P������

(k�)"101.31

1#18M��(k�)/28.818M�

�(k�)

. (1b)

The Eq. (1b) used to compute the partial pressure ofwater in the sugar is the Antoine formula, which assumesthat the water "lm surrounding the sugar crystals be-haves as free liquid water (see e.g., Incropera & de Witt,1990; Perry & Green, 1997). Note that this assumption(used also in Douglas et al., 1993) is realistic only whenthe moisture content is comparatively large (more than0.1}0.2%).

The time updates for the moisture and vapour massesin slice i at time k� are given by

MM ��(k�)"M�

�((k!1)�)!E

�(k�),

MM ��(k�)"M�

�((k!1)�)#E

�(k�). (1c)

We denote intermediate variables, before spatial updates,by using an overbar.Energy transfer: As already pointed out, energy transfer

occurs due to evaporation and convection; accordingly,the temperature changes are computed by enthalpybalance as follows:

¹M ��(k�)

"¹��((k!1)�)

#

(h�A

��#C

��E�(k�)) (¹�

�((k!1)�)!¹�

�((k!1)�))

C��M�

�#C

��MM �

�(k�)

,

¹M ��(k�)

"¹��((k!1)�)!

¸���E�(k�)#h

�A

��(¹�

�((k!1)�)!¹�

�((k!1)�))

C��M�

�#C

��MM �

�(k�)

,

(1d)

where C��

, C��

, C��

, and C��

are the heat capacities ofair, vapour, sugar and moisture, respectively, h

�is the

convection heat transfer coe$cient, and ¸���

is the latentheat of vaporisation of water. As before, A

�is the avail-

able surface area within slice i. In the above equations itis assumed that the moisture and vapour mass changeswithin a slice are small enough that they may be con-sidered as being negligible for enthalpy balance purposes.Transport: The dynamical model is realised by calculat-

ing the heat and mass transfers for each slice, and thenshifting the appropriate values along to the next slice.Notice that the air temperature and vapour masses ineach slice are simply shifted along to the next slice aftereach time update. However, the air/vapour mixturemoves through the dryer much more quickly than thesugar/moisture mixture, so the sugar temperatures andmoisture masses are only partially shifted after each timeupdate. So, the shifts of the four state variables of eachslice (moisture and vapour masses, sugar and air temper-atures) are given by

¹��(k�)"¹M �

�(k�),

M��(k�)"MM �

�(k�),

¹��(k�)"(1!�)¹M �

�(k�)

#

�¹M ����

(k�)(C��M�

���#C

��MM �

���(k�))

C��M�

�#C

��MM �

�(k�)

,

M��(k�)"(1!�)MM �

�(k�)#�MM �

���(k�), (1e)

where �"(velocity of sugar)/(velocity of air).The model (1) is based on "rst-principles, and it is

characterised by many physical constants and

252 S.M. Savaresi et al. / Control Engineering Practice 9 (2001) 249}266

Table 1Measured input/output variables

Measured variable Measurement unit Method of measurement

InputsSugar temperature 3C Measured with a thermometerSugar inlet #ow-rate ton/h Manually counted number of fugal dropsSugar inlet moisture content % Samples taken and analysed in laboratoryAir temperature 3C Measured with a thermometer (dry-bulb measurement)Air inlet #ow-rate ton/h Turbine anemometer used over a 1 min periodAir absolute humidity % Computed from wet-bulb temperature measurements

OutputsSugar temperature 3C Measured with a thermometerSugar exit moisture content % Samples taken and analysed in laboratory

parameters. This model can now be used in two slightlydi!erent ways: as a xxed physical model, or as a grey-boxmodel. In the former case, the numerical value of thewhole set of parameters is calculated from a priori know-ledge of the physical characteristics of the system; thiscomputation is typically followed by a validation proced-ure, which is made using a set of data collected on the realplant. In the latter case, a few parameters (typically theparameters whose physical-principle-based estimation isdi$cult or unclear) are assumed to be unknown, anda posteriori estimated from real data.

Apparently, the di!erence between these two ap-proaches is subtle and somewhat fuzzy: they both makeuse of a "rst-principles model, and a set of measured data.Grey-box modelling typically has the advantage of pro-viding a better "t between model and data; on the otherhand, the estimated value of the free parameters ina grey-box model may loose a clear physical meaning.This is due to the intuitive fact that the uncertainties,noise, and modelling errors are condensed and taken intoaccount by a small subset of parameters only.

In this work a grey-box point of view is adopted,because of the paucity of data required to "t manyparameters. Speci"cally, the model parameters which areassumed to be unknown and used as `tuning knobsa aregiven by:

� the free surface area per slice of the sugar in the drum,A

�(m�);

� the heat transfer coe$cient, h�

(kW/m� K);� the mass transfer coe$cient, m

�(kg/m� s kPa);

It is important to notice that, due to the model struc-ture (see (1a) and (1d)), the number of parameters to beestimated is in fact two for each slice: A

�h�

and A�m

�. In

the rest of the paper the total sugar-free surfaceA"��

�����

will be considered "xed at the value of5000 m� (this value is a re-scaled version* for a di!erentsugar #ow-rate * of a value empirically estimated ona similar rotary drum dryer* see Bitmead et al., 1997),

simply assuming that A�"A/N. This is an acceptable

approximation when the sugar is very dry; on the con-trary, if the sugar is wet and important sticking e!ectsoccur, A

�is a function of i.

Finally, it is important to remark that the structure ofthe above model (1) has been already extensivelyvalidated using real data in Douglas et al. (1993) on twosugar plants located in Victoria and Kalamia, andin Bitmead et al. (1997) on a sugar plant located inMacknade. The validation, however, has been done onlyin operating conditions characterised by sugar moisturecontent higher than 0.2%.

3. Analysis of the measured data

Four dryer performance trials were undertaken atthe Plane Creek plant during July 1998 (Gri$th, 1998).Each trial lasted about 1 h. Table 1 describes the mea-sured input/output variables. Sugar moisture content isgiven by the mass ratio between liquid water and drysugar.

Notice that the sugar inlet #ow-rate is measured sim-ply by manually counting the number of drops from thecentrifuges (usually called `fugalsa), that representthe last stage of the plant before the dryer. Since only theaverage amount of sugar contained in each fugal isknown, the measured inlet #ow-rate represents onlya rough estimate of the actual one. Also note that theoutlet air temperature and humidity are unavailable forthe measurement because of the use of water scrubbers toremove sugar dust.

The four trials were performed under slightly di!erentconditions to ascertain the e!ects of these conditionsupon dryer performance. Trial �1 was performed in themid-afternoon under standard operating conditions.Trial �2 was undertaken in the early morning to deter-mine the e!ects of the cooler air and humidity variations.Trials �3 and �4 were performed during the afternoonof the same day, but the dryer load was changed, in order

S.M. Savaresi et al. / Control Engineering Practice 9 (2001) 249}266 253

Table 2Distillation of measured data

Trial �1 Trial �2 Trial �3 Trial �4

Lowerbound

Centralvalue

Upperbound

Lowerbound

Centralvalue

Upperbound

Lowerbound

Centralvalue

Upperbound

Lowerbound

Centralvalue

Upperbound

InputsSugar temperature (3C) 53.6 54.3 55.1 53.5 53.8 54.2 55.0 55.6 56.2 55.0 55.6 56.2Sugar #ow-rate (ton/h) 37.6 39.1 40.7 37.8 39.1 40.5 50.0 51.5 52.9 31.4 32.3 33.3Sugar moisture content(%)

0.606 0.665 0.725 0.749 0.825 0.901 0.799 0.843 0.888 0.799 0.843 0.888

Air temperature (3C) 27.7 27.8 27.9 20.2 20.4 20.6 22.6 22.7 22.8 22.6 22.7 22.8Air #ow-rate (ton/h) 19.2 19.7 20.1 19.1 19.3 19.6 18.9 19.2 19.5 18.9 19.2 19.5Air absolute humidity (%) 0.844 0.850 0.856 0.580 0.590 0.600 0.675 0.680 0.685 0.675 0.680 0.685

OutputsSugar temperature (3C) 37.2 37.5 37.8 30.3 30.7 31.1 31.3 31.8 32.2 28.8 29.1 29.4Sugar moisture content(%)

0.046 0.048 0.050 0.061 0.064 0.066 0.040 0.042 0.045 0.026 0.029 0.031

to understand better the e!ect of load variations on theoutput variables.

The sampling time was 5 min. Therefore, for each vari-able, only 10}13 samples per-trial are available.

During each trial, the six inputs and the two outputs ofthe dryer are assumed to be constant (even though obvi-ously a!ected by noise). According to this assumption,the average value of each measured variable and their`range of indeterminationa are numerically computed; it isassumed that, within such a range, every value is equallylikely and good for data-"tting purposes.

Speci"cally, the mean value of each measured variable* say y(t) * is computed using the standard samplemean-value estimation

y�("1

n

�� ��

y(t),

where n is the number of available data-points while thelower and upper bounds (say ¸

�and ;

�) of the `range of

indeterminationa are computed as

¸�"y�(!

�K�

�N,

;�"y�(#

�K�

�N,

where �K�

is the estimated standard deviation of the mea-sured variable, computed as

�K�"�

1

n

�� ��

(y(t)!y�( )�.

Rigorously speaking, the de"nition of `range of indeter-minationa as [¸

�,;

�] has a simple but precise math-

ematical meaning: it is the interval [�!�, �#�], � and� being the expected value and the standard deviation of

y(t), respectively. This is a sound de"nition, if the follow-ing set of assumptions holds:

� the measured variables can be modelled as a constantvalue plus white noise: y(t)"y� #�(t) �+=N(0, ��);namely it is assumed that the process y(t) is at steadystate, and the additional noise has no residual dynam-ics;

� y(t) is a stationary process, namely the probabilitydistribution of y(t) is independent of the time index;

� the probability distribution of y(t) in the interval[�!�, �#�] is approximately #at. Note that thisassumption is roughly ful"lled if we make the standardassumption of Gaussian, uniform, or similar distribu-tion of y(t).

These assumptions "t reasonably with the true data-generation process. In Table 2, the lower bound, themean/central value and the upper bound of the `range ofindeterminationa is reported for each variable. Suchvalues will be used in the rest of the work, for model-"tting purposes.

Remark. The main remark to be made about the data ofTable 2 concerns the output sugar moisture content. No-tice that the output sugar moisture content is always verylow (about [0.03, 0.06]%, which is much smaller than the0.2% `targeta moisture content). This is due both to thee$ciency of the Plane Creek dryer, which is characterisedby a comparatively high length-to-diameter ratio, and tothe fact that all the trials were made in winter-time, whenthe outside air is comparatively dry and cool.

It is important to notice that, in these conditions(namely when the moisture content is lower than 0.1%),discriminating between two values of moisture contentshas little or no meaning. A value in this region can be`conventionallya approximated by zero. A major im-plication of this fact is that the output sugar moisture

254 S.M. Savaresi et al. / Control Engineering Practice 9 (2001) 249}266

Fig. 3. (a) Example of sugar temperature pro"les, in `standard-modea.(b) Example of sugar moisture content pro"les, in `standard-modea.

content cannot* in practice* be used for model "ttingpurposes. A model capable of accurately predicting thesugar moisture content within the [0, 0.1]% region mustnecessarily be much more complicated than (1), since, inthis region, the Antoine formula for the computation ofthe partial pressure of moisture in the sugar is no longervalid, and di!usion e!ects should be taken into account(hygroscopic properties, impurity levels, spontaneouscrystallisation, etc.). The problem of "nely modelling thedrying rate at very low moisture content has been alreadyconsidered in the literature (see e.g. Farkas, Remenyi,& Biro, 1998b; Van Boxtel, & Knol, 1996; Toyoda, 1992).However, as already pointed out, the relevance of devel-oping a model capable of accurately predicting the moist-ure content in this region is * for control purposes* negligible; as a consequence, in the rest of the paperthe simple model (1) will continue to be used, withoutdiscriminating between di!erent values of moisture con-tent in the range [0, 0.1]%.

4. Fitting the data with the model: optimisation andanalysis

As already pointed out, the model (1) was "rst de-veloped for the interpretation of the CSR Ltd. Macknadeplant data collected during the crushing season 1997(Bitmead et al., 1997), and it is characterised by twoparameters (m

�and h

�) which are unknown. The rest of

this section is devoted to the problem of tuning theparameters m

�and h

�in order to obtain the `besta "t

between the output values predicted by the model andthose measured on the real plant. Speci"cally, in Section4.1 it will be shown that the model in `standard-modeacannot "t the measured data, whatever the values ofm

�and h

�are; in Section 4.2 it will be shown that, with

a suitable choice ofm�

and h�, the measured output sugar

temperature can be accurately predicted, if the model isallowed to operate both in `standard-modea and in`overdried-modea. In both cases, the optimal values ofm

�and h

�are obtained by minimisation of the summed

squared error between measured and predicted outputs.

4.1. Model operating in `standard-modea:analysis and discussion

The most intuitive and natural approach to the prob-lem of "tting the measured data (Table 2) with the model(1) is to use the model in `standard-modea, namely theoperating mode characterised by a sugar moisture con-tent higher than zero at any point of the drum. InFig. 3 an example of the computed pro"le of the sugartemperature and moisture content along the drum instandard mode is displayed; apparently, in this operatingmode both sugar temperature and moisture content havea regular (almost linear) behaviour along the drum.

Owing to the fact that there are just two parametersinvolved in the optimisation/"tting process, the problemof searching for the `optimala values of parametersm

�and h

�is comparatively easy, and * in practice

* can be solved by exhaustive exploration, namely by"nely gridding the ranges of admissible values for suchparameters. The result obtained by running the optimisa-tion process is somewhat surprising: the input/outputdata of Table 2 cannot be "tted by a model constrainedto operate in `standard-modea.

With the aim of gaining some insight into the mainreasons of this behaviour of the model, a local linearmodel was computed about a nominal operating condi-tion of the model working in `standard-modea. If there isno switching from one mode to another, a linearisedmodel just introduces small approximation errors, whileproviding a useful and handy analysis tool.

In order to compute a local linear model, "rst a set ofnominal inputs for the non-linear model, and two nom-inal values for m

�or h

�has to be selected. It is easy to see

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Table 3Nominal point about which the local linear model is computed

Nominal value

InputsSugar temperature (3C) 53.8Sugar #ow-rate (ton/h) 39.1Sugar moisture content (%) 0.825Air temperature (3C) 20.4Air #ow-rate (ton/h) 19.3Air absolute humidity (%) 0.59

OutputsSugar temperature (3C) 30.877Sugar moisture content (%) 0.062

ParametersHeat transfer coe$cient h

�(kW/m�K) 0.003

Mass transfer coe$cient m�

(kg/m�s kPa) 2.7�10�

that if h�"0.003 kW/m�K and m

�"2.7�10� kg/

m�s kPa (the values used for the data collected onthe CSR Ltd. Macknade plant in 1997 * seeBitmead et al., 1997), the I/O variables of Trial �2 are"tted quite accurately. Henceforth, we take the centralvalues of the inputs in Trial �2 as `nominalinputsa. In Table 3 the nominal inputs, outputs andparameters are summarised. Since the output moisturecontent is strictly larger than zero, the nominaloperating condition is a `standard-modea operatingcondition.

It is important to stress that the validity of the follow-ing analysis only marginally depends on the nominalinputs and parameters taken. This fact has been empiric-ally tested by computing local linear models about di!er-ent sets of inputs and parameters (those of Trials �1,�3, and �4). The resulting local linear models are closeto each other. This reveals that, if we do not switchoperating mode, the model is in fact only slightly non-linear.

The local linear model is numerically computed bygiving an independent #1% variation to each input,about the nominal equilibrium point. Note that this isthe easiest way of computing the linear approximation,even if, in principle, it could be computed directly fromthe steady-state equations of (1), or even by direct small-signals excitation of the real plant; clearly, due to theinherent di$culty of collecting real data, the latterapproach is not practicable. The equations of the ob-tained linear model are given by:

(Sugar¹empOut-30.877)

"0.2593(Sugar¹empIn-53.8)#0.3427(SugarFlow-39.1)

#0.3030(SugarMoistIn-0.825)#0.2971(Air¹emp-20.4)

!0.2176(AirFlow-19.3)#1.8136(AirHumid-0.59), (2a)

(SugarMoistOut-0.062)

"!0.0281(Sugar¹empIn-53.8)#0.0095(SugarFlow-39.1)

#1.0061(SugarMoistIn-0.825)!0.0034(Air¹emp-20.4)

#0.0031(AirFlow-19.3)#0.1356(AirHumid-0.59) (2b)

In order to understand better and to compare the e!ectsof input variations on the outputs, in Fig. 4a and b theabsolute variations of output sugar temperature andmoisture content to #1% input variations are dis-played. The following observations can be drawn:

� The sugar temperature, the sugar #ow-rate and the airtemperature are the input variables that mainly a!ectthe output sugar temperature, whereas the sugarmoisture content and air humidity seem to play anegligible role in determining output sugar temper-ature.

� The sugar temperature, the sugar #ow-rate and thesugar moisture content are the input variables thatmainly a!ect the output sugar moisture content.Although, all the characteristics of input air (temper-ature, humidity and #ow-rate) seem to have a negli-gible e!ect on the sugar moisture content.

� It is interesting to notice (see Eq. (2b)) that the gainfrom input moisture content to output moisture con-tent is almost exactly 1. This suggests that model (1)cannot accurately explain the output sugar moisturecontent when the sugar is overdried, since the gainfrom input to output moisture content abruptlyswitches from 1 to 0, while an accurate moisture con-tent prediction when the sugar is overdried wouldrequire a smoother transition from gain 1 to gain 0. Asalready pointed out, this is due to the fact that theAntoine formula for the computation of the partialpressure of the moisture in the sugar is no longer validwhen the sugar moisture content is very low (in therange [0, 0.1]%).

An intuitive yet simple analysis to understand roughlythe extent to which the model in `standard-modea isunable to model the measured I/O behaviour of thePlane Creek sugar dryer is to predict the output sugartemperature of Trials �1, �3, and �4 using the locallinear model (2).

In Table 4 the results obtained by feeding the linearmodel (2) with the input measurements of Trials �1, �3,and �4 are summarised.

It is important to notice that, in order to be consistentwith the approach based upon the de"nition of `ranges ofindeterminationa for each measured variable, the inputvalues which provide the best "t with the measuredoutput temperatures were selected, within their ranges ofindetermination.

The large prediction error made by the linear model (2)in the case of Trials �1 and �3 clearly denotes that themodel in `standard-modea is inadequate to provide an

256 S.M. Savaresi et al. / Control Engineering Practice 9 (2001) 249}266

Fig. 4. (a) E!ect of #1% input variations on the output sugar temperature. (b) E!ect of #1% input variations on the output sugar moisture content.

Table 4Fitting the output sugar temperature using the linear model

Trial � Measured output sugartemperature (3C)

Output sugar temperature predicted bythe linear model (3C)

Error (3C)

1 37.5 34.5 !2.03C2 (nominal) 30.9 30.9 *

3 31.8 35.7 #3.94 29.1 29.3 #0.2

accurate description of the dryer behaviour. Speci"cally,notice that, since the linear model strongly underesti-mates the output temperature in Trial �1 and stronglyoverestimates the output temperature in Trial �3, thesugar drier behaviour in Trials �1 and �3 must beexplained using two di!erent models or two di!erent`working conditionsa.

4.2. `Beyond the kneea: xtting the model with measureddata

In the previous subsection it was shown that the modelin `standard-modea is unable to "t the measured output

sugar temperatures. The main indication we get from this`negativea result is that the sugar dryer is likely to becharacterised by operating modes di!erent from the`standarda one.

An alternative operating mode, which is quite intuitiveand simple to interpret is the mode that will be called the`overdried-modea. The `overdried-modea is character-ised by sugar moisture content e!ectively equal to zerofrom a certain point of the drum on. This mode refers tothe case when the sugar at the output is overdried. It isworth noticing that a zero-moisture condition is just anideal condition that, in practice, never happens, sincea little amount of moisture always remains in the sugar.

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Fig. 5. (a) Example of sugar temperature pro"le, in `overdried-modea.(b) Example of sugar moisture content pro"le, in `overdried-modea.

This operating mode of the model, however, is usefulsince it clearly stresses and represents what actually hap-pens in the drum when the evaporation process of thesugar moisture becomes negligible. As it is apparent fromFig. 5 (where an example of sugar temperature andmoisture content pro"le is depicted), in `overdried-modea the temperature pro"le has a discontinuity in its"rst derivative when the zero-moisture condition isreached. This causes a `kneea in the sugar temperaturepro"le, the slope of the latter part of the temperaturepro"le being much lower, since* `beyond the kneea*the temperature decreases only due to convection.

The discontinuity between the standard and the over-dried mode, clearly visible in Fig. 5, is just an approxima-tion of the plant behaviour: the true moisture andtemperature pro"les are obviously characterised bya smooth transition between these two working condi-tions. As already said, this is due to the fact that, forlow-moisture conditions, the model presented here can-not accurately predict the moisture content; however, forthe purposes of this work, a "ner model of the transitionregion is somewhat unnecessary and redundant.

It is worth observing here that, in the literature, this`two-stage behavioura has already been observed in ma-terials other than sugar, and labelled with a di!erentnomenclature. In van Boxtel and Knol (1996) (wherea #uid-bed dryer model is developed and proposed), forinstance, the `standarda and `overdrieda modes arenamed constant yux period (CFP) and constant surfaceperiod, respectively. Constant rate period (CRP) andfalling rate period (FRP) is another way of namingthe same phenomenon. Another piece of literature wheremultiple-stage behaviour was observed and described isthe work of Toyoda and co-authors (Toyoda, 1989,1992; Toyoda, Farkas, & Kojima, 1995, 1996), wherethe so-called `two-tanks modela of rough rice is proposed.In these works three di!erent drying conditions(named drying period I, II, and II) are outlined: theintermediate working condition refers to the transitionphase between standard and overdried modes. Finally,note that in these papers di!erent working conditionsare named `periodsa, since it is assumed that di!erentworking modes appear at di!erent times; this is notthe case of a rotary sugar dryer, where di!erent dryingstages can exist simultaneously in di!erent regions of thedrum.

The new search for the `optimala model parametershas been done under the following assumptions:

� The output sugar moisture content is not taken intoaccount in the "tting procedure, since in all trials theoutput moisture content is very low. It was expectedthat the sugar output moisture content predicted bythe model is somewhere in the range [0, 0.1]%.

� The model was allowed to work both in `standard-modea and in `overdried-modea.

� According to the results obtained in the previous sub-section (Table 4), within their `range of indetermi-nationa, the inputs of Trial �1 which maximise theoutput temperature, central input values of Trial �2,inputs of Trials �3 and �4 which minimise theoutput temperature (see Table 5) have been selected.Using these input values, the goal is to "t the centralvalues of output sugar temperatures.

Under the above assumptions, it is easy to see that anexact matching of all the central values of output sugartemperatures can be achieved. This con"rms the fact thatthe `overdried-modea closely re#ects what really hap-pens in the sugar dryer, and that the model (1) is a simplebut e!ective way of explaining the main phenomenaoccurring in the sugar dryer. Speci"cally, the best "t withthe measured data has been obtained using the followingvalues for the tuning parameters:

h�"0.0038 (kW/m�K),

m�"4.05�10� (kg/m�s kPa).

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Table 5Input values used for parameter-tuning

Trial �1 Trial �2 Trial �3 Trial �4

Sugar temperature (3C) 55.1 53.8 55.0 55.0Sugar #ow-rate (ton/h) 40.6 39.1 50.0 31.4Sugar moisture content (%) 0.606 0.775 0.888 0.888Air temperature (3C) 27.9 20.4 22.6 22.6Air #ow-rate (ton/h) 19.2 19.3 19.5 19.5Air absolute humidity (%) 0.844 0.590 0.675 0.675

Table 6Fitting results

Trial �1 Trial �2 Trial �3 Trial �4

Estimated output sugar temperature 37.5 30.7 31.8 29.1Measured output sugar temperature (central-val.) 37.5 30.7 31.8 29.1Estimated output sugar moisture content 0 0 0.005 0Measured output sugar moist. content (central val.) 0.048 0.063 0.042 0.029

Fig. 6. (a) Sugar temperature pro"les predicted by the model. (b) Sugarmoisture content pro"les predicted by the model.

The estimation results are summarised in Table 6, where-as in Fig. 6 the corresponding temperatures and moisturecontent pro"les along the drum are depicted.

By inspecting the results above outlined, the followingremarks can be made:

� The dryer works `beyond the kneea in 3 cases out of 4.The only case of output moisture content higher than0 (`standard-modea) is Trial �3.

� The sugar in Trial �1 is, by far, the most `overdrieda,since the moisture content gets to zero just 3 m fromthe drum inlet. This fact provides a simple explanationfor the very high output sugar temperature, whichcannot be otherwise explained.

� The low temperature of the output sugar in Trial �3,despite the comparatively high input sugar temperature,air temperature, and sugar #ow rate, is explained by thefact that it is the only `non-zero-moisturea condition,thus allowing a better sugar cooling.

The `two-stagea temperature pro"le predicted by themodel is very di$cult to validate by real data. As a mat-ter of fact, it is a `spatiala pro"le (not a `timea pro"le).This implies that, in order to be validated, input/outputmeasurements are not enough: sugar samples must besimultaneously taken at di!erent positions along thedrum. Apparently, the collection of such a sample setis inherently a very di$cult task. For the Plane Creekplant only input/output data are available, and this vali-dation is not possible. However, a few simultaneous datasnapshots along the drum were taken (with an ad-hocexperiment and instruments) at the Macknade plant(experiments made in 1997 * see Bitmead et al., 1997).In Fig. 7 the temperature pro"le measured in a workingcondition where the output sugar moisture is very low(overdrying condition) is displayed. This pro"le con"rms

S.M. Savaresi et al. / Control Engineering Practice 9 (2001) 249}266 259

Fig. 7. A sugar temperature content pro"le measured at the Macknade plant, in an overdrying condition. The two main working conditions arehighlighted with two straight dashed lines.

Table 7Nominal values of the model used for local linear analysis for a modelin `overdried-modea

Nominal value

InputsSugar temperature (3C) 53.8Sugar #ow-rate (ton/h) 39.1Sugar moisture content (%) 0.825Air temperature (3C) 20.4Air #ow-rate (ton/h) 19.3Air absolute humidity (%) 0.59

OutputsSugar temperature (3C) 29.814Sugar moisture content (%) 0

ParametersHeat transfer coe$cient h

�(kW/m�K) 0.0038

Mass transfer coe$cient m�

(kg/m�s kPa) 405�10�

the two-stage behaviour predicted by the model. The twoworking stages (highlighted with two straight dashedlines in Fig. 7) are clearly separated and visible. More-over, note that the transition phase between standard andoverdried mode (occurring at about 6}7 m from the druminlet) is very short. This also con"rms that, in a simpli"edmodel for control purposes, the accurate modelling of suchan intermediate phase can be neglected.

5. Controlling the output sugar of a dryer:hints and observations

The aim of this section is to propose control strategiesto regulate the output temperature and moisture contentof a rotary drum sugar dryer. First, in Section 5.1 apreliminary qualitative discussion on the best controlactions for di!erent working conditions is proposed. Allthe possible working states of the dryer are clustered intonine di!erent operating conditions, and a control strat-egy is outlined for each of them.

In Section 5.2 an innovative regulation algorithm isproposed. Its main features are:

� it uses output sugar temperature measurements only;� it self-detects the dryer's working conditions;� it keeps the dryer working `on the edgea between

standard and overdried mode;� it is very simple.

In order to develop the control strategies presented inthe rest of this section, it is useful "rst to compute thelinear approximation of the model working in `over-dried-modea. The linear approximation of the model (1)when working in `standard-modea has been alreadyderived in Section 4.1.

In Table 7 the nominal inputs, outputs, and para-meters about which the linear model is computed arelisted. Notice that the inputs are the central values of

260 S.M. Savaresi et al. / Control Engineering Practice 9 (2001) 249}266

Fig. 8. E!ect of #1% input variations on the output sugar temperature (`standard-modea and `overdried-modea).

Trial �2, whereas the parameters are those estimated inSection 4.2.

The equations of the local linear model in `overdried-modea condition are given by:

(Sugar¹empOut-29.81)"0.7647(Sugar¹empIn-53.8)

#0.1627(SugarFlow-39.1)

!17.648(SugarMoistIn-0.825)

#0.3868(Air¹emp-20.4)

!0.2793(AirFlow-19.3)

!0.4576(AirHumid-0.59), (3a)

SugarMoistOut"0. (3b)

Obviously, for small input variations, the output sugarmoisture content remains zero.

In Fig. 8 the absolute variations of output sugartemperature to #1% input variations are displayed,both in the case of `standard-modea and `overdried-modea. The analysis of Fig. 8 suggests the followingremarks:

� The most impressive di!erence between the behaviourof the dryer in `standard-modea and in `overdried-modea is the e!ect of the input sugar moisture contenton the output sugar temperature: in `standard-modea,increasing the input sugar moisture content has littleor no e!ect on the output sugar temperature; whereas,when the dryer works in `overdried-modea, evena small increase of the input moisture content results ina remarkable reduction of the output sugar temper-ature. This is easily explained by the fact that in `over-dried-modea in the last part of the drum there is noevaporation, which is the main phenomenon helpingthe sugar cooling. The huge bene"ts of moving a drier

from `overdried-modea to `standard-modea can befully appreciated in Fig. 9. The two curves refer to thesame situation (in particular, central input values ofTrial �1 are used), the only di!erence being that theinput sugar moisture content is 0.65 in the `overdried-modea, and 1.0 in the `standard-modea. Apparently,by simply adding some water at input, the outputsugar experiences a 6.53C cooling.

� Input air humidity variation has opposite e!ects onoutput sugar temperatures in `standard-modea and in`overdried-modea: in the "rst case increasing the airhumidity results in an increase of the sugar outputtemperature, whereas in `overdried-modea thisreduces the temperature.

� The sensitivity of output sugar temperature to inputsugar temperature variations is much higher in `over-dried-modea than in `standard-modea. This is due tothe fact that, in `standard-modea, the moisture in thesugar has a sort of "ltering e!ect (the gain is about 0.4),whereas in `overdried-modea a change in sugar inputtemperature a!ects more directly the output temper-ature (the gain is about 0.8). This is true also for airtemperature variations.

5.1. Control strategies

Using the linearised models (2) and (3), whosebehaviour is graphically summarised in Fig. 8, somesimple qualitative control strategies can now be easily"gured out. It is worth observing that these basiccontrol actions could be, in principle, derived by elemen-tary mass and heat balance equations (or even by directdata inspection). The linearised models (2) and (3)(graphically condensed in Fig. 8), however, provide a verysimple, intuitive and e!ective decision tool for a humanoperator.

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Fig. 9. (a) Example of sugar temperature pro"les, in the twooperating modes: `standard-modea (thin line) and `overdried-modea(bold line). (b) Example of sugar moisture content pro"les, in the twooperating modes: `standard-modea (thin line) and `overdried-modea(bold line).

For the sake of simplicity, the working domain of thedryer was divided into nine main clusters, according tothe combination of three possible output sugar moisturecontents (`lowa, `O.K.a, or `higha) and three possibleoutput sugar temperatures (`lowa, `O.K.a, or `higha).

The control strategies suggested by the model in thesenine conditions are the following (see Table 8):Moisture content low}Temperature low: The dryer is

working `beyond the kneea. The easiest thing to do is tospray water at the drum inlet. If water is sprayed, anadditional cooling of the sugar is expected. Therefore, it ispossible to take advantage of sugar cooling by decreasingthe air #ow-rate, turning the cooler o!, or even increasingthe sugar #ow-rate.Moisture content low}Temperature O.K.: The dryer is

working `beyond the kneea. The easiest thing to do is tospray water at the drum inlet. If water is sprayed, thesugar is expected to cool down. Therefore, it is possible to

take advantage of sugar cooling by, e.g. decreasing the air#ow-rate.Moisture content low}Temperature high: The dryer is

working `beyond the kneea. The easiest thing to do is tospray water at the drum inlet. If water is sprayed, thesugar is expected to cool down. This might be enough toget the right sugar output temperature. If not, input airmust be cooled.Moisture content O.K.}Temperature low: The input vari-

ables a!ecting the sugar moisture content should be keptuntouched. If the sugar is well cooled, the possibility maybe considered of turning the cooler o! or reducing the air#ow-rate.Moisture content O.K.}Temperature O.K.: Keep un-

touched.Moisture content O.K.}Temperature high: The input

variables a!ecting the sugar moisture content should bekept untouched. Cool input air.Moisture content high}Temperature low: The best "x is

to increase input sugar temperature. If this is not enough,de-humidi"cation of input air can be considered.Moisture content high}Temperature O.K.: Increase input

sugar temperature and cool input air. If not enough,de-humidi"cation of input air can be considered.Moisture content high}Temperature high: The "rst thing

to do is to decrease input air humidity (it reduces bothtemperature and moisture content of the output sugar)and cool input air. If the moisture content is still high, butthe sugar is over-cooled, raise the input sugar temper-ature. If not enough, the only thing to do is reduce sugarinput #ow-rate.

The above scheme provides useful and non-trivialguidelines for the control of the dryer. Unfortunately, thepractical implementation of such control actions is di$-cult since it requires an accurate measurement of bothoutput sugar temperature and moisture content. Thisproblem will be addressed in the following subsection.

5.2. Keeping the dryer `on the edgea: the control scheme

As already pointed out, considerable bene"ts can beobtained by keeping the rotary sugar dryer working in`standard conditionsa. Apparently, this might be easilyobtained by spraying water at the input, according to theactual output moisture content.

The implementation of this control scheme is * how-ever * very challenging. As a matter of fact the on-lineun-manned measurement of the output sugar moisturecontent is quite a di$cult task, since an accurate moisturecontent measurement can be done only by laboratoryanalysis of sugar samples, or by means sophisticated andexpensive sensor equipment (see e.g. Rodriguez, Vasseur,& Courtois, 1996a; Toyoda et al., 1995; Toyoda, Kojima,Miyomoto, & Takeuchi, 1997). As a consequence, a controlloop using the output sugar moisture content as feedbackvariable is, at the present stage, hardly practicable.

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Table 8Control strategies

TemperatureP Low O.K. High�Moisture content

Low (`beyond the kneea) Spray water at input Spray water at input Spray water at inputDecrease air #ow-rate Decrease air #ow-rate Cool input airTurn air-cooler o!Increase sugar #ow-rate

O.K. (Turn air cooler o!) * Cool input air(Decrease air #ow-rate)

High Increase sugar temperature Increase sugar temperature& cool input air

Decrease air humidity

Decrease air humidity Decrease air humidity Cool input air (& increase sugartemperature)(Decrease sugar #ow-rate)

To overcome this problem, a simple and implemen-table control scheme is proposed, having the aim ofkeeping the sugar dryer working `on the edgea between`standard-modea and `overdried-modea. Notice that thisis a wise control goal since:

� the `edge-conditiona is as good as the `standard con-ditiona;

� the value of output moisture content is only slightlylower than the target moisture content; this sub-opti-mality can be easily overcome by spraying a tinyamount of water at the output of the dryer.

The most appealing feature of the control schemeproposed is that it just requires the measurement of theoutput sugar temperature, which is a much easier taskthan measuring the moisture content. To this purpose,the traditional probe thermometers used at CSR plants,which su!er a performance decay due to sugar stickingaround the probe, are being replaced by infra-red ther-mometers, providing a much more reliable measurement,and requiring little or no maintenance.

Before presenting the algorithm, it is worth pointingout that it provides sub-optimal tracking performance:the regulation of the output sugar moisture is comparat-ively rough, energy consumption is not minimised, andstart-up trajectories are not optimised. As such, it canhardly be compared with more sophisticated techniquesused (or proposed) for di!erent types of dryers (see e.g.Courtois, 1996 or Quirijns, van Willigenburg, van Boxtel,& van Straten, 1999 for an overview). However, hereoptimality was not the goal in designing the controller: atthe present stage robustness and simplicity are the crucialfeatures for a rotary sugar dryer regulator.

The basic idea of the control scheme proposed isto exploit fully the fact that switching from standardto overdried mode results in the change of the sign ofthe gain from input moisture content to output sugar

temperature. In other words, when the dryer isworking in over-drying conditions adding water at thedryer inlet results in a temperature decrease at theoutput, whereas when the dryer is working in `standardmodea, adding water results in a slight increase ofthe temperature.

The bulk of the control scheme proposed is depicted inFig. 10. The entire control scheme is based upon theinjection of a `impulse-likea signal (whose duration � isquite short, e.g. 3 min), which is periodically superim-posed (e.g. every ¹"30 min) to the average amount ofwater sprayed at the sugar dryer inlet (signal inFig. 10). The role of this signal is to excite the system, inorder to detect the current operating condition of thedryer, and to change the amount of sprayed water ac-cordingly.

Following clock-wise the block diagram of Fig. 10,from signal to signal (see also Fig. 11 where all thesignals involved are displayed in the time-domain), therole of each element of the control scheme can be sum-marised and explained as follows:

� Signal is the short-term response of the output sugartemperature to the water spay impulse; as a matter offact it is obtained as the di!erence between the actualoutput sugar temperature and its average (low-pass"ltered) value. According to the results depicted inFig. 8, it was expected that signal is characterised bylarge negative impulses if the dryer is working in over-dried-mode, and by small positive impulses if it isworking in standard mode.

� The multiplication between signal and the delayedsignal (producing signal ) has just the role ofensuring that signal is exactly zero outside the `im-pulse-windowa, in order to avoid feeding the integ-rator with small but quite obnoxious non-zero low-frequency signals. Notice that the delay r

, which must

S.M. Savaresi et al. / Control Engineering Practice 9 (2001) 249}266 263

Fig. 10. The control scheme.

Fig. 11. The signals involved in the control scheme (example).

equal the residence time of the sugar in the drum(about 7 min in the case of the plane creek plant) isnecessary since the e!ect of an impulse on appearson only after r

minutes.

� The non-linear static characteristic has the role ofre-balancing the size of positive and negative impulsesin (basically, it keeps unchanged the positive im-pulses, and multiplies the negative impulses by

(�¹emp�

/�Moist��

)� �����������

(�¹emp�

/�Moist��

)��������������

,

namely the absolute value of the ratio between themoisture-temperature gains of the dryer in standardand in overdried mode.

� The time delay � (which must be strictly larger than r )

is used to avoid interference between the `testing-phasea (during the impulse injection) and the `adjust-ment-phasea (after impulse injection).

� The role of the integrator is to produce a permanentadjustment to the amount of sprayed water, till thenext impulse injection. The adjustment signal issuperimposed on the constant value of sprayed water=M

��determined by the plant operator or, alterna-

tively, by some automatic supervision algorithmaccording to the average external weather conditions.

The most interesting and peculiar features of the con-trol scheme outlined above are the following:

� The `excitationa signal made up by a row of impulse-like signals allows a reliable estimation of the workingcondition of the dryer, since it is locally very strongin amplitude. However, being quite short in time,its e!ect on the average characteristics of the outputsugar is negligible, especially after mixing in thehopper. To this purpose, it is important to stressthat a `stronga excitation signal is called for, sincethe high variance of the six main input variables(temperature, #ow and humidity of input sugar and

264 S.M. Savaresi et al. / Control Engineering Practice 9 (2001) 249}266

air) of the dryer would hide the e!ects of a weakexcitation signal.

� The time-decoupling between the excitation impulse-like signal and the actual variation of the averageamount of water sprayed simpli"es the dynamic be-haviour of the regulation loop.

Needless to say, the control scheme proposed here andoutlined in Fig. 10 is only the framework of the overallcontrol algorithm used in a `real-worlda implementation.Problems like the pre-treatment of air, supervision of thiscontrol loop and its interaction with the slowly varyingcharacteristics of the sugar and air characteristics at thedryer inlet must obviously be considered.

6. Related work

The modelling and control of dryers is an issue that hasbeen extensively studied in recent years both from a the-oretical and from a practical point of view. The existingliterature on this topic can be given a "rst classi"cationaccording to the type of dryers, and to the desiccatedmaterials. Many types of dryers are used: drum dryers(Courtois & Trystram, 1994; Rodriguez et al., 1996a,Rodriguez, Vasseur, & Courtois, 1996b), cross-#owdryers (Douglas, Jones, & Mallick, 1994a}c), solar dryers(Farkas, MeH szaros, & Seres, 1998a), #uidised-bed (vanBoxtel, & Knol, 1996; Temple & van Boxtel, 2000) and"xed-bed (Farkas, Remenyi, & Biro, 1998b) dryers,mixed-#ow (Courtois, Nouafo, & Trystram, 1995)and cross-#ow (Platt, Rumsay, & Palazoglu, 1992)dryers, and rotary dryers (Douglas et al., 1993) are just themain example of existing dryers. The variety of desic-cated material is huge: maize (Courtois, Lebert,Duquenoy, Lasseran, & Bimbinet, 1991), rice (Bonazziet al., 1994; Toyoda, 1989, 1992), corn (Courtois, 1995;Courtois et al., 1995; Trelea, Trystram, & Courtois,1997), agricultural products (Toyoda et al., 1997),tea leaves (Temple & van Boxtel, 1999) are just afew examples.

An important feature that can be used to categorisethe literature is the modelling approach: black-box orxrst-principles. Traditionally, black-box approaches arerarely used in this "eld, since physical insight in themodel is important, and a large set of `gooda (stationaryand characterised by high signal-to-noise ratio) in-put/output measurements is rarely available. The black-box models typically used are standard ARMA, BJ, orOE models, if linearity is assumed (Toyoda et al., 1995),or neural-nets (or similar non-linear parametricfunctions) if non-linear phenomena must be captured(Farkas et al., 1998b,1998c; Trelea et al. 1997). Onthe other hand, traditional "rst-principles models rangefrom partial di!erential equations (sometimes replacedby lumped-parameter models obtained by spatial dis-

cretisation * see e.g. Douglas et al., 1993) to sophisti-cated stochastic models (MeH szaros, Farkas, & Balint,1999).

The control strategy used to regulate the dryer is an-other main distinctive feature. A vast selection of controlapproaches has been tested: from classical (PID-based orLQG) and recently developed (H

) techniques for linear

systems, up to `trendya non-linear control schemes (neu-ral-networks or fuzzy-logic based approaches* see e.g.Zhang & Litch"eld, 1993). A comprehensive overview ofcontrol strategies for dryers regulation is in Courtois(1996) or in Quirijns et al. (1999).

It is worth mentioning that, in dryer control problems,the issue of measuring the moisture content of the desic-cated material has always attracted a special attention.The fast, cheap and accurate measurement of moisturecontent is a formidable problem, which is still open. Thisproblem is particularly important since it typically im-poses strong limitations on the control strategies that canbe used in practice. Papers explicitly dealing with thisissue are, e.g. Rodriguez et al. (1996b), Toyoda et al.(1995, 1997).

Finally, as already pointed out, the authors wish torecall that (to the best of their knowledge), in the recentliterature there are very few works speci"cally dealingwith the problem of modelling and controlling rotarysugar dryers. The work most closely related to the pres-ent paper is Douglas et al. (1993), where a "rst-principlesmodel is proposed and validated, starting from the earlyworks by Friedman and Marshall (1949) and Thorne andKelly (1980).

7. Conclusions

In this paper the problem of "tting a set of datacollected in June 1998 in the rotary sugar dryer at CSRLtd Plane Creek by means of a recently developed grey-box model is considered.

The main results obtained here are:

� The model can accurately predict the output temper-ature if the moisture content predicted by the model isallowed to be exactly zero from one point of the drumon. This working-mode of the model has been calledthe `overdried-modea, and is characterised by peculiarbehaviour, considerably di!erent from the `standard-modea. The model's ability to predicting an `over-dried-modea is extremely useful for developing a suit-able control strategy.

� The model (both in `standard-modea and in `over-dried-modea) provides useful guidelines for developinga sound control strategy, in the main working condi-tions of the sugar dryer.

� By exploiting a special feature of the gain from inputmoisture content to output sugar temperature, a very

S.M. Savaresi et al. / Control Engineering Practice 9 (2001) 249}266 265

simple control scheme was proposed, capable of keep-ing the dryer working on the edge between standardand overdried mode, using output sugar temperaturemeasurements only.

Acknowledgements

Research supported by USA National Science Foun-dation Grant ECS-0070146, and by CARIPLO Founda-tion for Scienti"c Research.

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