2008Dynamic Modeling and Feedback Control for Conveyors-belt Dryers

www.elsevier.com/locate/jfoodeng

Journal of Food Engineering 84 (2008) 458–468

Dynamic modeling and feedback control for conveyors-belt dryersof mate leaves

E.F. Zanoelo *, A. Abitante, L.A.C. Meleiro

Federal University of Parana, Department of Chemical Engineering, Polytechnic Center, Jardim das Americas, Curitiba-PR, CEP: 81530-900, Brazil

Received 22 February 2007; received in revised form 22 May 2007; accepted 2 June 2007Available online 30 June 2007

Abstract

A semi-empirical model is proposed to reproduce the kinetics of drying in a continuous shallow packed bed dryer of mate leaves attransient conditions. The mathematical expression representing the dynamic model, which was obtained from a mass balance for water inthe solid phase of the drying chamber, was validated at steady-state condition in an industrial continuous dryer. The transient model wassolved with the numerical method of lines by involving a backward differentiation formula (BDF) to approximate the first order spatialand time derivative. Based upon this reliable model, a control strategy was suggested to maintain the discharge moisture content in theacceptable range of 2.4–3.4% (dry basis) by adjusting the velocity of conveyor-belt to compensate disturbances in the operating condi-tions. The performance of a proportional-integral-derivative (PID) and a proportional-integral (PI) controller was verified by a compar-ison between open- and closed-loop responses of discharge moisture content to random changes in the feed moisture content, dryingtemperature and air velocity. The simplex method was applied during the tuning procedure of the controller parameters by minimizingthe integral squared error (ISE) of the process output when a step change in the set-point was imposed.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Conveyor-belt; Drying; Mate leaves; Control; Experimental; Model

1. Introduction

Leaves of mate (Ilex paraguariensis) are dried on com-mercial scale in South America because from their extractsis produced a very appreciated non-alcoholic beveragequite similar in taste and color to the black and green teaobtained by the infusion of dry shoots from the Camellia

sinensis bush (Kawakami & Kobayashi, 1991; Zanoelo,2005). Although the overall production of dry mate is esti-mated in 300 thousands tonnes per year (Goldenberg, 2002;Kawakami & Kobayashi, 1991), it represents approxi-mately only 11% of black and green tea produced roundthe world (International Tea Council, 1997). A more equil-ibrated competition between these products in the interna-tional scenario requires the reduction of manufacturingcosts and the standardization of dry mate quality.

0260-8774/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jfoodeng.2007.06.008

* Corresponding author. Tel.: +55 41 3361 3202; fax: +55 41 3361 3674.E-mail address: [email protected] (E.F. Zanoelo).

Although these technological aspects are strongly con-nected to the control of moisture content in the dischargeof industrial dryers, experimental results for this parameterpresented in this investigation shown that it is rarely con-trolled in the often used conveyors-belt dryer of mateleaves.

The main aim of this investigation is to propose a strat-egy of feedback control of moisture content of mate leavesby adjusting the speed of the conveyor-belt to give the nec-essary residence time to maintain the discharge moisturecontent in the acceptable range of 2.4–3.4% (dry basis).A schematic of the drying plant of mate leaves involvedin this investigation is illustrated in Fig. 1. In essence, athin-layer of mate leaves to be dried is spread on one endof a moving metal screen (conveyor-belt) and is slowly car-ried through a drying chamber up to the discharge on theother. As properly indicated in Fig. 1, the entire designof the control system is based upon instantaneous measure-ments of discharge moisture content. A dynamic model

mailto:[email protected]

Nomenclature

a ratio between the total surface area of masstransfer and bed volume (m2 m�3)

ds equivalent particle diameter (m)G air mass velocity (kg m�2 s�1)ISE integral squared errork mass transfer coefficient (kg m�2 s�1)km modified mass transfer coefficient defined by Eq.

(2) (s�1)L length of the conveyor-belt (m)M moisture content of mate leaves (kg water kg�1

dry matter)Me equilibrium moisture content of mate (kg water

kg�1 dry matter)

Mi inlet moisture content (kg water kg�1 dry mat-ter)

Rh relative humidity (decimal)t drying time (s)Tg average air temperature (�C)uc speed of the conveyor-belt (m s�1)ug superficial air velocity (m s�1)x axial position along the conveyor-belt dryer (m)e bed porositye(t) deviation between set-point and realized value

of moisture content in the discharge of the dryerqs density of dry leaves of mate (kg m�3)

E.F. Zanoelo et al. / Journal of Food Engineering 84 (2008) 458–468 459

representing a mass balance for water in the solid phase ofdrying chamber is proposed to obtain reliable parametersof the PI and PID controllers that could be effectivelyapplied in real industrial plants. The reliability of the modelis verified by comparison between experimental dryingcurves at steady-state conditions in a continuous industrialdryer of mate leaves. A comparison between open- andclosed-loop responses of the process output submitted torandom changes in feed moisture content between 0.22and 0.44 (d.b.), drying temperature from 98 to 110 �Cand air velocity in the range from 0.05 to 0.37 m s�1 wascarried out in order to check the performance of the PIDand PI controllers.

Instantaneous methods for moisture content measure-ment in mate leaves, whose availability is fundamental topropose this automatic control strategy for conveyor-beltdryers, based on direct moisture measurements of thisproduct, has never been used in real-scale drying plants.However different techniques, which have been successfullytested in different solid food products (Hall, Robertson, &Scotter, 1988; Mizukami, Sawai, & Yamaguchi, 2006;Rywotycki, 2003; Temple, 2000), support the viability ofthe current investigation. Among these available prompt

hot air

feed thin bed

motor to manipulate the speed of the conveyor

PI controller

Fig. 1. Schematic of the dry

procedures, electrical spectroscopy (Mizukami et al.,2006) and near infrared reflectance (Temple, 2000) have agreat potential for on-line applications and were success-fully tested for moisture content readings in tea shoots.The resemblances between C. sinensis and I. paraguariensis

in terms of thermo-physical properties and chemical con-stituents encourage the application of these methods inmate leaves.

2. Materials and methods

2.1. Experimental moisture content measurements

A preliminary experimental data set of moisture contentin the discharge of thirteen continuous industrial dryers ofmate leaves, which are installed in different small and med-ium industries located in the south of Brazil, was obtainedto confirm or reject the need of improving the control ofthis parameter. Despite the differences among these indus-tries, a first stage of enzymatic deactivation at 300–350 �C,where mate leaves are fed with a moisture content ofapproximately 60 ± 5% (wet basis), was always observedin the manufacturing processes. These high temperatures

hot air

moisture content sensor

discharge

of mate leaves

dryingchamber

ing plant of mate leaves.

460 E.F. Zanoelo et al. / Journal of Food Engineering 84 (2008) 458–468

reduce enzyme activity responsible for biochemical reac-tions that may change the taste and flavor of mate liquors,as well as the color of leaves from green to brown.Although a reduction of moisture content up to approxi-mately 25 ± 10% (wet basis) was observed during this oper-ation, a further decrease of this parameter is still expectedsince all the thirteen investigated industries are alsoequipped with either a rotary or a conveyor-belt dryer. Inorder to determine the moisture content of mate leaves inthe discharge of these industrial equipments by conven-tional gravimetry (International Standards Organization,1980), samples of mate leaves were manually removed fromthe bed and placed inside an oven at a controlled tempera-ture of 105 �C for about 24 h. A total of 21–24 measure-ments were performed for each factory during a testperiod of approximately 4–8 h.

Experimental drying curves at different operating condi-tions were obtained in a laboratory tray dryer in order toidentify an empirical correlation for the effective masstransfer coefficient from the literature (Panchariya, Popo-vic, & Sharma, 2002; Temple & van Boxtel, 1999a; Zano-elo, in press; Zanoelo, Di Celso, & Kaskantzis, 2007)able to better reproduce transport of water from the leaves.In particular, a constant mass of mate leaves of approxi-mately 20.4 ± 0.3 g with initial moisture content of51 ± 10% (w.b.) and equivalent particle diameters of0.042 m were distributed over a perforated metallic trayto have a shallow bed of particulates no higher than30 mm. Heated air was pumped into the drying chamberat constant flow velocity of about 0.156 m s�1 and at threedifferent temperatures in the range of 60–90 �C by 15 �Cstep, respectively. The internal temperature was monitoredby a K-type thermocouple, while air velocity was measuredwith a calibrated hot wire anemometer. A psychrometricchart and simultaneous measurements of wet-bulb anddry-bulb temperatures at ambient conditions were used tofound a value of humidity equal to 0.0128 g of water pergram of dry air. Surface temperature of mate leaves duringdrying was monitored by using a calibrated infrared ther-mometer. Loss in mass was determined off-line by register-ing periodical weight measurements of the tray with anelectronic balance located outside the chamber. Despitethe error introduced by removing the sample tray fromthe drying chamber for weighing, this procedure is consid-ered sufficiently rapid to assure the reproducibility of thedrying curves (Panchariya et al., 2002). Perfect replicationof the experimental runs was not possible as drying pro-ceeded with slight different initial moisture content. How-ever, except for this variable, four replications werecarried out at identical temperatures and air velocity.

Axial profiles of moisture content of mate leaves along acontinuous commercial conveyor-belt dryer were obtainedat quasi steady-state conditions to verify the reliability ofthe proposed mathematical model at real-scale dryingplants. This equipment consists of two conveyors 30 mlong and 4.5 m wide, stacked arranged and made up of per-forated metal trays attached to roller chains on either side.

Although the speed of the conveyors may be manuallyadjusted to obtain an empirical control of the drying pro-cess, both the top and bottom trays were moving at a con-stant velocity of 0.004 m s�1. Wet leaves with a moisturecontent of approximately 0.33 ± 0.11 in dry basis werefed into the top moving tray to form an even layer of solidsheated with air at 59 ± 4 �C. After the upper stage, theleaves of mate drop on to the bottom level where externalair passes upward at 104 ± 6 �C. A set of more than onehundred anemometer readings were involved to determinean average value of air velocity equal to approximately0.21 m s�1, while the calculated standard deviation of thismean was ±0.16 m s�1. These operating conditions repre-sent arithmetic means of results obtained on two differentvisits to the same factory. To assure the reliability of mois-ture content data fifteen and three samples of mate leaveswere removed from each different axial position along thedryer in the first and second visit, respectively. A conven-tional gravimetric method (International Standards Orga-nization, 1980) involving an oven maintained at aconstant temperature of 105 �C and a digital balance witha precision of 10�4 g was used to determine the moisturecontent of these samples.

2.2. Mathematical modeling

Several semi-empirical models have been proposed toreproduce the drying kinetics of tea shoots (Panchariyaet al., 2002; Temple & van Boxtel, 1999a) and mate leaves(Zanoelo, in press; Zanoelo et al., 2007) in packed and fluid-ized bed dryers. All of these expressions are represented byordinary differential equations that accounts only for timederivatives, while models to simulate the transient behaviorin conveyors-belt dryers are typically described by partialdifferential equations that involves both spatial and timederivatives. However, the great contribution of these inves-tigations for the dynamic drying modeling is the availabilityof reliable effective mass transfer coefficients that takes intoaccount both the internal and external resistances for watertransport from the solid to the fluid phase. Even if all thesecoefficients reported in the literature (Panchariya et al.,2002; Temple & van Boxtel, 1999a; Zanoelo, in press; Zano-elo et al., 2007) were in the same magnitude, they will bechecked in order to select the coefficient that most properlydescribes the experimental behavior at different operatingconditions in a laboratory tray dryer.

In the current investigation a mass balance for water in astationary infinitesimal volume element of the solid phaseover the conveyor leads to a transient one-dimensional firstorder partial differential equation. The volume element,which is a porous medium, involves a fluid and a solidphase, represented by the drying medium and a mixtureof liquid water and dry matter, respectively. In the currentmodeling approach the solute enters or leaves the systemby means of the overall motion of the tray that supportsthe shallow packed bed, as well as by simultaneous internaldiffusion of liquid water from the bulk to the material


surface and external convection (Zanoelo, in press). Thesephenomenological aspects are described by the first andsecond terms on the right side of Eq. (1), respectively.

oMot¼ �uc

oMox� kað1� eÞqs

ðM �M eÞ ð1Þ

The proposed drying model includes important simplifi-cations: (i) mass transfer is a combination of simultaneousinternal and external finite resistances; (ii) moisture contentgradients and changes in air properties along the bed layerwere neglected as usually accepted for thin-layer drying;(iii) shrinkage effects on drying rates were excluded; (iv)instantaneous thermal equilibrium between mate leavesand surrounding air is achieved, which means that heattransfer is neglected. This latter assumption is supportedby transient profiles of temperature for the leaves of mateduring drying, which will be presented in the next sectionof this manuscript (see Fig. 4).

An important point to be noticed for modeling solutionis that the semi-empirical drying model of Lewis (Tang,Cenkowski, & Izydorczyk, 2005; Wiriyaumpaiwong,Soponronnarit, & Prachayawarakorn, 2004; Zanoelo,Cardozo-Filho, & Cardozo-Junior, 2006) expresses a spe-cial case of the mass balance when moisture content is con-stant with respect to the axial position. As a consequence,the entire term that multiplies the difference between mate-rial and equilibrium moisture content is the drying con-stant that appears in the Lewis model. This parameter(km) is referred to as an effective or apparent coefficientbecause it represents a certain combination of internaland superficial barrier to mass transfer.

km ¼ka

ð1� eÞqs

ð2Þ

The great contribution of this approach is that the dry-ing constant of the Lewis model was previously determinedfor mate leaves in packed bed (Eq. (3)) and fluidized batchdryers (Eq. (4)), as well as for tea shoots in thin-layer dry-ers (Eqs. (5) and (6)). All the model parameters involved inthe empirical expressions for the drying constant weretuned on experimental drying curves obtained at differentoperating conditions which are summarized in Table 1.

km ¼ 3:6� 10�5T g � 4:344� 10�3G

þ 9:03� 10�5T gG� 1:746� 10�3 ð3Þkm ¼ 1:56� 10�4T g � 7:507� 10�3 ð4Þkm ¼ 2:8� 10�4ugðT g � 45Þ � 6:7� 10�4 ð5Þkm ¼ 1� 10�6ðT gÞ2:08u1:11

g ð6Þ

Table 1Operating conditions in the tuning procedure of the empirical equations for t

Eq. ug (m s�1) Tg (�C)

(3) 0.082–1.12 50–103(4) 0.6–1.0 50–100(5) 0.048–0.63 50–150(6) 0.25–0.65 80–120

The equilibrium moisture content of mate leaves is esti-mated through an empirical correlation previouslyreported in the literature (Zanoelo, 2005). Eq. (7) is basedon the modified model of Halsey (Osborn, White, Sulai-man, & Walton, 1989), which accounts for the influenceof temperature and relative humidity of air.

M e

1þM e

¼ 10�2 � expð�5:7� 10�3T g þ 3:02ÞlnðRhÞ

� �0:662

ð7Þ

The inlet dryer and the initial moisture content of mateleaves are only the two boundary conditions required toevaluate the constants of integration emerged when theEq. (1) is integrated.

The unsteady-state one-dimensional drying model wassolved with the numerical method of lines by involving abackward differentiation formula (BDF) to approximatethe first order spatial and time derivatives. A computa-tional routine for a rapid solution of this partial differentialequation, which was based on this numerical technique,was written in FORTRAN.

2.3. Controller design

Presented the transient drying model and the mathemat-ical procedure to solve it, the subsequent step is to design acontrol system to maintain the discharge moisture contentwithin a certain set-point range despite load disturbances.In particular, dynamic variations in the feed moisture con-tent, drying temperature and air velocity were considered.Moisture content in the discharge of the continuous dryeris controlled by manipulation of the speed of the movingtray to give the mate leaves the necessary residence timeto maintain that variable inside the desired set-point. Themanipulative variable was constrained between 0.0 and0.1 m s�1. A closed-loop diagram of the drying process issketched in Fig. 2.

A proportional-integral-derivative (PID) controller thatis almost exclusively used for controlling of variable-speeddrives used in conveyors (Barton & Lewin, 2000), and aproportional-integral (PI) controller were tested theoreti-cally in the current investigation. As already observed ina similar work available in the literature (Temple, van Stra-ten, & van Boxtel, 2000) for the control of tea dryers, pre-liminary controller tuning determined by the Cohen andCoon and Ziegler–Nichols (Stephanopoulos, 1984) meth-ods was not found to be robust over the range of condi-tions checked. Therefore, PID and PI parameters(proportional gain, integral and derivative times) weretuned on target moisture content by applying the simplex

he drying constant of the Lewis model

ds (m) Reference

0.03 Zanoelo et al. (2007)5.2 � 10�3–1.1 � 10�2 Zanoelo (in press)5 � 10�4 Temple and van Boxtel (1999a)5 � 10�4 Panchariya et al. (2002)

+_ Controller (PI-PID)

Final ControlElement

(Eletric Motor)

ManipulatedVariable

uc

Process(Conveyor-Belt Dryer)

ControlledVariable

M

Sensor(Measurementof Moisture

Content)

Set Point

MSP Error Signal

ug Tg Mi

Disturbances

Fig. 2. Closed-loop diagram of the drying process.

1 2 3 4 5 6 7 8 9 10 11 12 13Industry

0

2

4

6

8

10

Moi

stur

e co

nten

t of m

ate

leav

esin

the

disc

harg

e of

dry

ers

(% w

.b.)

Fig. 3. Moisture content in the discharge of thirteen continuous industrialrotary or conveyor-belt dryers of mate leaves.


method of optimization to minimize the integral squarederror (ISE).

ISE ¼Z 1

0

½eðtÞ�2 dt ð8Þ

where e(t) represents the deviation between set-point andrealized value of moisture content in the discharge of thedryer.

During the tuning procedure the drying simulationstarts with an empty bed. Then, leaves of mate with a mois-ture content of 0.33 in dry basis are continuously fed on asingle conveyor-belt dryer 10 m long, where find hot airentering the moving bed at 104 �C and 0.26 m s�1. At thisinitial steady-state condition the speed of the tray isadjusted at 0.1 m s�1 to give the leaves a residence timeof only 100 s and steady moisture content in the dischargeof approximately 0.25 (d.b.). Once the dryer has stabilized,a step decrease of 88% in set-point is imposed at 100 selapsed time.

A comparison between open- and closed-loop responsesof discharge moisture content to random changes in all thethree perturbation variables in terms of magnitude andtime frequency was carried out to verify the performanceof the PID and PI controllers.

3. Results and discussion

3.1. Control of moisture content in the discharge of industrial

dryers

In the absence of a Brazilian legislation in terms of thecommercial limits for the moisture content of mate leaves(ANVISA, 2005) and considering that the acceptable upperlimit for packed dry leaves of mate in Argentine (9.5%) isnot enough restrictive (INYM, 2002), limits for tea (C. sin-

ensis) were followed (Temple & van Boxtel, 2000). In par-ticular, based on technical criteria a range of 2.5–3.5%(w.b.) is stated for dryer output moistures of tea shoots.According to the literature (Temple & van Boxtel, 2000)an acceptable range well below the maximum moisturecontent allowed for packed teas (7% w.b.) was definedbecause during the sorting and packing stages water

adsorption may elevate the moisture from 3% to well overthe acceptable level of 7%. As equilibrium moisture contentfor tea shoots and mate leaves at ambient temperatures arevery similar, a comparable amount of adsorbed water isexpected for both these material.

Fig. 3 presents experimental results of moisture contentin the discharge of different industrial dryers of mateleaves. According to averaged readings, only the factories5 and 8 produce leaves of mate within the range of outputdryer moisture of 2.5–3.5% (w.b.), while all the others havea final product that well exceed the upper limit justdeclared. A still more negative scenario is observed whenthe standard deviation of the mean involving several mea-surements of this parameter for a period of 4–8 h is takeninto account. In this case, only the company 5 is able toproduce dry leaves of mate in accordance with the levelexpected for moisture content in the discharge.


Two major negative technological aspects may bepromptly revealed when the moisture content in the dis-charge of commercial dryers is not controlled, as reportedin Fig. 3. The first great disadvantage, which is not evi-denced in this investigation, is the unnecessary consumeof energy caused by occasional and recurrent reductionof moisture content beyond its lower limit. On other hand,the insufficient water removal almost exclusively observedin Fig. 3 avoids complete enzyme inactivation and productstabilization in storage, which could result in an excessiveconcentration of oxidized phenolic compounds such as tan-nins, which are chemical species associated with browncolor and bitter taste of mate liquor (Cheftel & Cheftel,1992). Despite the comparable gravity of both these prob-lems, their impacts on the value of the final product aredrastically different and may explain the non-conservativeresults shown in Fig. 3. An excessive dehydration ispromptly felt in the manufacturing costs because it imme-diately increases the energy consumption, while an insuffi-cient removal of water from the leaves has a negative effecton the quality, whose control is a long-term benefit. Insummary, in the absence of either a restrictive national leg-islation in terms of moisture content for packed mateleaves or a quality management system such as the ISO9000 series to be attended, mate manufacturers prefer tominimize energy use on drying than to improve qualityand to have high added value products.

3.2. Effective mass transfer coefficient and model validation

As already mentioned, different empirical equations forthe effective mass transfer coefficient were coupled to thedrying model to simulate the loss in mass during dehydra-tion of mate leaves in a laboratory tray dryer at 60, 75 and90 �C. The reliability of these expressions was verified by acomparison between experimental and calculated dryingcurves. In particular, the coefficient of correlation (R2)and the mean square error (MSE) were calculated byinvolving Eqs. (3)–(6) and are reported in Table 2. An anal-ysis based on the highest values of R2 and the lowest valuesof MSE elects the coefficients from Eq. (6) to reproduce theoverall resistance of mass transfer from the leaves of mateto drying medium in the operating conditions here investi-gated. In fact, a good agreement between experimental andcalculated results in plots of moisture content of mateleaves against time is visually confirmed in Fig. 4, when thisexpression is involved. The increase of the residual devia-tion, which is observed when the drying temperature is

Table 2Correlation coefficient (R2) and mean square error (MSE) of the empirical eq

Air temperature (�C) Eq. 3 Eq. 4

R2 MSE R2 M

60 0.924 0.007 0.142 075 0.815 0.023 0.073 090 0.859 0.020 0.275 0

reduced, is mainly attributed to the use of temperaturesfar from the range (80–120 �C) within the consistency ofEq. (6) was previously checked (Panchariya et al., 2002).Standard deviations for the experimental moisture contentdata were not presented because of insignificant differenceswere found for four replicates.

Although a detailed discussion on phenomenologicalaspects of mass transfer is not the primary objective of thisinvestigation, it is relevant to explain how the reliability ofEq. (6) that was tuned on experimental drying curves fortea (C. sinensis) shoots is preserved on drying of mateleaves, despite the differences between the particles in termsof size and composition. This is likely attributed to the factthat both these sets of experiments were carried out in thin-layer dryers, at analogous conditions of convective masstransfer. As a consequence, even if drying of mate is notexclusively governed by convection (Zanoelo, in press)but a combination of this phenomenon and diffusion, itsreasonable to infer that either the diffusivities of water inthese different dry matter are similar, or the effect of a pos-sible difference on the effective mass transfer coefficient thattakes into account both diffusion and convection isnegligible.

Despite the consistence of Eq. (6), the current operatingconditions are much closer to the range of temperature andair velocity applied to obtain the empirical parameters ofEq. (5) (see Table 1). Since these data were also tuned onexperimental drying curves in thin-layer dryers, Eq. (5)should reproduce the current drying curves more accu-rately than Eq. (6). Even though this occurs at 75 and90 �C, as deduced from Table 2, an unexpected negativevalue of km at 60 �C makes the use of Eq. (5) impracticableat the current conditions. As several replicates were per-formed to obtain the drying constants of the Lewis modelin the investigation proposed by Temple and van Boxtel(1999a), this negative value of km is credited to a possiblemistake in the tuning procedure. In fact, when the straightline that should represents Eq. (5) was plotted in a km ver-sus [ug(Tg � 45)] diagram in the original paper written byTemple and van Boxtel (1999a), a positive intercept isnoticed, while the same model parameter is negative inEq. (5).

Eq. (3) is able to describe more than 80% of the moisturecontent variation due to changes in drying time. However,a better result was not achieved probably due to small dif-ferences in the particle size or in bed heights between thisinvestigation and the study proposed by Zanoelo et al.(2007). Although this is not a conclusive explanation, it is

uations for the drying constant of the Lewis model

Eq. 5 Eq. 6

SE R2 MSE R2 MSE

.079 Negative Negative 0.903 0.009

.115 0.922 0.010 0.937 0.008

.104 0.984 0.002 0.969 0.004

0 1000 2000 3000Time (s)

0

0.4

0.8

1.2

1.6

M (

d.b.

)

0 2000 4000Time (s)

0

0.4

0.8

1.2

1.6

M (

d.b.

)

0 2000 4000 6000Time (s)

0

0.4

0.8

1.2

1.6

M (

d.b.

)

(a1) (b1) (c1)

0 200 400 600Time (s)

0

20

40

60

80

100

T (

ο C)

0 400Time (s)

0

20

40

60

80

100

T (

ο C)

0 200 400 600Time (s)

0

20

40

60

80

100

T (

ο C)

(a2) (b2) (c2)

Fig. 4. Experimental (symbols) and calculated (lines) drying curves, as well as experimental temperature profiles of mate leaves (symbols), at 90 �C (a),75 �C (b) and 60 �C (c) in a laboratory tray dryer (ug = 0.156 m s�1 and absolute humidity is 0.0128 kg water kg�1 dry air). Effective mass transfercoefficient calculated by Panchariya et al. (2002).


correct to state that the conditions of internal and externalmass and heat transfer are certainly different when theseexperimental systems are compared. With respect to Eq.(4), which has presented the lowest correlation coefficient

0 10 20 30

0 10 20 30

0

0.2

0.4

0.6

M (

d.b.

)

0

0.1

0.2

0.3

M (

d.b.

)

(a1) Axial position (m)

(b1) Axial position (m)

1st visit - top tray

1st visit - bottom tray

Fig. 5. A comparison between experimental (symbols) and calculated (lines) axdryer of mate leaves.

and the highest mean square error, no surprise is foundsince it was based on experiments performed under appro-priate conditions of fluidization while the present experi-mental system involves drying in packed thin beds. As a

0

0.02

0.04

0.06

0.08

0.1

M (

d.b.

)

0

0.1

0.2

0.3

0.4

M (

d.b.

)

0 10 20 30

0 10 20 30(a2) Axial position (m)

(b2) Axial position (m)

2nd visit - top tray

2nd visit - botton tray

ial profiles of moisture content along a two-stage industrial conveyor-belt


consequence, the high heat and mass transfer rates typi-cally found when the particles are fluidized are not foundin the present investigation and Eq. (4) overestimates therates of drying. All the drying curves calculated by usingEq. (4) are well below the experimental results reportedin Fig. 4. A detailed analysis concerning the different per-formances of thin-layer and fluidized bed drying is pre-sented by Kunii and Levenspiel (1991) and summarizedby Temple and van Boxtel (1999b) for the case of blacktea dehydration.

In order to supports the modeling hypothesis of instan-taneous thermal equilibrium between samples of mateleaves and drying medium, the surface temperature of theparticles inside the drying chamber were monitored withan infrared thermometer. Thickness of samples(ffi4 � 10�4 m) was assumed enough thin to neglect theexistence of internal gradients of temperature. Fig. 4reveals that it takes only approximately 2 min to observean increase of temperature of mate leaves up to the temper-ature of drying medium.

0 1000

0 1000

0 1000

Ti

96

100

104

108

112

Tg

(°C

)

Ti

0

0.1

0.2

0.3

0.4

u g (

m/s

)

Ti

0.2

0.25

0.3

0.35

0.4

0.45

Mi (

d.b.

)

a

b

c

Fig. 6. Random disturbances

As already explained, some additional moisture contentdata were required to validate the drying model in a contin-uous conveyor-belt dryer of mate leaves operating on acommercial scale. Obviously, these moisture content mea-surements were taken on a condition totally independentof the runs used to elect the Eq. (6) as the best amongthe empirical model for the effective mass transfer coeffi-cient. Each stage in the continuous dryer was individuallysimulated because of different temperatures are found inthese conveyors. The good fit of the calculated values tothe actual measurements shown in Fig. 5 evidences thatEq. (1) is suitable for reproducing the drying kinetics ofmate leaves on real-size scale. It is worth mentioning thatthese predicted results were obtained by employing the val-ues of km from Eq. (6). In spite of the large number of read-ings at a fixed position, the high uncertainty of the meanmoisture content values represented by the sample stan-dard deviations is a consequence of a pseudo-stationarycondition, where high random time fluctuations in dryingoperating variables are evidenced. Despite the importance

2000 3000 4000

2000 3000 4000

2000 3000 4000

me (s)

me (s)

me (s)

in operating conditions.


of temperature on the effective coefficient of mass transfer,the low amplitude of change in this factor of no more than±7% (59 ± 4 �C) reduces its effect on moisture content var-iation. As a consequence, the main responsible for thisbehavior is the influence of air velocity and inlet dryermoisture content on drying rate (km), whose time varia-tions are in the order of ±75% (0.21 ± 0.16 m s�1) and of33% (0.33 ± 0.11 d.b.), respectively. Flow turbulence inthe bed dryer is the cause of the very high amplitude ofchange in air velocity, while the disturbances in the inletdryer moisture content are credited to the uncontrolledway in which the stage of enzymatic deactivation that pre-cedes drying is carried out. However, for the current pur-pose it is important to observe that increasing theresidence time in the conveyor-belt dryer reduces the sam-ple standard deviations presented in Fig. 5. This is a rele-

Ti

0

0.1

0.2

0.3

0.4

M (

d.b.

)

0 1000

0 1000 2

Ti

0

0.04

0.08

0.12

u c (

m/s

)

s

closed-loop

open-loopb

a

Fig. 7. Feedback control of moisture content in the discharge of a conveyoconditions reported in Fig. 6. (a) manipulative variable in the closed-loop sys

0 0.2 0.4

0

0.1

0.2

0.3

M (

d.b.

)

t=3600 s

Fig. 8. Axial profile of moisture content along the con

vant aspect since the main aim of this investigation is thecontrol of moisture content in the discharge of continuousindustrial dryers, where the model reproduces correctly theexperimental results.

3.3. Controller performance

The sum of the squared deviations between actual set-point (0.03 d.b.) and transient responses of discharge mois-ture content to a step change in the set-point from 0.25 to0.03 in dry basis was minimized by involving an uncon-strained optimization method (simplex) (Jenson & Jeffreys,1994). A set of PI and PID parameters in which the processcontrol is stable was obtained by involving this procedureof tuning. In particular, for both the cases the process gain

me (s)

2000 3000 4000

000 3000 4000

me (s)

et-point

r-belt dryer of mate leaves affected by random variations of operatingtem; (b) open and closed-loop responses of discharge moisture content.

0.6 0.8 1x/L

veyor-belt dryer after 3600 s of drying operation.


and integral time were 1.16 and 761 s, respectively, whilethe derivative time for PID controller was 0.2 s.

The performance of the tuned PID and PI controllerswere evaluated over a range of operating conditions char-acterized by random variations in the main process distur-bances according to Fig. 6. Due to the small value of thederivative time, identical closed-loop responses of moisturecontent is shown in Fig. 7b by involving a PID and a PIcontroller. In essence, this means that the derivative actionis not necessary and a proportional-integral controller (PI)is suitable to control the moisture content in conveyor-beltdryers of mate leaves.

Fig. 7a shows the control actions related to the closed-loop simulations. The results shown in Fig. 7b evidence atight control of discharge moisture content in the rangeof 2.4–3.4% (d.b.), while in the uncontrolled situationmoisture content fluctuates between about 0.19 and 0.32(d.b.) for the same disturbances, which are unacceptablevalues. None value of moisture content is measured up to100 s because of the dryer starts operation with an emptybed and this is the residence time that wet leaves will taketo emerges from a tray 10 m long which is moving at0.1 m s�1. Since in this period the PI controller is notapplied because of moisture content in the discharge isnot sensed, a constant value of the manipulative variableis noticed. After 100 s the conveyor-belt is completelyloaded and the moving tray is stopped to reduce the dis-charge moisture content to the set-point. When the mois-ture content is close to approximately 3% (d.b.), thespeed of the conveyor is increased to allow a continuousdrying of mate leaves. From this point, the manipulativevariable is automatically adjusted to compensate load dis-turbances in air temperature and velocity, as well as in inletmoisture content. Fig. 8 reports axial profiles of moisturecontent of mate leaves along the conveyor-belt. Fluctua-tions in the exponential drying curve are attributed to thedifferent operating conditions along the dryer between3500 and 3600 s. Despite this strange fluctuating behaviorthe target value of 3% (d.b.) is obtained in the dischargeof the dryer.

4. Conclusion

A dynamic drying model represented by a first orderpartial differential equation was obtained from a water bal-ance in the solid phase of a conveyor belt-dryer. A back-ward differentiation formula (BDF) was applied toapproximate the first order spatial and time derivativeand the numerical method of lines was involved to solvethe mathematical model numerically. Four different empir-ical equations for the effective coefficient of mass transferwere checked in order to reproduce experimental dryingcurves of mate leaves in a laboratory tray dryer at four dif-ferent temperatures. The empirical expression proposed byPanchariya et al. (2002) in terms of air velocity and temper-

ature was elected to reproduce the overall resistance ofwater transfer from the mate leaves to the drying medium.The reliability of the current drying model and the effectivemass transfer coefficient represented by the constant of theLewis model was validated by comparison between exper-imental and calculated results of moisture content in a con-veyor-belt dryer operating at typical industrial conditions.PID and PI controllers were proposed to maintain the dis-charge moisture content in the acceptable range of 2.4–3.4% (dry basis) by adjusting the velocity of the movingtray in order to compensate disturbances in the operatingconditions. In particular, time variations in the feed mois-ture content, drying temperature and air velocity were con-sidered responsible for driving the process away from thesteady-state condition. The derivative action of the PIDcontroller was revealed insignificant and a comparisonbetween open- and closed-loop responses of dischargemoisture content evidences that a proportional-integralcontroller (PI) is suitable to control the moisture contentin conveyor-belt dryers of mate leaves.

References

ANVISA-National Health Surveillance Agency. (2005). Technical regula-tions for coffee, barley, tea, mate and soluble products. RDC 277,Brasilia, Brazil.

Barton, A. D., & Lewin, P. L. (2000). Experimental comparison of theperformance of different chain conveyor controllers. Journal of

Systems and Control Engineering, 214(I5), 361–369.Cheftel, J. C., & Cheftel, H. (1992). Introduccion a la Bioquimica y

Tecnologia de Los Alimentos (Vol. 1). Zaragoza, Spain: Acribia Ed..Goldenberg, D. (2002). Mate: a risk factor for oral and oropharyngeal

cancer. Oral Oncology, 38(4), 646–649.Hall, M. N., Robertson, A., & Scotter, C. N. G. (1988). Near-infrared

reflectance prediction of quality, theaflavin content and moisturecontent of black tea. Food Chemistry, 27, 61–75.

International Standards Organization. (1980). Tea-determination of lossin mass at 103 �C. ISO Standard 1573, Geneva, Switzerland.

International Tea Council. (1997). Annual Bulletin of Statistics, London,England.

INYM-National Institute of Yerba Mate. (2002). Regulations for dryingof mate, Resolucion 49, Posadas, Argentine.

Jenson, V. G., & Jeffreys, G. V. (1994). Mathematical methods in chemical

engineering (2nd ed.). Academic Press.Kawakami, M., & Kobayashi, A. (1991). Volatile constituents of green

mate and roasted mate. Journal of Agricultural and Food Chemistry, 39,1275–1279.

Kunii, B., & Levenspiel, O. (1991). Fluidization engineering. Boston, M.A.,USA: Butterworth-Heinemann.

Mizukami, Y., Sawai, Y., & Yamaguchi, Y. (2006). Moisture contentmeasurements of tea leaves by electrical impedance and capacitance.Biosystems Engineering, 93(3), 293–299.

Osborn, G. S., White, G. M., Sulaiman, A. H., & Walton, L. R. (1989).Predicting equilibrium moisture proportions of soybeans. Transactions

of the ASAE, 32(6), 2109–2113.Panchariya, P. C., Popovic, D., & Sharma, A. L. (2002). Thin-layer

modelling of black tea drying process. Journal of Food Engineering, 52,349–357.

Rywotycki, R. (2003). Electric sensor for prompt measurement ofmoisture content in solid food products. Journal of Food Process

Engineering, 25, 473–483.Stephanopoulos, G. (1984). Chemical process control. Englewood Cliffs,

N.J., USA: Prentice Hall.


Tang, Z., Cenkowski, S., & Izydorczyk, M. (2005). Thin-layer drying ofspent grains in superheated steam. Journal of Food Engineering, 67,457–465.

Temple, S. J. (2000). Control of fluidized bed tea drying. Netherlands:Thesis Wageningen University.

Temple, S. J., & van Boxtel, A. J. B. (1999a). Thin layer drying of blacktea. Journal of Agricultural Engineering Research, 74(2), 167–176.

Temple, S. J., & van Boxtel, A. J. B. (1999b). Modelling of fluidized beddrying of black tea. Journal of Agricultural Engineering Research,

74(2), 203–212.Temple, S. J., & van Boxtel, A. J. B. (2000). Control of fluid bed tea

dryers: controller design and tuning. Computers and Electronics in

Agriculture, 26(2), 159–170.Temple, S. J., van Straten, G., & van Boxtel, A. J. B. (2000). Control of

fluid bed tea dryers: controller performance under varying operatingconditions. Computers and Electronics in Agriculture, 29(3), 217–231.

Wiriyaumpaiwong, S., Soponronnarit, S., & Prachayawarakorn, S. (2004).Comparative study of heating processes for full-fat soybeans. Journal

of Food Engineering, 65, 371–382.Zanoelo, E. F. (2005). Equilibrium moisture isotherms for mate leaves.

Biosystems Engineering, 92(4), 445–452.Zanoelo, E.F. (in press). A Theoretical and experimental study of

simultaneous heat and mass transport resistances in a shallowfluidized bed dryer of mate leaves. Chemical Engineering and

Processing.Zanoelo, E. F., Cardozo-Filho, L., & Cardozo-Junior, E. L. (2006).

Superheated steam-drying of mate leaves and effect of drying condi-tions on the phenol content. Journal of Food Process Engineering, 29,253–268.

Zanoelo, E. F., Di Celso, G. M., & Kaskantzis, G. (2007). Drying kineticsof mate leaves in a packed bed dryer. Biosystems Engineering, 96(4),487–494.

2008Dynamic Modeling and Feedback Control for Conveyors-belt Dryers

Documents

Transcript of 2008Dynamic Modeling and Feedback Control for Conveyors-belt Dryers