S U T T E R W O R T I - 4 I N E M A N N

0 9 5 9 o l 5 2 4 ( 9 4 ) 0 0 0 0 3 - 4

J. Proc ( b n r Vol. 5. No. 3, pp. 183 189, 1995 Copyright t7 1995 Elsevier Science Ltd

Printed in Great Britain. All rights reserved 0959-1524/95 $10.00 ~ 0.00

Self-tuning predictive control of processing temperature for food extrusion

Jinglu Tan* and James M. Hofer

Department of Agricultural Engineering, University of Missouri, Columbia, MO 65211, USA

Received 7 April 1994; revised 27 October 1994

A self-tuning regulator was developed for temperature control in a food extrusion process. Process models with on-line identification were used to predict the processing temperature and major disturbances. The regulator was designed in an explicit formulation based on feedforward and internal-model-based predic- tive control strategies. An extended prediction window was used in the identification and control algo- rithms for enhanced robustness against uncertainties in time delays. The control system was implemented and tested experimentally. The effectiveness of the algorithms was demonstrated.

Keywords: adaptive control; food extrusion; processing temperature

Extrusion is a widely used process in the food industry today. Figure 1 shows a simple extruder schematic. Food materials (starch, added moisture and other ingre- dients) are fed into the extruder barrel at controlled rates. In the barrel, the materials are mixed and pressed towards the die orifice by a set of screws of different geometric shapes. The barrel is divided into several zones. Each barrel zone is equipped with electric heating and water cooling, both of which are indepen- dently controllable. In the process, the extrudate is heated, pressurized and subjected to shear. Heat trans- fer occurs between the extrudate and barrel, and shaft work is done on the extrudate by the screws. The shaft work rate per unit extrudate mass is commonly referred to as the specific mechanical energy (SME) in the extru- sion literature ~. The shaft work is largely converted into heat through friction, raising the extrudate temperature. The extrudate temperature is therefore influenced by heating, cooling, shaft work input and material feed rate.

The processing temperature is important to the quality of extruded products. A stable and specifiable extrudate temperature profile along the extruder barrel length is desirable 2. In existing food extruders, the extrudate temperature is not directly monitored and controlled. Instead, the barrel temperature in each zone is regulated independently. A desired extrudate temper- ature, however, cannot be easily obtained by setting the barrel temperature because there is not a simple rela- tionship between the two. Furthermore, a regulated and

*To whom correspondence should be a d d r e s s e d .

stable barrel temperature does not lead to a stable extrudate temperature. For a given barrel temperature, significant changes in extrudate temperature can occur as a result of variations in feed materials.

Until recently, only limited success has been achieved on extrudate temperature control. This can be attrib- uted to two major sources of difficulty. First, the dynamics in the extrusion process is difficult to model 4. The shaft work, which strongly influences the extrudate temperature, heavily depends on the rheological proper- ties of the extrudate. The complex, non-linear and time- dependent nature of food material properties makes it hard to establish simple and adequate dynamic rela- tionships among the process variables. Second, a signif- icant time delay exists between each manipulatable variable and extrudate temperature. This creates a strin- gent requirement for accurate models and sophisticated control strategies for extrudate temperature regulation.

Using auto-regressive moving-average models with auxiliary inputs (ARMAX), Hofer and Tan 5 developed a predictive regulator for extrudate temperature. The ARMAX models were developed experimentally by exciting the process with an orthogonal pseudo random binary sequence. A prediction algorithm was designed

Feed

\ l /

I g I 8 I 7 I 5 I 5 I 4 I 3 I 2 I 1 I Temperature Zones

Figure 1 Schematic of a food extruder

183

184 Self-tuning predictive control: J. Tan and J. M. Hofer

to predict the major disturbance to extrudate tempera- ture, which provided the input for a feedforward loop. Two model-based predictive feedback loops adjusted heating and cooling. The regulator was implemented on a twin-screw food extruder and significant improvement in extrudate temperature stability was achieved over the original barrel temperature controllers.

The regulator developed, however, had limited robustness against the time-variant nature of the process. Although data from an individual experiment could be adequately modelled, the model coefficients varied significantly from one experiment to another even without apparent changes in the experimental conditions. This made frequent tuning of the regulator necessary. Moreover, experiments showed that the time delays associated with the control variables (heat input and cooling strength) could also vary.

The objectives of this study were to develop control algorithms effective for the time-variant dynamics and variable time delays associated with processing temper- ature in food extrusion, and to implement a self-tuning extrudate-temperature regulator for a temperature zone. This entailed the development of algorithms for on-line process identification, adaptive disturbance prediction and predictive control. The effectiveness of the algor- ithms was experimentally tested.

Experimental equipment

In this research, experiments for process identification and control implementation were carried out with an APV-Baker MPF 50/25 intermeshing twin-screw food extruder (Baker-Perkins, Grand Rapids, MI, USA). A Keithley DAC 500P unit (Keithley Instruments, Inc., Cleveland, OH, USA) interfaced with an IBM/AT was used for data acquisition and control. K-type thermo- couples were used to sense extrudate temperature. For most experimental developments, yellow corn meal (Lauhoff Grain Company, Danville, IL, USA) was used to make a puffed product. Rice flour (Rivland Partnership, Houston, TX, USA) was used as an alter- native starch material to test the robustness of the self- tuning regulator developed. The screw speed was 300 rpm, the material feed rate was 45.4 kg/h, and the average moisture content was 20% (wet basis). These were often used operating conditions for the extruder.

The extruder barrel is divided into nine zones as shown in Figure 1. Each zone is equipped with two 900 W induction heaters. Water is circulated through the barrel to provide cooling. The electrical heating and water cooling for each zone could be independently turned on or off by a set of relays and solenoid valves. To study the dynamic effects of heating and cooling on extrudate temperature and to execute control actions in a continuous fashion, digital PWM (pulse-width-modu- lated) actuators were designed, built and installed in the extruder. The actuators allowed heating and cooling to vary from zero to their respective full capacities in an effectively continuous fashion.

Process identification

The extrudate goes through a rising temperature profile as it moves from the feeding port to the die. The major- ity of the temperature rise occurs in the last three zones (zones 7, 8 and 9) for the extruder used. Zone 8 was used as the plant system in this research to test the iden- tification and control strategies.

The extrudate temperature in a zone is determined by how the zone exchanges energy and work with its envi- ronment. Heat transfer is affected by heating input and cooling strength, both of which are defined as fractions of their respective full capacities. Shaft work input is related to the mechanical work done by the screws (SME). Convective energy transfer depends on the upstream temperature and mass flow rate. As the devel- opments were limited to a single zone so as to empha- size strategies for handling the time-variant dynamics and time delays, the material feed rate and net heat inputs to the adjacent zones of zone 8 were held constant. The upstream temperature was then only a function of shaft work and thus its effects on the extru- date temperature in the zone of interest were automati- cally lumped into the shaft work term. The extrudate temperature can thus be described by:

T =f(H,C,W,t) (1)

where T is extrudate temperature, H is heating input, C is cooling strength, W is shaft work (specific mechanical energy input) and t is time.

A model structure for extrudate temperature was developed and validated in Hofer and Tan 5, which takes the following ARMAX form:

rT(k) 1 T(k + 1)= [aTl(k) aT2(k ) ar3(k)] lT(k - 1)| LT(K -

C( k - d c ) +[bc(k) bH(k)]IH(k - dH) ]

Ivc( -dw) ] +[61(k) &z(k) 63(k)][W(k d w - 1 )

LW(k d w 2)

+ [o'(k)][oa(k)]

(2)

where aTl(k), aT2(k), aT3(k), bc(k), bH(k), ~Sl(k), ~52(k), ~3(k), and a(k) are coefficients; d o dH, and d w are the time delays associated with C, H and W; oa is a white noise sequence; and k is an integer.

Though it appears on the right-hand side of Equation (2), shaft work W cannot be used as a manipulative variable to regulate extrudate temperature. This is because: (1) W is not arbitrarily specifiable, and (2) it affects all the zones simultaneously. In fact, shaft work variations are the major disturbances causing extrudate temperature to vary. Experiments show that W has a smaller time delay and larger coefficients than those for

Self-tuning predictive control: J. Tan and J. M. Hofer 185

H and C, indicating a quicker and stronger influence on T. To minimize the effects of W by adjusting H and C, prediction of W is thus necessary. W is a function of screw speed, feed rate, and motor torque. Changes in screw speed and feed rate are usually known before- hand. For given screw speed and feed rate, the motor torque depends on the material properties, primarily the feed moisture content, which can be measured with a desired lead time by installing sensors at a proper loca- tion in the material-feeding system. Other unmeasurable disturbances can be assumed as white noise. Shaft work (W) can thus be predicted by using the following auto- regressive moving-average model with moisture content as an auxiliary inpuff:

1 W(k + 1) = [an,z(k) aw2(k)] Lw(k _ 1)l (3)

+ bM(k)M(k - d~) +c(k)e(k)

where a,q(k), aw2(k), b~k) and c(k) are coefficients, M is the feed moisture content, d~ is the moisture time delay and e is a white noise sequence.

On the basis of the model structures for extrudate temperature and shaft work (Equations (2) and (3)), the normalized least-mean-squares algorithm (NLMS) was used for on-line parameter identification. The NLMS algorithm is6:

O(k)=O(k 1)4 p~(k 1) ~(k) (4) 1 + O(k 1 ) T O ( k - 1)

where 0(k) is the parameter vector (model coefficients), 0(k) is the input and output data vector, ~(k) is a pre- diction error and p is the forgetting factor (usually, 0 < p < 1). For the extrudate temperature model:

0(k) = [arl(k) ar:(k) ar3(k) bc(k) bn(k) 61(k) 62(k) S~(k) o'(k)] v

O(k) = [ T ( k ) T(k 1) T(k 2) C(k-dc) H(k-dH) W(k-d,,) W(k dn-I ) W(k-dw-2) co(k)] T

and for the shaft work model:

O(k)--[a.v(k) aw:(k) b~k) c(k)] T

$(k)--[W(k) W(k-1) M(k dM) e(k)] T

Equation (4) shows that the amount of correction to the parameters after each sampling is proportional to prediction error ~. It was found in this research that the proper selection of ~ is important to the performance of the identification algorithm. Usually, ~ is defined as the one-step-ahead prediction error, i.e. the difference between the current process output reading and the model prediction made one sampling step earlier. For long-term prediction, a long-term prediction error seems more appropriate than the one-step-ahead predic- tion error. For the predictive extrudate regulator devel- oped in this research, the models were used to predict T and W a number of steps (depending on the time delays) into the future; thus, long-term prediction errors were used in the identification algorithm. Furthermore,

because of the uncertainties associated with the time delays and the involvement of two different time delays (d c and DH) in Equation (2), the equations were used to predict the output variables over a period in the future called the prediction window. The average error over the prediction window was used as ~ in Equation (4) to determine the coefficients for Equations (2) and (3). For extrudate temperature, ~ was defined as:

~T(k)_ 1 ~[T(k)-T~(k)] ~[8,(k)~,.(/,- j + l ) ] 11 I l l i = m / I

(5)

and for shaft work:

1 q ~ ( k ) - E [W(k) w,. (k ) ]

q p i=p (6)

where T(k) and W(k) are respectively the measured extrudate temperature and shaft work, Ti(k) and Wjk) are respectively the current temperature and shaft work predicted i steps before, and ~(k) (j = 1, 2, 3) are the coefficients for the W terms in Equation (2). m and n define the prediction window for temperature, and p and q define it for shaft work. m and p were chosen between unity and the estimated lower limit of the related minimum time delay, n and q were greater than the estimated upper limit of the related maximum time delay. The use of such moving-average type of errors improved the identification algorithm in terms of accu- racy of long-term prediction and robustness against process noise.

The second term on the right-hand side of Equation (5) is the part of the temperature prediction error result- ing from errors in shaft work prediction (~w)- This error is deducted from the total temperature prediction error because W is an input (part of the data vector) to the temperature equation. The identification algorithm should minimize errors resulting from incorrect coeffi- cients rather than those caused by inaccurate input data. The prediction errors of W are due to inaccuracies in the shaft work model and are minimized by identifi- cation of the model coefficients in Equation (3).

With the NLMS algorithm, it is straightforward to impose constraints on any or all identified coefficients. Based on the physical process, it is obvious that the coefficient for heating (H) in Equation (2) should always be positive and that for cooling ((7) should always be negative because heat input always causes a temperature rise while cooling always causes a tempera- ture drop. Since an increase in moisture content reduces the material viscosity and consequently lowers the motor torque and shaft work, the coefficient for moist- ure (M) in Equation (3) should always be negative. Because of process noise, however, these conditions may be violated; hence, they should be imposed as constraints in the identification algorithm. If an identi- fied coefficient lies outside its legal boundary, the coef- ficient can be set to either the boundary value or the last legal value determined. The latter was used in this research.

186 Self-tuning predictive control: J. Tan and d. M. Hofer

The identification algorithm and model structures were first tested via computer simulations on the basis of experimental data. Data were collected by measuring the input and output variables (H, C, M, T and W) while the input variables were perturbed by distur- bances. The algorithm was employed to identify the model parameters for T and W from the data. Different initial coefficient values were used to test the conver- gence of the algorithm and the forgetting factor was adjusted to give a desired convergence rate.

the predictor form of Equation (2) for inputs C and H respectively. Gcc and Gcn were designed so that each of the two closed-loops (from N to T c and from N to T H in Figure 3) had a pole at a desirable location. This would give a first-order correction to deviations of extrudate temperature from its set point. The designed Gcc and Gci ~ were:

Gc c = (1 - oc)z 1(1 - aT1Z-1 -- aT2 z-2 -- av~z 3) (7)

(1 - z l)b c

Control development

Based on the identification algorithm, an explicit, predictive, self-tuning regulator was designed for extru- date temperature control. The block diagram of the control system designed is shown in Figure 2. The plant block is the extruder zone described by Equation (2). Its output is extrudate temperature T and inputs are heating H and cooling C. Shaft work W is a disturbance to the plant. The parameter estimator blocks represent the identification algorithm. The coefficients estimated by the shaft work parameter estimator based on measurements of W and M are provided to a shaft work predictor, which is simply Equation (3) written in a predictor form. The temperature parameter estimator computes the coefficients for the temperature model (Equation (2)) on the basis of measured T, H, C and predicted W. The control law determines the needed control actions in terms of H and C based on the temperature model, predicted W and measured extru- date temperature.

The control algorithms denoted by the control law block include four loops as shown in Figure 3: two internal-model-based control loops consisting of controllers Gcc and Gcn, and extrudate temperature predictors G c and Gn; a feedforward loop for minimiz- ing the W effects consisting of GFF C and GFFH; and a feedback loop involving GFB. Because of the large time delays involved with plant input variables C and H, predictive control strategies were employed to design the controllers.

Gcc and GcH are respectively cooling and heating controllers designed on the basis of the internal-model approach. Temperature predictors Gc and G H are just

Gc H = (1 - fl)z 1(1 avlZ-1 _ aT2Z 2 _ _ aT3Z 3) (8) (1 - - Z 1 ) b H

where a and fl are the desired pole locations for the two loops respectively, and z is the z transform variable. The proper values for a and fl were determined through experimental tuning of the control system.

One of the two control loops is theoretically redun- dant because the system has only one output. Practically, however, both heating and cooling are needed for prompt error corrections in extrudate temperature. Heating is obviously essential in a cooking process and cooling is also indispensable because natural cooling is too ineffective to offset the effects of excessive shaft work. From a control point of view, the availability of multiple inputs is desirable as it gives extra degrees of freedom for enhanced control perfor- mance.

To effectively use both heating and cooling, a scheme must be devised for the coordination between the two. This was accomplished by dividing the work load between heating and cooling in a staggered fashion. Because cooling has a larger time delay than heating, C is determined first under the assumption that the H value affecting the temperature for the same future instant would be zero. This assumption minimizes the total energy input. To determine H, the effects of the past C values are taken into consideration. The current H and a past C ( d c d H steps ago) will affect the temper- ature at the same future time. This time difference allows for a second opportunity to predict and correct a future temperature and consequently improves the control performance.

The feedforward loop was designed to cancel the

W

Shaft Work Parameter Estimator

Shaft Work Predictor

PFedidced W

-I Plant I T

I

e F -

ContrOlLaw

f Figure 2 Block diagram of the predictive self-tuning regulator system

W(z)

T Figure 3 Block diagram of the control loops

C ( z )

H(z)~

Self-tuning predictive control: J. Tan and J. M. Hofer 187

effects of W by adjusting C and H. The transfer func- tions for GFF C and GFF H c a n be found by comparing the C and H terms with the W term in Equation (2) as:

GFFC = 51 + 52 z I + 53 z Z Z dc dw (9) bc

GFFH = 51 + 52 2 1 + 53 2 2 Z dH dw (10)

b/¢

Since d w is smaller than d c and d m z dc-dw and z dn aw in Equations (9) and (10) indicate predictions of W, which are accomplished by using Equation (3).

The concept of output horizons in generalized predic- tive control 7 was employed in the control algorithms to improve system robustness. The time delays were uncer- tain and variable to some degree; thus, it was unreliable to determine the control actions based on output prediction for a specific point of time in the future. As a result, predictions were made for a series of future time instants about a target point given by the time delay values used. The control actions were determined from the average of the series of predictions. This approach was used for both the internal-model-based and the feedforward control loops. The use of such a predicted-output window improved the control robust- ness against inaccuracies and variations in the time delays.

The last control loop includes feedback controller GFB

and extrudate temperature feedback T. GFB is simply an integrator added to compensate for non-stationary effects (slow drifts) in the process and steady-state offsets.

Experimental results

After testing of the identification and control algo- rithms via computer simulations, the predictive, self- tuning temperature regulator was implemented, tuned and tested on the twin-screw food extruder. A series of exponential changes in moisture content were intro- duced to produce the disturbance effects of material variations such as batch changes. The disturbance

signal is shown in Figure 4. Such seemingly minor changes (1-1.5%) in moisture content could significantly change the rheological properties of the extrudate and as a result the shaft work input (SME). Without proper compensation, this would cause considerable variations in extrudate temperature.

Figure 5 shows the measured extrudate temperature with the new self-tuning control compared to that with the original barrel-temperature control under the influ- ence of the moisture disturbance. Clearly, the new control system brought about substantial improvement over the barrel-temperature controller in terms of temperature stability. The self-tuning regulator reduced the overshoot by 60%. In terms of sum of squares for error from the set-point, the self-tuning regulator reduced the variation by 1200°/,,. It is also interesting to note that the adaptive ability of the regulator contributed significantly to the improvement in perfor- mance. Compared with the non-adaptive regulator reported in Hofer and Tan 5, the self tuning regulator reduced the sum of squares for error by 260%.

The control actions are shown in Figure 6 (only a data segment plotted for clarity). The variables were normalized (divided by their respective averages) so that they could be plotted in one graph. The input curves, C, H and W, have been shifted to the right by a distance equal to their respective time delays so that the varia-

5

4 v

a

"6 2

123

a, 0 D

e)

E -3 - 4

,~ f

........ New Control - - Originol Control

- - 5 I I I I I I I t I 0 600 1200 1800 2400 3000 3600 4200 4800 5400

Time (s)

Figure 5 Performance comparison of the new control system with the original control tested with corn meal

1.5-

1 . 0 -

3~ 0.5-

o.o- 8,

6 -o.~-

1~ - 1 . 0 -

- 1 . 5 -

- 2 . 0 0

I I I I I I I I 600 t200 1800 2400 3000 .3600 4200 4800 5400

~rne (~)

Figure 4 Process disturbance in moisture content

W

4200 46.0o 47.00 4a.00 49.00 ~ 5000 51'oo 520° Joo 5,'00 550° Time (s)

Figure 6 Control actions produced by the predictive self-tuning regulator

188 Self-tuning predictive control: J. Tan and J. M. Hofer

tions in T, C, H and W are synchronized for easy visu- alization of the trend relationships among them. As can be seen, the controller responded as expected to changes in shaft work and temperature. For example, as shaft work went up starting from approximately 4900 s, cooling increased and heating decreased so that the deviation in temperature was minimized. Between 5050 and 5350 s, when much compensation was needed for the high IV, both C and H were saturated as a result of the limited capacities of the cooling and heating systems, which limited the control performance. If the cooling system and heater capacities are increased, the control performance can be further improved.

The identification algorithms for both extrudate temperature and shaft work performed well. Figures 7 and 8 respectively show the predicted extrudate temper- ature and shaft work compared with measured values. The predicted temperature was close to the measured except for some peak points. The predicted shaft work closely followed the measured. This indicates that the identification algorithms effectively identified the model coefficients to minimize prediction errors. Accurate prediction is key to an effective predictive control system.

Figure 9 shows some examples of the temperature model coefficients identified during the control experi- ments. Some coefficients appeared to converge, but others continuously varied. This shows that the food extrusion process is time-variant and adaptive strategies are needed for effective control.

3.0-

2 . 5 -

2.0-

g 1.5. 1.0-

0.5. C3

L o 0.0"

-0 .5 " L 0) c~ - 1 . 0 - E

- 1 . 5 -

- 2 . 0 -

- 2 . 5 0

Figure 7

if

....... Actual Temperature - - Predicted Temperature

I 600 12100 18100 I 2400 30100 36100 42100 48100 5 ; 0 0

Time (s)

Predicted ex t ruda te t empera tu re com pa red with m e a s u r e m e n t

7-

o

f.~

-- Actual ........ Predicted

5- i ~,

1

-1

- 3

- 5 I I I i i I I 0 500 1000 1500 2000 2500 3000 3500 4000

Time (s)

Figure 8 Predic ted shaf t work (SME) c o m p a r e d with m e a s u r e m e n t

F}TI ~ -

6,

b,

I I I I 0 600 1200 1800 2400 ,3000 3600 4200 4800 5400

Time (S)

Figure 9 Examples of identified coefficients for the t empera tu re mode l

To test the robustness of the control system, an experiment was performed with rice flour, another often used starch material with different physical and chemi- cal properties from corn meal. Again, a puffed product was made with a feed rate of 45.4 kg/h, screw speed of 300 rpm, and average moisture content of 20% (w.b.). The same disturbance in moisture content was used. The control system including the algorithms, model structures, time delays and initial coefficients were unchanged. Figure 10 shows the regulated extrudate temperature. (Note that the experiment lasted for only half the duration of the corn meal experiments because of a material shortage at the time of experiment.) Comparison of Figure 10 with Figure 5 shows that the extrudate temperature for rice flour varied in a similar fashion to that for corn meal. The maximum overshoot was held within 2°C. This demonstrates that the control system could not only effectively handle the time- variant dynamics of the process but also has certain robustness against material changes.

C o n c l u s i o n s

Through a real-world application, this study demon- strates the effectiveness of the self-tuning predictive control strategies employed and developed. In spite of

"8"

o 1

0

~- - 2 E

-3-

-4-

-5 0

Figure I0

l I I I 500 1000 1500 2000

"nme (s)

Control performance tested with rice flour

I 2500 3000

Self-tuning predictive control: J. Tan and J. M. Hofer 189

the complex time-variant nature of the food extrusion process, the processing temperature can be effectively regulated by self-tuning predictive control to minimize the influence of material property variations. Both the extrudate temperature and the shaft work (specific mechanical energy) input can be adequately modelled and predicted with ARMAX models plus on-line iden- tification. For the food extrusion process, self-tuning abilities can significantly improve the control perfor- mance. The employment of an output prediction window can improve the robustness of identification and control algorithms when time delays are variable and uncertain.

References

1 Harper, J. M. in 'Extrusion Cooking', (Eds C. Mercier, P. Linko and J. M. Harper) American Assoc. of Cereal Chemists, Inc., St. Paul, MN

2 Dastych, J., Wiemer, P. and Unbehauen, H. 'Proc. IFAC Adaptive Contr. of Chern. Proc. 'Copenhagen, Denmark, 1988

3 Hofer, J. M. 'Adaptive Control of Processing TemperatureJor Food Extrusion', MS Thesis, University of Missouri, Columbia, MO, USA, 1992

4 Kulshreshtha, M. K., Zaror, C. A. and Jukes, D. J. Food Control 1991, 1, 80

5 Hofer, J. M. and Tan, J. Food Control 1993, 4, 17 6 Goodwin, G. C., and Sin, K. S. 'Adaptive Filtering. Prediction and

Control', Prentice-Hall, Englewood Cliffs, N J, 1984 7 Clarke, D. W., Mohtadi, C. and Tufts, P. S. Automatica 1987, 23,

137