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Modeling and control of a food extrusion process
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predictive controllers are compared. Finally, conclusions are drawn and further work outlined. EXTRUDER MODELLING PROCESS DESCRIPTION Extrusion is a shaping operation in which a material is pressurised by some means to force it through a die. The material is generally a solid at ambient temperature, and extrusion usually requires processing the material at a higher temperature, under which the material softens or melts to facilitate flow. A typical extruder consists of a barrel inside which one or more helical screws rotate to propel the feed material towards a die opening at the discharge end of the extruder, as illustrated in Figure 1.
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The high pressure generated during this process forces the material to exit the extruder through the die. At the same time, heat is generated due to friction and the material is exposed to high rates of shear stress. This usually leads to some kind of material transformation and determines the shape, size and texture of the extrudate. MECHANISTIC MODELLING The steady state model presented by Kulshreshtha et al. (1991) and its dynamic version, Kulshreshtha etal. (1992), represent the most recent one-dimensional mechanistic modelling approach for twin-screw cooking extrusion. Both the steady state and the dynamic model are based on elemental heat and energy balances. Given the screw speed, feed rate, moisture content, feed temperature and barrel temperature profile this model calculates the temperature and pressure profiles along the barrel and the overall shaft-power required.
The model has been implemented in the MATLAB software environment with several modifications and extensions for the purposes of this project: 1. The model solution schemes and the numerical techniques suggested by Kulshreshtha et al. (1991,1992) are unnecessarily complex and inefficient, requiring repeated iteration to calculate the position of the moving boundary between each solids conveying zone (SCZ) and melt zone (MZ).
Instead, the partial differential equations describing mass and energy balances down the length of the extruder have been discretised and solved using a finite element technique. This is equivalent to dividing the extruder into a number of continuously stirred tank reactors (CSTRs) - with back-flow occurring in the MZ elements - connected in series. Using this method, the SCZ-MZ interface is simply determined, occurring where the CSTRs become completely filled. 2. The above discretisation procedure has positive implications for more accurate flow modelling. Kulshreshtha's basic model for simplification purposes assumes that a twin-screw extruder has plug-flow behaviour. The leakage back-flow between consecutive C-shaped chambers is simply treated as a reduction in forward flow, which is an unrealistic simplification (Jager et al., 1992). The discretisation procedure allows the separation of the forward flow (due to positive displacement by the screws) and the back-flow (due to leakage around the screw flights) leading to a more accurate flow representation. 3. The model has been extended to include variables which may be helpful for describing product quality. Product gelatinisation, specific volume, specific mechanical energy, and residence time are now predicted by the model. The methods employed to extend the model are described in more detail below THE GELATINISATION MODEL Starch gelatinisation during extrusion is a complex reaction for which the mechanisms are not fully understood. A review of the literature revealed that there have been only two different modelling approaches investigated, those suggested by Wang et al (1992) and Cai and Diosady (1993). Although it is not possible to conclude which of these approaches is the more appropriate at this stage, the model suggested by Cai and Diosady has been validated over a wider range of operating conditions, and is therefore the model chosen for our implementation.
Examples of the dynamic response of starch gelatinisation to changes in feed rate, screw speed and moisture content are shown in Figures 2(a) to 2(c), where inverse response characteristics as well as process dead-time can be observed.
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The predicted residence time distribution of an inert tracer was compared with experimental RTD data obtained by injected sodium chloride at the feed port of the extruder. Figures 3(a) and 3(b) are a comparison between the predicted and measured concentrations of the tracer in the extrudate over time. It can be seen that increasing screw speed has the effect of reducing the "dead-time" of the process, but has little effect on the variance of the distribution. Increasing feed-rate, however, has little effect on the dead-time of the
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Although the gelatinisation model parameters have yet to be determined experimentally for the cooking extruder being studied, parameters were estimated to match reported values of gelatinisation in similar extruders.
RESIDENCE TIME DISTRIBUTION (RTD) The effect of the residence time distribution on product quality is an important consideration, as a high variance for the RTD implies a highly inconsistent degree of cooking for the product. For this reason, it is advantageous to be able to predict the RTD for a given set of operating conditions, so that the extruder can be operated in such a way as to produce a homogeneously cooked product.
(b) Figure 3: Experimental and model predicted RTD curves. process, but leads to a narrower distribution. The excellent fit obtained between the experimental and model predicted RTD curves might be interpreted as further evidence of the general applicability of the model developed here.
EXTRUDATE EXPANSION Extruders are often used to produce puffed products such as breakfast cereals, flat breads and snacks. For such products the expansion ratio is clearly an important quality variable. The model of Fan et al. (1994) which describes the dynamics of bubble growth in starchy extrudates has been implemented in the
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general extruder model to provide predictions of the expansion ratio and bubble size.
A comparison of the model prediction experimental data is presented in Figure 4.
RHEOLOGICAL MODELS
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Dough mixes are non-Newtonian fluids, and their rheological behaviour is quite complex• The selection of a suitable theological model is crucial to the validity of the resulting extruder model, as it directly influences the flow behaviour, heat generation, and pressure development within the extruder. In a previous paper (Elsey et al., 1996) two different power law model structures (those of Kulshreshtha et al., 1991 and Vergnes et al., 1987) were compared for their accuracy at describing experimental extrusion data. However, the power law models that are typically applied often do not have a firm theoretical basis, and are therefore simply correlations of a form that appear to fit experimental data over a reasonable range of conditions.
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It is interesting to note that this model form is efficient in that it contains only six parameters, comparable to the model of Vergnes et al. (1987) which employed seven• Perhaps one advantage of this modelling approach is that other process variables which are not typically considered in extrusion rheological models can be included• For example, if an appropriate sampling valve were used to collect samples of the melt, the degree of cook could be determined and included in the model for melt viscosity• Considering that typical power law rheology models require fitting of their parameters to specific feed materials in any case, there are clearly advantages in evolving an entire rheological model from this experimental data. Having developed a process model that compared well with experimental observations, process control schemes can now be investigated. ADAPTIVE INFERENTIAL EESTIMATION Typical control variables for a cooking extrusion process are product temperature and die temperature• These variables are typically chosen because they give some indication of the state of the process and are easily measured at rates suitable for on-line process control. Ideally however, real quality measures would be the control variables, such as degree of cook, mean residence time, or product expansion ratio. Unfortunately, the feasibility of on-line measurement of these variables is limited as either the instrumentation does not exist or the analysers require long cycle times. The resulting delays would prevent early detection of the effects of load disturbances, resulting in degraded process operation.
PSE '97-ESCAPE-7 Joint Conference Estimators that are capable of alleviating the problem of large measurement delays and irregular sampled feedback have been previously developed (Guilandoust et al., 1987; Tham et al., 1992). Since the primary controlled variable is usually related to other process outputs, the estimators make use of these secondary outputs to infer the state of the primary output each time the secondary outputs are measured. The estimators are implemented within an adaptive framework to ensure their applicability to time varying processes. The parameters of the algorithm are estimated whenever measurements of the primary output become available. As a result, estimates of the primary output are obtained at the faster rate at which the secondary outputs are measured. To assess the feasibility of this adaptive inferential estimator (AIE) for applications to extrusion control, the AIE algorithm of Guilandoust et al., (1987) was used to provide estimates of the product gelatinisation fraction of an extruded starchy material, as simulated by the extruder model described earlier in this work. Product gelatinisation fraction of extruded starchy products can be determined off-line using a rapid viscoanalyser. A typical analysis takes approximately 20 minutes, and thus this measurement would normally be unsuitable for process control purposes. Figure 4 shows the simulated response of product gelatinisation fraction when the extruder model inputs screw speed, moisture content and feed rate are stepped. The estimated output of the AIE algorithm is also shown, and clearly a reasonable estimate of the primary output has been obtained.
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PROCESS CONTROL A preliminary investigation of the suitability of PI and model predictive control (MPC) for single-input-singleoutput control has been performed. Simulations were performed using in turn moisture content, feed rate and screw speed as the manipulated variable to move the degree of gelatinisation between set-points. Results of these simulations are shown in Figure 5. It can be seen that the best control performance was obtained using screw speed as the control variable within a MPC scheme. The use of moisture as a control
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variable was unsuccessful as the range of variation required in the set-point changes could not be achieved via moisture content manipulation. In the case of using feed rate as the manipulated variable, PI control could not be used as the product gelatinisation fraction exhibits an inverse response to changes in feed rate In general, the performance of either moisture content or feed rate as the control variable was far from ideal due to the presence of dead-times between the control
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action and the process's response. Clearly though, the performance of MPC is far superior to that for PI control. Such a result is expected as MPC has the advantage of having an internal model of the process to use in optimising its control action. CONCLUSIONS An outline of the process systems engineering techniques relevant to the modelling and control of a food extrusion process has been presented. Emphasis has been directed towards the predicting and controlling realistic quality variables such as product gelatinisation fraction in preference to secondary process indicators such as temperature and pressure. A flexible dynamic model of the extrusion process has been developed, rheological modelling investigated, an adaptive inferential estimator for product ge!atinisation fraction developed, and simple control strategies investigated. It is expected that the control of real quality variables will result is a more reliable control scheme. This is the subject of current research. ACKNOWLEDGEMENTS The authors would like to thank Dr Ming Tham for his assistance with the adaptive inferential estimation algorithm implementation, and the CSIRO Department of Food Science and Technology Australia for providing the extrusion data used in theses studies. REFERENCES
Cai, W. and Diosady, L.L. (1993). A model for gelatinisation of wheat starch in a twin-screw extruder. J. Food Sci. 58:872-875, 887. Guilandoust, M.T., Morris, A.J. and Tham, M.T. (1987). Adaptive inferential control, lEE Proceedings, 134d-3, 171-179. Elsey, J., Riepenhausen, J., McKay, B., and Barton, G.W. (1996). Dynamic modelling of a cooking extruder. Chemeca 1996, Sydney, Australia. Fan, J., Mitchell, J.R. and Blanshard, J.M.V. (1994). A computer simulation of the dynamics of bubble growth and shrinkage during extrudate expansion. J. Food Eng. 23, 337-356. Jager, T., van Zuilichem, D.J., Stolp, W. (1992). Residence time distribution, mass flow, and mixing in a co-rotating, twin-screw extruder. In Food Extrusion Science and Technology, J.L. Kokini, C.T. Ho and M. V. Karwe, Eds., Marcel Decker, New York, pp. 165-176. Kulshreshtha, M. K., Zaror, C. A., Jukes, D. J. and Pyle, D. L. (1991). A generalised steady state model for twin screw extruders. Trans IChemE, Part C, Food and Bioproducts Proc., 69 (C4): 189199. Kulshreshtha, M.K. and Zaror, C.A. (1992). An unsteady state model for twin screw extruders. Trans IChemE, Part C, Food and Bioproducts Proc., 70 (C4): 21-28.
McKay, B., Willis, M.J., Barton, G.W., (1996). Steadystate modelling of chemical process systems using genetic programming. Accepted for publication in Comp. and Chem. Eng. Tham, M.T., Montague, G.A. and Morris, A.J., (1991). J. Proc. Cont., 1, 3-14. Wang, S. S., Chiang, W. C., Zheng, X., Zhao, B., Cho, M. H. and Yeh, A. (1992). Application of an energy equivalent concept to the study of the kinetics of starch conversion during extrusion. In Food Extrusion Science and Technology, J.L. Kokini, C. T. Ho and M. V. Karwe, Eds., Marcel Decker, New York, pp. 165-176.
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predictive controllers are compared. Finally, conclusions are drawn and further work outlined. EXTRUDER MODELLING PROCESS DESCRIPTION Extrusion is a shaping operation in which a material is pressurised by some means to force it through a die. The material is generally a solid at ambient temperature, and extrusion usually requires processing the material at a higher temperature, under which the material softens or melts to facilitate flow. A typical extruder consists of a barrel inside which one or more helical screws rotate to propel the feed material towards a die opening at the discharge end of the extruder, as illustrated in Figure 1.
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/////////////////II Figure 1: Schematic representation of a co-rotating twin-screw extruder.
The high pressure generated during this process forces the material to exit the extruder through the die. At the same time, heat is generated due to friction and the material is exposed to high rates of shear stress. This usually leads to some kind of material transformation and determines the shape, size and texture of the extrudate. MECHANISTIC MODELLING The steady state model presented by Kulshreshtha et al. (1991) and its dynamic version, Kulshreshtha etal. (1992), represent the most recent one-dimensional mechanistic modelling approach for twin-screw cooking extrusion. Both the steady state and the dynamic model are based on elemental heat and energy balances. Given the screw speed, feed rate, moisture content, feed temperature and barrel temperature profile this model calculates the temperature and pressure profiles along the barrel and the overall shaft-power required.
The model has been implemented in the MATLAB software environment with several modifications and extensions for the purposes of this project: 1. The model solution schemes and the numerical techniques suggested by Kulshreshtha et al. (1991,1992) are unnecessarily complex and inefficient, requiring repeated iteration to calculate the position of the moving boundary between each solids conveying zone (SCZ) and melt zone (MZ).
Instead, the partial differential equations describing mass and energy balances down the length of the extruder have been discretised and solved using a finite element technique. This is equivalent to dividing the extruder into a number of continuously stirred tank reactors (CSTRs) - with back-flow occurring in the MZ elements - connected in series. Using this method, the SCZ-MZ interface is simply determined, occurring where the CSTRs become completely filled. 2. The above discretisation procedure has positive implications for more accurate flow modelling. Kulshreshtha's basic model for simplification purposes assumes that a twin-screw extruder has plug-flow behaviour. The leakage back-flow between consecutive C-shaped chambers is simply treated as a reduction in forward flow, which is an unrealistic simplification (Jager et al., 1992). The discretisation procedure allows the separation of the forward flow (due to positive displacement by the screws) and the back-flow (due to leakage around the screw flights) leading to a more accurate flow representation. 3. The model has been extended to include variables which may be helpful for describing product quality. Product gelatinisation, specific volume, specific mechanical energy, and residence time are now predicted by the model. The methods employed to extend the model are described in more detail below THE GELATINISATION MODEL Starch gelatinisation during extrusion is a complex reaction for which the mechanisms are not fully understood. A review of the literature revealed that there have been only two different modelling approaches investigated, those suggested by Wang et al (1992) and Cai and Diosady (1993). Although it is not possible to conclude which of these approaches is the more appropriate at this stage, the model suggested by Cai and Diosady has been validated over a wider range of operating conditions, and is therefore the model chosen for our implementation.
Examples of the dynamic response of starch gelatinisation to changes in feed rate, screw speed and moisture content are shown in Figures 2(a) to 2(c), where inverse response characteristics as well as process dead-time can be observed.
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The predicted residence time distribution of an inert tracer was compared with experimental RTD data obtained by injected sodium chloride at the feed port of the extruder. Figures 3(a) and 3(b) are a comparison between the predicted and measured concentrations of the tracer in the extrudate over time. It can be seen that increasing screw speed has the effect of reducing the "dead-time" of the process, but has little effect on the variance of the distribution. Increasing feed-rate, however, has little effect on the dead-time of the
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Although the gelatinisation model parameters have yet to be determined experimentally for the cooking extruder being studied, parameters were estimated to match reported values of gelatinisation in similar extruders.
RESIDENCE TIME DISTRIBUTION (RTD) The effect of the residence time distribution on product quality is an important consideration, as a high variance for the RTD implies a highly inconsistent degree of cooking for the product. For this reason, it is advantageous to be able to predict the RTD for a given set of operating conditions, so that the extruder can be operated in such a way as to produce a homogeneously cooked product.
(b) Figure 3: Experimental and model predicted RTD curves. process, but leads to a narrower distribution. The excellent fit obtained between the experimental and model predicted RTD curves might be interpreted as further evidence of the general applicability of the model developed here.
EXTRUDATE EXPANSION Extruders are often used to produce puffed products such as breakfast cereals, flat breads and snacks. For such products the expansion ratio is clearly an important quality variable. The model of Fan et al. (1994) which describes the dynamics of bubble growth in starchy extrudates has been implemented in the
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general extruder model to provide predictions of the expansion ratio and bubble size.
A comparison of the model prediction experimental data is presented in Figure 4.
RHEOLOGICAL MODELS
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Dough mixes are non-Newtonian fluids, and their rheological behaviour is quite complex• The selection of a suitable theological model is crucial to the validity of the resulting extruder model, as it directly influences the flow behaviour, heat generation, and pressure development within the extruder. In a previous paper (Elsey et al., 1996) two different power law model structures (those of Kulshreshtha et al., 1991 and Vergnes et al., 1987) were compared for their accuracy at describing experimental extrusion data. However, the power law models that are typically applied often do not have a firm theoretical basis, and are therefore simply correlations of a form that appear to fit experimental data over a reasonable range of conditions.
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It is interesting to note that this model form is efficient in that it contains only six parameters, comparable to the model of Vergnes et al. (1987) which employed seven• Perhaps one advantage of this modelling approach is that other process variables which are not typically considered in extrusion rheological models can be included• For example, if an appropriate sampling valve were used to collect samples of the melt, the degree of cook could be determined and included in the model for melt viscosity• Considering that typical power law rheology models require fitting of their parameters to specific feed materials in any case, there are clearly advantages in evolving an entire rheological model from this experimental data. Having developed a process model that compared well with experimental observations, process control schemes can now be investigated. ADAPTIVE INFERENTIAL EESTIMATION Typical control variables for a cooking extrusion process are product temperature and die temperature• These variables are typically chosen because they give some indication of the state of the process and are easily measured at rates suitable for on-line process control. Ideally however, real quality measures would be the control variables, such as degree of cook, mean residence time, or product expansion ratio. Unfortunately, the feasibility of on-line measurement of these variables is limited as either the instrumentation does not exist or the analysers require long cycle times. The resulting delays would prevent early detection of the effects of load disturbances, resulting in degraded process operation.
PSE '97-ESCAPE-7 Joint Conference Estimators that are capable of alleviating the problem of large measurement delays and irregular sampled feedback have been previously developed (Guilandoust et al., 1987; Tham et al., 1992). Since the primary controlled variable is usually related to other process outputs, the estimators make use of these secondary outputs to infer the state of the primary output each time the secondary outputs are measured. The estimators are implemented within an adaptive framework to ensure their applicability to time varying processes. The parameters of the algorithm are estimated whenever measurements of the primary output become available. As a result, estimates of the primary output are obtained at the faster rate at which the secondary outputs are measured. To assess the feasibility of this adaptive inferential estimator (AIE) for applications to extrusion control, the AIE algorithm of Guilandoust et al., (1987) was used to provide estimates of the product gelatinisation fraction of an extruded starchy material, as simulated by the extruder model described earlier in this work. Product gelatinisation fraction of extruded starchy products can be determined off-line using a rapid viscoanalyser. A typical analysis takes approximately 20 minutes, and thus this measurement would normally be unsuitable for process control purposes. Figure 4 shows the simulated response of product gelatinisation fraction when the extruder model inputs screw speed, moisture content and feed rate are stepped. The estimated output of the AIE algorithm is also shown, and clearly a reasonable estimate of the primary output has been obtained.
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PROCESS CONTROL A preliminary investigation of the suitability of PI and model predictive control (MPC) for single-input-singleoutput control has been performed. Simulations were performed using in turn moisture content, feed rate and screw speed as the manipulated variable to move the degree of gelatinisation between set-points. Results of these simulations are shown in Figure 5. It can be seen that the best control performance was obtained using screw speed as the control variable within a MPC scheme. The use of moisture as a control
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variable was unsuccessful as the range of variation required in the set-point changes could not be achieved via moisture content manipulation. In the case of using feed rate as the manipulated variable, PI control could not be used as the product gelatinisation fraction exhibits an inverse response to changes in feed rate In general, the performance of either moisture content or feed rate as the control variable was far from ideal due to the presence of dead-times between the control
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PSE '97-ESCAPE-7 Joint Conference
action and the process's response. Clearly though, the performance of MPC is far superior to that for PI control. Such a result is expected as MPC has the advantage of having an internal model of the process to use in optimising its control action. CONCLUSIONS An outline of the process systems engineering techniques relevant to the modelling and control of a food extrusion process has been presented. Emphasis has been directed towards the predicting and controlling realistic quality variables such as product gelatinisation fraction in preference to secondary process indicators such as temperature and pressure. A flexible dynamic model of the extrusion process has been developed, rheological modelling investigated, an adaptive inferential estimator for product ge!atinisation fraction developed, and simple control strategies investigated. It is expected that the control of real quality variables will result is a more reliable control scheme. This is the subject of current research. ACKNOWLEDGEMENTS The authors would like to thank Dr Ming Tham for his assistance with the adaptive inferential estimation algorithm implementation, and the CSIRO Department of Food Science and Technology Australia for providing the extrusion data used in theses studies. REFERENCES
Cai, W. and Diosady, L.L. (1993). A model for gelatinisation of wheat starch in a twin-screw extruder. J. Food Sci. 58:872-875, 887. Guilandoust, M.T., Morris, A.J. and Tham, M.T. (1987). Adaptive inferential control, lEE Proceedings, 134d-3, 171-179. Elsey, J., Riepenhausen, J., McKay, B., and Barton, G.W. (1996). Dynamic modelling of a cooking extruder. Chemeca 1996, Sydney, Australia. Fan, J., Mitchell, J.R. and Blanshard, J.M.V. (1994). A computer simulation of the dynamics of bubble growth and shrinkage during extrudate expansion. J. Food Eng. 23, 337-356. Jager, T., van Zuilichem, D.J., Stolp, W. (1992). Residence time distribution, mass flow, and mixing in a co-rotating, twin-screw extruder. In Food Extrusion Science and Technology, J.L. Kokini, C.T. Ho and M. V. Karwe, Eds., Marcel Decker, New York, pp. 165-176. Kulshreshtha, M. K., Zaror, C. A., Jukes, D. J. and Pyle, D. L. (1991). A generalised steady state model for twin screw extruders. Trans IChemE, Part C, Food and Bioproducts Proc., 69 (C4): 189199. Kulshreshtha, M.K. and Zaror, C.A. (1992). An unsteady state model for twin screw extruders. Trans IChemE, Part C, Food and Bioproducts Proc., 70 (C4): 21-28.
McKay, B., Willis, M.J., Barton, G.W., (1996). Steadystate modelling of chemical process systems using genetic programming. Accepted for publication in Comp. and Chem. Eng. Tham, M.T., Montague, G.A. and Morris, A.J., (1991). J. Proc. Cont., 1, 3-14. Wang, S. S., Chiang, W. C., Zheng, X., Zhao, B., Cho, M. H. and Yeh, A. (1992). Application of an energy equivalent concept to the study of the kinetics of starch conversion during extrusion. In Food Extrusion Science and Technology, J.L. Kokini, C. T. Ho and M. V. Karwe, Eds., Marcel Decker, New York, pp. 165-176.