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RECENT PROGRESS AND INDUSTRIAL EXPERIENCES WITH NONLINEAR MODEL IDENTIFICATION FOR MPC APPLICATIONS IN POLYMER MANUFACTURING
14th IFAC Symposium on System Identification, Newcastle, Australia, 2006
RECENT PROGRESS AND INDUSTRIAL EXPERIENCES WITH NONLINEAR MODEL IDENTIFICATION FOR MPC APPLICATIONS IN POLYMER MANUFACTURING Hong Zhao, John Guiver, Paul Turner Aspen Technology, Inc. 2500 City West Blvd., Houston, Texas 77042, USA [email protected] Abstract: One of the most important areas for industrial Nonlinear Model Predictive Control (NMPC) applications has been polymer manufacturing. This brief paper presents recent progress and some of experiences in NMPC applications from industrial practitioners. Several aspects leading to a successful project are covered. Issues and a wish list are also provided for discussion and future research. Copyright © 2006 IFAC Keywords: Nonlinear models, process control, industrial control.
1. INTRODUCTION
2. PROCESS MODELLING
In the process industries, polymer manufacturing has been one of the major and most focused areas for Model Predictive Control (MPC) vendors to invest in nonlinear MPC technologies because of its fast return and significant economic benefits to the manufacturers. After a few years of technology evolution and development, starting with a pilot implementation in 2001, Aspen Technology has gained a large amount of experience in the field in implementing fully non-linear MPC on numerous different types of continuous polymer manufacturing processes. There are many benefits obtained by putting MPC on these industrial units, but one of the main goals is to minimize production of off-spec material both in steady state operation and when transitioning from one product grade to another. This goal raised many practical challenging problems from process modelling to MPC control algorithms. Prior to 2001, implementations using empirical models were typically done with some form of gain adaptation or gain scheduling, which, though suitable for steady state operation, is sub-optimal for transitions. This is due to the fact that process gains often change by an order of magnitude or more over a relatively short period of time, and the nonlinearities involved interact in a multivariate manner and cannot be removed by univariate transforms. Even if the gains are scheduled in a non-linear manner across the transition horizon [Piché et al 2000], this does not take into account these interactions, and no optimized path can be calculated. Recent progress in modelling and control algorithms such as the development of Bounded Derivative Network (BDN) technology (Turner and Guiver, 2005), has successfully addressed these issues, which has resulted in a growing number of successful NMPC applications in the polymer manufacturing processes (Naidoo et. al., 2005, Karagoz et al, 2004).
For an industrial MPC application, process modelling is a key step to its success. Based on industrial NMPC practitioners’ experiences (Naidoo et. al., 2005), the following modelling requirements have been identified for the NMPC applications in polymer industry: - The modelling strategy should allow users to take into account process specific knowledge. - Safe, intelligent and maintainable extrapolation and interpolation – i.e. guaranteed gain behaviour at all operating points. Specifically, gain sign inversion has to be prevented unless it is genuinely present. - Support non-linear dynamics, e.g. a different up and down responses, or rate of change dependent dynamics. - Minimal data requirements – it’s difficult to step test a polymer plant when the unit is not allowed to produce off-specification product. - Support multivariate non-linearity (e.g. multiple catalysts / donors), i.e., model structures where the true process steady state relationships are represented by curved surfaces in N-dimensional space. This implies that the current gain value depends on more than one input variable. Models with these characteristics cannot be linearized by using simple input or output linearization curves. - Fast reliable execution. - Ability to fine-tune the model while commissioning the controller. 2.1 Models Used for NMPC Application Input-Output Models According to limited reports, two representative input-output models often used in Polymer NMPC applications include MVC controller (Continental Controls) and Process Perfector (Pavilion Technologies). Martin et al. (1999) and Piché et al.(2000) described one of the modelling 134
algorithms in details. Their approach uses a static nonlinear model superimposed upon a linear dynamic model. It is assumed that the process input and output can be decomposed into a steady-state portion which obeys a nonlinear static model and deviation potion that follow a dynamic model.
important that the static mapping part of this, which provides the steady state gain information, satisfies the previously stated requirements for control. A major breakthrough in this area came with the development of Bounded Derivative Network (BDN) technology (Turner and Guiver 2005), which has made such structures applied to NMPC a great success. This new modelling method circumvents many real problems associated with standard neural networks in control such as model saturation (zero gain), arbitrary model gain inversion, “black box” representation and inability to interpolate sensibly in regions of sparse excitation. Although extrapolation is typically not an advantage unless the understanding of the process in complete, the BDN model can incorporate process knowledge in order that its extrapolation capability is inherently sensible in areas of data sparsity. This ability to impart process knowledge on the BDN model enables it to be safely incorporated into a model based control scheme. As a result, this new approach allows the building of empirical, fast-executing, control-relevant models that can be embedded directly in a nonlinear control law, removing the need for gain scheduling or pre-calculated gain interpolation completely.
The identification of the linear dynamic model is based on plant test data from pulse tests. To handle the high nonlinearity of the polymer processes, the gain of the low-order linear dynamic model is successively approximated along the control horizon by a linear interpolation of nonlinear gains sourced from a static nonlinear model such as a neural network. This interpolation strategy is superior to gain-scheduling in that it accounts for differences in gain along the horizon. However, the gain profile is pre-calculated at the start of a transition or before each controller cycle (based on the process values at the start and end points) and does not depend on the values of the decision variables within the optimization problem itself, thus making this approach suboptimal. This model also makes the assumption that the process dynamics remain linear over the entire range of operation; symmetric dynamics, e.g. different local time constants, cannot be represented by this model (Qin and Badgwell, 2003).
3. PROCESS EXPERIMENT ISSUES
First Principle Models First principle models are another option for MPC control if such models are available and are suitable for control (i.e. reliably invertible within the control law). Usually it is costly to calibrate such models with accurate dynamic predictions for model predictive control and they are limited in size (due to computational inefficiencies). There have been few reports on NMPC applications in polymer processes by using fully first principles models. It is claimed that NOVA-NLC from DOT products uses first principle models (Young et al., 2001); however, in practice, these models tend to be simple heat and energy balances rather than fullscale rigorous reactor models. The controller described in (Naidoo et al., 2005) also supports first principle models for concentration ratios and other simple input/output relationships, and these are a better option than identified models when such relationships are readily available.
The traditional plant test approach applied in linear MPC projects is challenging for nonlinear cases. It is difficult or impossible to catch all nonlinearities in the process through extensive multi-level plant testing, and traditional step testing or PRBS testing is not usually a practical option in a polymer plant. Fortunately, historical transition data is inherently dynamic – it can be used, along with process knowledge and first principles models if available, to build a model suitable for NMPC. An important point here, which helps to make such industrial applications feasible, is that the dependent variables with the highest non-linearities (i.e. the quality variables) are also the ones with the lowest order dynamics. These are precisely the variables for which good dynamic data typically exists due to historical transitions. For variables that typically run at set point, e.g. pressure, temperature and concentration ratio, etc., traditional testing can be done, because good quality dynamic data is not available for these variables.
In practice, modelling approaches combining first principles knowledge with empirical modelling have become more attractive and feasible. This can take the form of (a) using first principles models outright for some relationships, as described above, and (b) imposing process knowledge on the identification and structure of empirical models as described in the next section.
Recent progress in process modelling for NMPC has shown that the ability to incorporate process knowledge into a process model in a kind of “hybrid” format can lead to excellent practical solutions. For example, the new BDN models allow one to use historical operation data to identify the nonlinear multi-level steady-state model part and impose multiple constraints on model gains from known process knowledge. In such a way, the resulting BDN models will have safe and sensible gains over both in-grade and transitional operation ranges. It is reported that for polymer quality models, they can be very accurately modelled with a low order linear
Non-linear State Space Models Non-linear state space models were introduced into industrial NMPC in 1998 (Zhao et al., 1998, 2001) in the form of a Wiener structure. This structure, consisting of linear dynamics feeding a non-linear static mapping, supports the types of non-linear dynamics needed for Polymer MPC (Sentoni et al., 1998). However, it is 135
dynamic model feeding an empirically identified gain-constrained BDN model. These steady-state nonlinear BDN models can be calibrated on normal historical operating data, or sometimes, even recipe data, thus precluding the need for a plant test in most cases (Naidoo, et al., 2005). The effect of dynamic inaccuracies is reduced because the implementation allows the product quality inferential calculations and the control models to be the same. Measurement feedback is typically only performed at steady state (in-grade operation) where the effect of dynamic inaccuracies is much smaller. This overall approach provides a practical, robust and safe alternative path to achieve reliable, control relevant process models with good confidence and quality.
6. PRACTITIONERS’ WISH LIST - Find more and better ways to impose process and fundamental knowledge onto simple controlsuitable models structures - Bridge the gap between complex continuoustime rigorous models and simple discrete-time models with well-understood gain characteristics - Effective model uncertainty evaluation and validation methods REFERENCES Karagoz, O., J. Versteeg, M. Mercer, P. Turner (2004). Advanced control methods improve polymers' business cycle. Hydrocarbon Processing (April 2004), 45-49 Martin, G.D. (1999). Method and apparatus for dynamic and steady state modelling over a desired path between two end points, US Patent Number 5,933,345. Naidoo, K., J. Guiver, P. Turner, M. Keenan and M. Harmse (2005). Experiences with nonlinear MPC in polymer manufacturing, International Workshop on Assessment and Future Directions of NMPC, Freudenstadt-Lauterbad, Germany, August 26-30, 2005. Piché, S., B. Sayyar-Rodsari, D. Johnson, and M. Gerules (2000). Nonlinear model predictive control using neural networks. IEEE Control Systems Magazine, 53-62. Qin, S.J. and T.A. Badgwell (2003). A survey of industrial model predictive control technology, Control Engineering Practice, 11(7), 733-764. Sentoni, G., L. Biegler, J. Guiver and H. Zhao (1998). State-Space Nonlinear Process Modeling: Identification and Universality, AIChE Journal, 44(10), 2229-2239. Turner, P. and J. Guiver (2005). Introducing the bounded derivative network – superceding the application of neural networks in control, Journal of Process Control, 15 (4),407-415. Young, R.E; R.D. Bartusiak, R. W. and Fontaine (2001). Evolution of an industrial nonlinear model predictive controller, In: Chemical Process Control VI: Sixth International Conference on Chemical Process Control ( Rawlings, J.B., B.A. Ogunnaike, J.W. Eaton (Ed)), AIChE Symposium Series, 98,(326), 342351. Zhao, H., J. Guiver, G. Sentoni (1998), An identification approach to nonlinear state-space model for industrial MPC control, Proc. 1998 American Control Conference, Philadelphia, PA, USA, June 24-26, 1998. Zhao, H., J. Guiver, R. Neelakantan and L.T. Biegler (2001). A nonlinear industrial model predictive controller using integrated PLS and neural net state-space model, Control Engineering Practice, 9, 125-133.
4. KEY ISSUES FOR APPLICATIONS There are many practical matters that impact the success of a polymer control project including technology, process understanding, best-practice methodology, the use of reliable software with suitable functionality, and developing a deep understanding of practical operational requirements. Naidoo, et al. (2005) discussed many of these issues: - Cascaded structure with a master Quality Controller to control the process - Overshoot strategy to speed up grade transition - Optimized transition management for overall benefits; - Building an understandable process model by incorporating process knowledge and gain constraints - Integrated simulation, model validation and control tuning - Using business driven optimization to rank control objectives - Availability of a process recipe manager and grade transition sequencer in order to fully automate/schedule transitional procedures outside of the scope of the controller. 5. APPLICATION BENEFITS Demonstrated project results show: - Capacity Increase: 2-10% - Off-spec reduction during transition: 25-50% - Off-spec reduction during steady state operation: 50-100% The direct quantitative benefits are significant and are typically in the region of US$ 400,000 to US$ 1,000,000 per line per year. In addition, Qualitative benefits include: - Minimizing product transition times - Minimizing variability in quality - Maximizing production capacity - Reducing raw material consumptions - Reducing downtime and maintenance cost - Reducing safety stocks and slow-moving inventory
136
RECENT PROGRESS AND INDUSTRIAL EXPERIENCES WITH NONLINEAR MODEL IDENTIFICATION FOR MPC APPLICATIONS IN POLYMER MANUFACTURING Hong Zhao, John Guiver, Paul Turner Aspen Technology, Inc. 2500 City West Blvd., Houston, Texas 77042, USA [email protected] Abstract: One of the most important areas for industrial Nonlinear Model Predictive Control (NMPC) applications has been polymer manufacturing. This brief paper presents recent progress and some of experiences in NMPC applications from industrial practitioners. Several aspects leading to a successful project are covered. Issues and a wish list are also provided for discussion and future research. Copyright © 2006 IFAC Keywords: Nonlinear models, process control, industrial control.
1. INTRODUCTION
2. PROCESS MODELLING
In the process industries, polymer manufacturing has been one of the major and most focused areas for Model Predictive Control (MPC) vendors to invest in nonlinear MPC technologies because of its fast return and significant economic benefits to the manufacturers. After a few years of technology evolution and development, starting with a pilot implementation in 2001, Aspen Technology has gained a large amount of experience in the field in implementing fully non-linear MPC on numerous different types of continuous polymer manufacturing processes. There are many benefits obtained by putting MPC on these industrial units, but one of the main goals is to minimize production of off-spec material both in steady state operation and when transitioning from one product grade to another. This goal raised many practical challenging problems from process modelling to MPC control algorithms. Prior to 2001, implementations using empirical models were typically done with some form of gain adaptation or gain scheduling, which, though suitable for steady state operation, is sub-optimal for transitions. This is due to the fact that process gains often change by an order of magnitude or more over a relatively short period of time, and the nonlinearities involved interact in a multivariate manner and cannot be removed by univariate transforms. Even if the gains are scheduled in a non-linear manner across the transition horizon [Piché et al 2000], this does not take into account these interactions, and no optimized path can be calculated. Recent progress in modelling and control algorithms such as the development of Bounded Derivative Network (BDN) technology (Turner and Guiver, 2005), has successfully addressed these issues, which has resulted in a growing number of successful NMPC applications in the polymer manufacturing processes (Naidoo et. al., 2005, Karagoz et al, 2004).
For an industrial MPC application, process modelling is a key step to its success. Based on industrial NMPC practitioners’ experiences (Naidoo et. al., 2005), the following modelling requirements have been identified for the NMPC applications in polymer industry: - The modelling strategy should allow users to take into account process specific knowledge. - Safe, intelligent and maintainable extrapolation and interpolation – i.e. guaranteed gain behaviour at all operating points. Specifically, gain sign inversion has to be prevented unless it is genuinely present. - Support non-linear dynamics, e.g. a different up and down responses, or rate of change dependent dynamics. - Minimal data requirements – it’s difficult to step test a polymer plant when the unit is not allowed to produce off-specification product. - Support multivariate non-linearity (e.g. multiple catalysts / donors), i.e., model structures where the true process steady state relationships are represented by curved surfaces in N-dimensional space. This implies that the current gain value depends on more than one input variable. Models with these characteristics cannot be linearized by using simple input or output linearization curves. - Fast reliable execution. - Ability to fine-tune the model while commissioning the controller. 2.1 Models Used for NMPC Application Input-Output Models According to limited reports, two representative input-output models often used in Polymer NMPC applications include MVC controller (Continental Controls) and Process Perfector (Pavilion Technologies). Martin et al. (1999) and Piché et al.(2000) described one of the modelling 134
algorithms in details. Their approach uses a static nonlinear model superimposed upon a linear dynamic model. It is assumed that the process input and output can be decomposed into a steady-state portion which obeys a nonlinear static model and deviation potion that follow a dynamic model.
important that the static mapping part of this, which provides the steady state gain information, satisfies the previously stated requirements for control. A major breakthrough in this area came with the development of Bounded Derivative Network (BDN) technology (Turner and Guiver 2005), which has made such structures applied to NMPC a great success. This new modelling method circumvents many real problems associated with standard neural networks in control such as model saturation (zero gain), arbitrary model gain inversion, “black box” representation and inability to interpolate sensibly in regions of sparse excitation. Although extrapolation is typically not an advantage unless the understanding of the process in complete, the BDN model can incorporate process knowledge in order that its extrapolation capability is inherently sensible in areas of data sparsity. This ability to impart process knowledge on the BDN model enables it to be safely incorporated into a model based control scheme. As a result, this new approach allows the building of empirical, fast-executing, control-relevant models that can be embedded directly in a nonlinear control law, removing the need for gain scheduling or pre-calculated gain interpolation completely.
The identification of the linear dynamic model is based on plant test data from pulse tests. To handle the high nonlinearity of the polymer processes, the gain of the low-order linear dynamic model is successively approximated along the control horizon by a linear interpolation of nonlinear gains sourced from a static nonlinear model such as a neural network. This interpolation strategy is superior to gain-scheduling in that it accounts for differences in gain along the horizon. However, the gain profile is pre-calculated at the start of a transition or before each controller cycle (based on the process values at the start and end points) and does not depend on the values of the decision variables within the optimization problem itself, thus making this approach suboptimal. This model also makes the assumption that the process dynamics remain linear over the entire range of operation; symmetric dynamics, e.g. different local time constants, cannot be represented by this model (Qin and Badgwell, 2003).
3. PROCESS EXPERIMENT ISSUES
First Principle Models First principle models are another option for MPC control if such models are available and are suitable for control (i.e. reliably invertible within the control law). Usually it is costly to calibrate such models with accurate dynamic predictions for model predictive control and they are limited in size (due to computational inefficiencies). There have been few reports on NMPC applications in polymer processes by using fully first principles models. It is claimed that NOVA-NLC from DOT products uses first principle models (Young et al., 2001); however, in practice, these models tend to be simple heat and energy balances rather than fullscale rigorous reactor models. The controller described in (Naidoo et al., 2005) also supports first principle models for concentration ratios and other simple input/output relationships, and these are a better option than identified models when such relationships are readily available.
The traditional plant test approach applied in linear MPC projects is challenging for nonlinear cases. It is difficult or impossible to catch all nonlinearities in the process through extensive multi-level plant testing, and traditional step testing or PRBS testing is not usually a practical option in a polymer plant. Fortunately, historical transition data is inherently dynamic – it can be used, along with process knowledge and first principles models if available, to build a model suitable for NMPC. An important point here, which helps to make such industrial applications feasible, is that the dependent variables with the highest non-linearities (i.e. the quality variables) are also the ones with the lowest order dynamics. These are precisely the variables for which good dynamic data typically exists due to historical transitions. For variables that typically run at set point, e.g. pressure, temperature and concentration ratio, etc., traditional testing can be done, because good quality dynamic data is not available for these variables.
In practice, modelling approaches combining first principles knowledge with empirical modelling have become more attractive and feasible. This can take the form of (a) using first principles models outright for some relationships, as described above, and (b) imposing process knowledge on the identification and structure of empirical models as described in the next section.
Recent progress in process modelling for NMPC has shown that the ability to incorporate process knowledge into a process model in a kind of “hybrid” format can lead to excellent practical solutions. For example, the new BDN models allow one to use historical operation data to identify the nonlinear multi-level steady-state model part and impose multiple constraints on model gains from known process knowledge. In such a way, the resulting BDN models will have safe and sensible gains over both in-grade and transitional operation ranges. It is reported that for polymer quality models, they can be very accurately modelled with a low order linear
Non-linear State Space Models Non-linear state space models were introduced into industrial NMPC in 1998 (Zhao et al., 1998, 2001) in the form of a Wiener structure. This structure, consisting of linear dynamics feeding a non-linear static mapping, supports the types of non-linear dynamics needed for Polymer MPC (Sentoni et al., 1998). However, it is 135
dynamic model feeding an empirically identified gain-constrained BDN model. These steady-state nonlinear BDN models can be calibrated on normal historical operating data, or sometimes, even recipe data, thus precluding the need for a plant test in most cases (Naidoo, et al., 2005). The effect of dynamic inaccuracies is reduced because the implementation allows the product quality inferential calculations and the control models to be the same. Measurement feedback is typically only performed at steady state (in-grade operation) where the effect of dynamic inaccuracies is much smaller. This overall approach provides a practical, robust and safe alternative path to achieve reliable, control relevant process models with good confidence and quality.
6. PRACTITIONERS’ WISH LIST - Find more and better ways to impose process and fundamental knowledge onto simple controlsuitable models structures - Bridge the gap between complex continuoustime rigorous models and simple discrete-time models with well-understood gain characteristics - Effective model uncertainty evaluation and validation methods REFERENCES Karagoz, O., J. Versteeg, M. Mercer, P. Turner (2004). Advanced control methods improve polymers' business cycle. Hydrocarbon Processing (April 2004), 45-49 Martin, G.D. (1999). Method and apparatus for dynamic and steady state modelling over a desired path between two end points, US Patent Number 5,933,345. Naidoo, K., J. Guiver, P. Turner, M. Keenan and M. Harmse (2005). Experiences with nonlinear MPC in polymer manufacturing, International Workshop on Assessment and Future Directions of NMPC, Freudenstadt-Lauterbad, Germany, August 26-30, 2005. Piché, S., B. Sayyar-Rodsari, D. Johnson, and M. Gerules (2000). Nonlinear model predictive control using neural networks. IEEE Control Systems Magazine, 53-62. Qin, S.J. and T.A. Badgwell (2003). A survey of industrial model predictive control technology, Control Engineering Practice, 11(7), 733-764. Sentoni, G., L. Biegler, J. Guiver and H. Zhao (1998). State-Space Nonlinear Process Modeling: Identification and Universality, AIChE Journal, 44(10), 2229-2239. Turner, P. and J. Guiver (2005). Introducing the bounded derivative network – superceding the application of neural networks in control, Journal of Process Control, 15 (4),407-415. Young, R.E; R.D. Bartusiak, R. W. and Fontaine (2001). Evolution of an industrial nonlinear model predictive controller, In: Chemical Process Control VI: Sixth International Conference on Chemical Process Control ( Rawlings, J.B., B.A. Ogunnaike, J.W. Eaton (Ed)), AIChE Symposium Series, 98,(326), 342351. Zhao, H., J. Guiver, G. Sentoni (1998), An identification approach to nonlinear state-space model for industrial MPC control, Proc. 1998 American Control Conference, Philadelphia, PA, USA, June 24-26, 1998. Zhao, H., J. Guiver, R. Neelakantan and L.T. Biegler (2001). A nonlinear industrial model predictive controller using integrated PLS and neural net state-space model, Control Engineering Practice, 9, 125-133.
4. KEY ISSUES FOR APPLICATIONS There are many practical matters that impact the success of a polymer control project including technology, process understanding, best-practice methodology, the use of reliable software with suitable functionality, and developing a deep understanding of practical operational requirements. Naidoo, et al. (2005) discussed many of these issues: - Cascaded structure with a master Quality Controller to control the process - Overshoot strategy to speed up grade transition - Optimized transition management for overall benefits; - Building an understandable process model by incorporating process knowledge and gain constraints - Integrated simulation, model validation and control tuning - Using business driven optimization to rank control objectives - Availability of a process recipe manager and grade transition sequencer in order to fully automate/schedule transitional procedures outside of the scope of the controller. 5. APPLICATION BENEFITS Demonstrated project results show: - Capacity Increase: 2-10% - Off-spec reduction during transition: 25-50% - Off-spec reduction during steady state operation: 50-100% The direct quantitative benefits are significant and are typically in the region of US$ 400,000 to US$ 1,000,000 per line per year. In addition, Qualitative benefits include: - Minimizing product transition times - Minimizing variability in quality - Maximizing production capacity - Reducing raw material consumptions - Reducing downtime and maintenance cost - Reducing safety stocks and slow-moving inventory
136