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Identification for industrial model-based control

This survey explores the industry's use of models for Model Predictive Control (MPC), focusing on identification techniques and future trends. It delves into why industries prefer black-box models over first principles. Topics include linear and non-linear models, future directions, and industrial MPC formulations.

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Identification for industrial model-based control

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  1. Identification for industrial model-based control Vidar Alstad Department of Chemical Engineering NTNU June 8, 2005

  2. NOT IN ORIGINAL PRESENTATION! Title: "Identification for industrial model-based control. " Deatils: The committee would like a survey of what kind of models (soft/hard) are used by industry for model predictive control (MPC), how the models are identified, and the expected future direction. The candidate should also address the following question: "Why does industry today use almost exclusively black-box (soft) models?"

  3. Outline • Scope of presentation • Introduction & brief history of MPC • Model identification • Linear models used in industrial MPC • Non-linear models in industrial MPC • Future directions • Why still black-box models? • Concluding remarks

  4. Model based control (Brosilow and Joseph, 2001 ) Examples: Internal model control (Morari and Zafiriou, 1989) Model predictive control (Richalet et al, 1976, Cutler and Ramaker, 1979) Black-box and first principles Scope of presentation ”Control systems that explicitely embed a process model in the control algorithm”

  5. Predictive models Based on the current measured variables and the current and future inputs, the model must predict the future outputs (Rossitier, 2003) • Steady-state models Often steady-version of the above dynamic model or a separate comprehensive model (Qin and Badgwell, 2003) Scope of presentation • Types of models formulations used in MPC • Continuous processes

  6. Model predictive control (Gorinevsky, 2005) control horizon • At each time step, compute the optimal control inputs over the control horizon by solving an open loop optimization problem over the prediction horizon taking constraints into account • Apply the first value of the computed control input into the process • At the next time step, redo the calculation

  7. Control horizon Prediction horizon Prediction model Industrial MPC formulation

  8. Brief history of industrial MPC • LQR (Kalman, 1964) • Little impact in process industries due to lack of constraint handling (Richalet et al., 1976, Garcia et al. 1989) • IDCOM and DMC (Richalet et al., 1976, Cutler and Ramaker, 1979) • Input/output representation • Ad hoc constraint handling • QDMC (Cutler et al., 1983) • Explicit constraint handling (improved DMC) • IDCOM-M, HIECON, SMCA and SMOC (late 1980-1990s) • State space representation • Hard constraints and priorities • DMC-plus and RMPCT (2000+) • Improved identification technology • Non-linear MPC (Aspen, DOT-products)

  9. Industrial usage of MPC • Factors for widespread usage in process industries (Piche, et al. 2000) • Open-loop settling time minutes or hours • Well suited for multivariable control (MIMO) • Explicit constraint handling • Empirical modelling tools • Standard in refining, chemical, petrochemical, pulp and paper and food processing. • Many industrial commercial vendors.

  10. Non-exhaustive MPC Vendor List (Allgöwer, 2004) • ABB • ACT • Adaptics • Adaptive Resources • Adersa • Aspen Technology • Aurel Systems Inc. • Batch CAD • Bonner and Moore • Brainwave • C.F. Picou and Associates • Chemstations • Comdale Technologies • Control Arts Inc. • Control Consulting Inc. • Control Dynamics • Controlsoft Incorporated • Cybosoft • Cybernetica • DOT Products Objectspace Optimal Control Research Pavilion Technologies Predictive Control Ltd. Predictor Process System Consultants RSI Simulation and Advanced Simtech Texas Controls Inc. Trieber Controls Yokogawa APC US Process Control L.L.C. Eldridge Engineering Inc. Elsag Bailey Envision Systems Inc. Gensym Enterprise Control Technologies Fantoft Process Group MATHWORKS Honeywell Inferential Control Company IntellOpt Knowledgescape MDC Technology Neuralware Nexus Engineering

  11. Basics of identification • Introduce a sequence of inputs ujk • yjk contain the process information • By treating the time series of yk with uk , a model can be estimated. • Near all model types need experiments PROSESS Identification method Model Identification for MPC ”In a typical commissioning project, modeling efforts can take up to 90% of the cost and time” (Andersen and Kummel, 1992). ”Model identification is clearly the ”Achilles heel” of MPC (or any other model-based controller design technique)” (Ogunnaike and Ray, 1994)

  12. Instrument verification Time to steady-state (TSS) Data for initial identification Steps in industrial identification(Söderström and Stoica, 1989) Pre-test • Sequential • Simultanious • Signal type (PRBS or step) Test protocol Model • Model formulation to use Model identification • Model parameter estimation • Equation error • Output error Model validation Model validation: Measure goodness of model No Accept?

  13. Pre-test and test protocol Pre-test • Pre-testing (Seborg et al., 2004) • Estimate process gains • Time constants • Time delays • Plant instrumentation verification Test protocol Model • Test protocol • Signal type • Sequential vs. simultaneous • Closed loop or open loop Model identification Model validation Accept?

  14. MPC relevant signal design (McLellan, 2004) Require good estimate on steady-state gain and slower dynamics power Higher frequencies handled by the regulatory control layer. frequency Test signals for MPC identification • Data from tests should be informative, e.g. contain information on sufficient distinct frequencies. (Ljung, 1999). • Industrial test signals (McLellan, 2004) • Step signals • Pseudo-Random Binary signals (PRBS)

  15. power power frequency frequency Test signals for MPC identification PRBS y u y u STEP t t t t Provides good information on steady-state gain and higher frequencies. Provides very good information on steady-state gain Limited information on higher frequencies • Input magnitude • Duriation • Input magnitude • Duration • Minimum switching time • Desired frequency content

  16. Test signals and identification( Qin and Badgwell, 2003; Conner and Seborg, 2004; Morari and Lee, 1999; Li and Lee, 1996) • Open loop and sequential • Step • Easy to administer and easier to interpret data • Long test time • SISO identification • Easy identify model structure • No information on directionality • Good individual SISO match (either step or frequency response), poor MIMO model. • MISO identification • Simultanious excitation signals • Output models fit one-by-one • Better disturbance model • No information on directionality • Process upset • Open loop and simultanious

  17. Model formulation in industrial MPC (Qin and Badgwell, 2003) Non-linear Pre-test • Input/Output models • Nonlinear neural net (NNN) + auto-regressive with exogenous inputs (ARX) • State space • Nonlinear state space model (LSS) (NNN) • Nonlinear state space • Hybrid models Test protocol Model Empirical First principles Model identification • Input/Output models • Finite impulse response (FIR) • Finite step response (FSR) • Laplace transfer function (TF) • Auto-regressive with exogenous inputs (ARX) • State space • Linear state space model (LSS) Model validation Accept? Linear

  18. Non-linear Linear models Empirical • Majority of industrial MPC applications use linear empirical models (Qin and Badgewell, 2003) Linear • Input/Output models • Finite impulse response (FIR) • Finite step response (FSR) • Laplace transfer function (TF) • Auto-regressive with exogenous inputs (ARX) • State space • Linear state space model (LSS)

  19. Finite Step Response Parameters si is the sampled output after a unit step input Non-linear Input/output modelsFIR and FSR Empirical First principles Nonparametric models • Finite Impulse Response Linear • Parameters hi are the sampled output after a unit impulse input

  20. Non-linear Input/output modelsFIR and FSR (Qin and Badgwell, 2003; Ljung, 1999) Empirical First principles • General Finite Impulse Response (FIR) Linear • General Finite Step Response (FSR)

  21. Non-linear Input/output modelsFIR and FSR (Zhu et al., 2000, Ljung, 1999; Qin and Badgwell, 2003) Empirical First principles • Finite impulse response (FIR) and Finite step response (FSR) model • Can handle complex dynamics • Time delays, inverse response • Little prior process knowledge needed • Time to steady state (TTSS) • Nu,Nd,Nv • Model identification • No bias in parameters due to measurement noise • Bias due to truncation • Over-parametrized • Sample time selected so 30-120 coefficients describe the full open loop response • Cannot handle unstable or integrating processes • Output feedback Linear

  22. General MIMO Polynomial matrices, e.g. Non-linear Input/output modelsARX (Zhu et al., 2000; Ljung, 1999; Qin and Badgwell, 2003) Empirical First principles Parametric models Linear Autoregressive model with exogenous inputs (ARX) Example

  23. FIR special type of ARX Non-linear Input/output modelsARX (Zhu et al., 2000; Ljung, 1999; Qin and Badgwell, 2003) Empirical First principles Same autoregressive part for inputs and disturbances Disturbances enter near input of process (same denominator term) Handles stable, unstable and integrating dynamics Model order Linear v Ev  u B S S A-1 y • Other parametric models used • Box-Jenkins • Transfer function (converted to discrete time) Ed d

  24. Non-linear Empirical First principles Linear State space models (Qin and Badgwell, 2003) • Discrete state space • Handles stable, unstable and integrating processes • Systematic output feedback (Kalman filter) • Distinction between controlled and feedback variables • Unmeasured disturbance models • Linearized first principle model • Used in research literature

  25. Linear model identification (Qin and Badgwell, 2003) Pre-test • Prediction error methods • Minimize a least square criterion Test protocol using either Model • Equation error approach (one step ahead prediction) • Output error approach (multi step ahead prediction) Model identification • Finite impulse and step response (FIR and FSR) yield linear least square. Model validation Accept? • Predictor

  26. Equation error identification approach Linear least square Output error identification approach Nonlinear parameter estimation Linear model identification ARX (Qin and Badgwell, 2003) Prediction error • Past measurements fed back in model • Preferred industrial implementation • Parameter estimates biased given white measurement noise • One-step ahead prediction • Past estimates fed back in model • Numerically more challenging • Gauss-Newton methods • Gradient descent methods • Global methods • Parameter estimates unbiased • Multi-step ahead prediction

  27. Linear model identification state space models • Based on subspace model identification (Van Overschee, 1996) • Efficient method for estimating MIMO models as compared to existing PEM methods (Favoreel, et al, 2000) • Two step procedure • Estimate the state sequence from input/output data • Linear regression to find the system matrices • Can yield suboptimal estimates as compared to existing PEM methods (Van Overschee, 1996)

  28. Nonparametric models (FIR and FSR) Bias error due to truncation Poor with fast/slow dynamics Non-compact. Unable to model unstable and integrating processes Ad hoc bias sceeme output feedback Linear least square for parameter estimation Little process knowledge needed Parametric models (ARX and state space) Order selection (ARX) Ad hoc bias sceeme output feedback (ARX) No bias (if sufficient order) (ARX) Compact Handles unstable and integrating processes MIMO identification (state space) Output feedback (state space) Linear models – Summary(Qin and Badgwell,2003; Zhu and Butoyi, 2002; Ljung, 1999)

  29. Model formulation in industrial MPC (Qin and Badgwell, 2003) Non-linear Pre-test • Input/Output models • Nonlinear neural net (NNN) + auto-regressive with exogenous inputs (ARX) • State space • Nonlinear state space model (LSS) (NNN) • Nonlinear state space • Hybrid models Test protocol Model Empirical First principles Model identification • Input/Output models • Finite impulse response (FIR) • Finite step response (FSR) • Laplace transfer function (TF) • Auto-regressive with exogenous inputs (ARX) • State space • Linear state space model (LSS) Model validation Accept? Linear

  30. Non-linear Non-linear empirical models Empirical First principles Linear • Input/Output models • Nonlinear neural net (NNN) + auto-regressive with exogenous inputs (ARX) • State space • Nonlinear state space model (LSS) (NNN)

  31. Non-linear Input/output (Piche et al., 2000, Qin and Badgwell, 2003) Empirical First principles • Pavilion • Steady-state nonlinear model superimposed on a linear dynamic model Linear • Second order linear model for dynamics • Open loop step response for identification • Steady state nonlinear part modeled as a bounded derivative neural net. • Trained using historical closed loop data

  32. Non-linear State space( Zhao et al. ,1998;2001) Empirical First principles • Aspen Apollo™ Linear • Claimed that above model can approximate any discrete time nonlinear process with fading memory (Sentoni et al., 1998) • Bounded derivative network (Turner and Guiver, 2005) • Calculated bounds (max/min) on the gains • Globaly constrained, i.e. smooth transition to a linear approximation (constant gain) in regions of extrapolation. • Identification • MISO identification of linear state space model using Principal Component Analysis and Partial least squares methods • Neural net trained on prediction error for the linear model

  33. Non-linear Non-linear first principle models Empirical First principles • Mass, energy and impulse conservation equations (Kouvaritakis and Cannon, 2001) Linear • Empirical data needed • Plant data not sufficient • Uncertain parameters estimated using least square (Young, et al. 2001) • Robustness and reliablility of identification algorithm • “Art” in estimation of the parameters. (Young, et al. 2001) • Nonlinear test signal design • Open topic (Morari et al., 1999)

  34. Future directions Linear models • Parametric models (Qin, 2005) • State space representation (Qin and Badgwell, 2003) • Subspace identification methods • Output feedback Non-linear models • Non-linear empirical models (Piche et al., 2000) • Extensive testing • First principle models • Modeling and identification • Servo control problem with changes in operating point Identification • MIMO identification

  35. Why does industry still use black-box models? • Why not first principle nonlinear models? • Modeling and maintenance cost (Pische, 2000) • Justification criteria • Often process and operation specific • Test signal and identification (Morari and Lee, 1999) • Modeling tools • Non-convex online optimization, computationally expensive (Morari and Lee, 1999) • Historical reasons • Regulator problem • Sufficient performance using a linear models (Keep it simple!) • Non-linearities handled by variable transformations • Easy to identify • Linear least square (ARX, FIR/FSR) • Subspace methods • Efficient online optimization • Empircal nonlinear models • “… next step beyond linear modeling of chemical processes.’’ (Henson and Seborg, 1997)

  36. Concluding remarks • Predictive models for MPC • Linear empirical models • Sequential and open loop testing • Non-linearity addressed using empirical models (e.g. neural net) • First principle models not widely used due to cost of design and maintenance • Improvements in identification technology would have an positive impact on MPC technology Acknowledgements: Bjørn Glemmestad, Vinay Kariwala, Audun Faanes, Tor Steinar Schei, Stig Strand, Kjetil Fjaalestad, Svein Olav Hauge and Olav Slupphaug

  37. Bibliography • C. Brosilow and B. Joseph. Techniques of Model-Based Control. Prentice Hall International Series, 2001. • M. Morari and E. Zafiriou, Robust Process Control, Prentice-Hall, Englewood Cliffs, 1989 • J. A. Rossitier, Model based predictive control – A practical Approach, CRC Press, 2003 • J. R. Parrish and C. B. Brosilow, Inferential Control Algorithms, Automatica, 21(5):527-538, 1985. • J. Richalet, A. Rault, J.L. Testrud, J. Papon, Algorithmic control of industrial processes, In Proceedings of the 4th IFAC symposium on identification asd system parameter estimation., 1976. • C.R. Cutler and B.L. Ramaker. Dynamic matrix control- a computer control algorithm. AIChE national meeting, Houstin TX, 1979 • R. Kalman, When is a linear control system optimal?, Journal of Basic Engineering, Transactions on ASME, Series D, 86 • B. Kouvaritakis and M. Cannon (Editors), Nonlinear predictive control – theory and practice, IEE Control engineering series 61, 2001. • M. Nikolaou, Model Predictive Controllers: A Critical Synthesis of Theory and Industrial Needs. accepted, Advances in Chemical Engineering Series, Academic Press, 1998 • S. Piche, B. Sayyar-Rodsari, D. Johnson and M. Gerules, Nonlinear model predictive control using neural networks. IEEE Control Systems Magazine, 2000. • C.R. Cutler, A. Morshedi and J. Haydel. An industrial perspective on advanced control. In AIChE annual meeting, Washington, DC, 1983. • E. Demoro, C. Axelrud, D. Johnston and G. Martin, Neural network modelling and control of polypropylene process, Society of Plastics Engineers International Conference, Houston TX, 1997. • B.A. Ogunnaike and W.H. Ray. Process Dynamics, Modeling and Control. Oxford University Press, 1994 • Y. Zhu, E. Arrieta, F. Butoyi, and F. Cortes. Parametric versus nonparametric models in MPC process identification. Hydrocarbon Processing, 79(2), 2000. • T. Söderström and P. Stoica, System identification, Prentice Hall Int., 1989 • D.E. Seborg, T. Edgar and D.A. Mellichamp, Process Dynamics and Control, 2nd edition, Wiley, 2004. • H.W. Andersen, and M. Kummel, Evaluating estimation of gain directionality—Part 2: a case study of binary distillation. Journal of Process Control, 2 (2), 67–86, 1992 • W. Li, and J.H. Lee, Frequency-domain closed-loop identification of multivariable systems for feedback control. AIChE Journal, 20, 2813–2827, 1996 • W. S. Levine, The Control Handbook, CRC Press, 1995 • L. Ljung, System Identification, 2nd ed, Prentice Hall, 1999 • Y. Zhu, Case studies on closed loop identification for MPC, Control Engineering Practice, 10, 2002

  38. Bibliography (2) • Y. Zhu, Multivariable process identification for MPC, Journal of Process Control, 8(2), 1998 • J.S. Conner and D.E Seborg, An evaluation of MIMO Input design for Process identification, Ind.Eng.Chem.Res, 43, 2004 • Y. Zhu, E. Arrieta, F. Butoyi and F. Cortes, Parametric versus nonparametric models in MPC process identification, • H.Zhao, J. Guiver and G. Sentino, An identification approach to nonlinear state space model for industrial multivariable model predictive control, Proceedings of the American Control Conference, June, 1998 • H. Zhao, J. Guiver, R. Neelakantan, L.T. Biegler, A nonlinear industrial model predictive controller using integrated PLS and neural net state-space model, Control Engineering Practice, 9, 2001 • R.B. Gopaluni, R.S. Patwardhan and Shah, S.L., MPC relevant identification – tuning the noise model, Journal of Process Control, 14, 2004 • P., Van Overschee, B, DeMoor, Subspace Identification for Linear Systems: Theory-Implementation-Applications. Kluwer Academic Publishers 1996. • G. B. Sentoni, L. T. Biegler, J.B. Guiver, & H. Zhao, State space non-linear process modeling, AiChE Journal, 1998. • P. Turner and J. Guiver, Introducing the bounded derivative network-superceding the application of neural networks in control, Journal of Process Control, 15, 2005. • Aspen Tech., Aspen Apollo™ - Non-Linear Advanced Control Solution for Polymers, http://www.aspentech.com/brochures/Aspen_Apollo.pdf, 2005 • F.Allgöwer, Presentation held at APACT’04, Bath, April 26-28, 2004 • S.J. Qin and T.A. Badgwell, An overview of nonlinear model predictive control applications, In J.C. Kantor, C.E. Garciea & B. Carnahan (Eds.), Nonlinear model predictive control. Basel: Birkhauser, 2000 • M. McLellan, Course notes, CHEE825/435, 2004 • N. Bonavita, R. Martini and T. Matsko, Improvment in the Performance of Online Control Applications via Enhanced Modeling Techniques, ERTC Computing, Milano, 2003 • E.F. Camacho and C. Bordons, Model Predictive Control, Springer, 2000 • R.E. Young, R.D. Burtusiak and R.W. Fontaine, Evolution of an Industrial Nonlinear Model Predictive Controller, CPC 6, Arizona, 2001 • M. Henson and D.E. Seborg, Nonlinear Process Control, Prentice Hall, 1997

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