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On-line estimation A comparison and evaluation of alternative recursive and batchwise approaches

On-line estimation A comparison and evaluation of alternative recursive and batchwise approaches. Tore Lid, On-line estimation. Outline. Introduction The Kalman filter The Extended Kalman Filter Moving Horizon Estimator Simple example Conclusions. What is estimation?.

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On-line estimation A comparison and evaluation of alternative recursive and batchwise approaches

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  1. On-line estimation A comparison and evaluation of alternative recursive and batchwise approaches Tore Lid, On-line estimation

  2. Outline • Introduction • The Kalman filter • The Extended Kalman Filter • Moving Horizon Estimator • Simple example • Conclusions

  3. What is estimation? Estimation is the calculated approximation of a result which is usable even if input data may be incomplete, uncertain, or noisy.

  4. Why estimate? Monitor Control

  5. The process model The process Measured inputs Measured outputs

  6. The state space model

  7. The linear state space model

  8. The Kalman Filter A priori estimate A posteriori estimate

  9. The Kalman Filter A priori estimate

  10. The Kalman Filter A posteriori estimate

  11. The Kalman Filter

  12. The Kalman Filter

  13. The Kalman Filter time t(k) t(k+1)

  14. Nonlinear state space model

  15. The Extended Kalman Filter

  16. The Extended Kalman Filter Time update Measurement update

  17. Moving horizon estimator

  18. Moving horizon estimator

  19. Moving horizon estimator

  20. Moving horizon estimator

  21. Example • Measurements: • Mass in Eq. Tank • Mass in Tank 1 • Mass in Tank 2 • Mass in Tank 3 • Waste liquid mass flow Objective: Estimate possible tank leakage

  22. Example Linear state space model Simulation Estimation

  23. Example

  24. Conclution • Extended Kalman filter • Has a fixed computational load • Linearization degrades the performance • Does not handle constraints on states and disturbances • Moving horizon estimator • Handle constraints on states and disturbances • Should be used with care, may have negative side effects • No linearization of nonlinear process models • The computation of the arrival cost is still a challenge • High computational load for large systems • R and Q has to be estimated

  25. Acknowledgements • Tor Steinar Schei • Magne Hillestad • Stig Strand • Marius Govatsmark

  26. References • [1] Tor Steinar Schei, On-line Estimation for Process Control and Optimization Applications, Presented at DYCOPS June 6-8th 2007, 8th International Symposium on Dynamics and Control of Process Systems • [2] C.V. Rao and J. B. Rawlings, Constrained Process Monitoring: Moving Horizon Approach, AIChE Journal, 2002, 48, 1, 97-108 • [3] G. Welch and G. Bishop, An Introduction to the Kalman Filter, University of North Carolina at Chapel Hill, Department of Computer Science,TR 95-041 • [4] E. L Haseltine and J. B. Rawlings, A Critical Evaluation of Extended Kalman Filter and Moving Horizon Estimation, Ind. Chem. Eng. Res. 2005, 44, 2451-2460

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