on-line estimation a comparison and evaluation of alternative recursive and batchwise approaches
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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?. - PowerPoint PPT PresentationTRANSCRIPT
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On-line estimation
A comparison and evaluation of alternative recursive and batchwise approaches
Tore Lid, On-line estimation
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Outline
• Introduction• The Kalman filter• The Extended Kalman Filter• Moving Horizon Estimator• Simple example• Conclusions
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What is estimation?
Estimation is the calculated approximation of a result which is usable even if input data may be incomplete, uncertain, or noisy.
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Why estimate?
Monitor
Control
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The process model
The process
Measuredoutputs
Measured inputs
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The state space model
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The linear state space model
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The Kalman Filter
A priori estimate
A posteriori estimate
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The Kalman FilterA priori estimate
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The Kalman FilterA posteriori estimate
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The Kalman Filter
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The Kalman Filter
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The Kalman Filter
timet(k) t(k+1)
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Nonlinear state space model
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The Extended Kalman Filter
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The Extended Kalman Filter
Time update Measurement update
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Moving horizon estimator
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Moving horizon estimator
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Moving horizon estimator
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Moving horizon estimator
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ExampleMeasurements:•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
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ExampleLinear state space model
Simulation Estimation
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Example
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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
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Acknowledgements
• Tor Steinar Schei• Magne Hillestad• Stig Strand• Marius Govatsmark
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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