Abstract
For many real processes, the parameters of the governing linear difference equations are not constant. They rather vary over time due to internal or external influences. Also, quite often non-linear processes can only be linearized in a small interval around the current operating point. If the operating point changes, also the linearized dynamics will change in this case. For slow changes of the operating point, one can obtain good results with linear difference equations that contain time-varying parameters. The method of recursive least squares (see Chap. 9) can also be used to identify time-varying parameters. Different methods are introduced in the following that allow to track the changes of time varying parameters with the method of least squares.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Eykhoff P (1974) System identification: Parameter and state estimation. Wiley-Interscience, London
Fortescue TR, Kershenbaum LS, Ydstie BE (1981) Implementation of self-tuning regulators with variable forgetting factor. Automatica 17(6):831–835
Goodwin GC, Sin KS (1984) Adaptive filtering, prediction and control. Prentice-Hall information and system sciences series, Prentice-Hall, Englewood Cliffs, NJ
Gröbner W (1966) Matrizenrechnung. BI-Hochschultaschenbücher Verlag, Mannheim
Hu XL, Ljung L (2008) New convergence results for the least squares identification algorithm. In: The International Federation of Automatic Control (ed) Proceedings of the 17th IFAC World Congress, Seoul, Korea, pp 5030–5035
Isermann R (1992) Identifikation dynamischer Systeme: Besondere Methoden, Anwendungen (Vol 2). Springer, Berlin
Isermann R, Lachmann KH, Matko D (1992) Adaptive control systems. Prentice Hall international series in systems and control engineering, Prentice Hall, New York, NY
Kofahl R (1988) Robuste parameteradaptive Regelungen: Fachberichte Messen, Steuern, Regeln Nr. 19. Springer, Berlin
Lai TC, Wei CZ (1982) Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. Ann Stat 10(1):154–166
Mikleš J, Fikar M (2007) Process modelling, identification, and control. Springer, Berlin
Siegel M (1985) Parameteradaptive Regelung zeitvarianter Prozesse. Studienarbeit. Institut für Regelungstechnik, TH Darmstadt, Darmstadt
Söderström T, Ljung L, Gustavsson I (1974) A comparative study of recursive identification methods. Report 7427. Dept. of Automatic Control, Lund Inst of Technology, Lund
Young PC (2009) Time variable parameter estimation. In: Proceedings of the 15th IFAC Symposium on System Identification, Saint-Malo, France
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer Berlin Heidelberg
About this chapter
Cite this chapter
Isermann, R., Münchhof, M. (2011). Parameter Estimation for Time-Variant Processes. In: Identification of Dynamic Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78879-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-540-78879-9_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78878-2
Online ISBN: 978-3-540-78879-9
eBook Packages: EngineeringEngineering (R0)