Approximation of a linear dynamic process model using the frequency approach and a non-quadratic measure of the model error

Janiszowski, Krzysztof B

doi:10.2478/amcs-2014-0008

Abstract

The paper presents a novel approach to approximation of a linear transfer function model, based on dynamic properties represented by a frequency response, e.g., determined as a result of discrete-time identification. The approximation is derived for minimization of a non-quadratic performance index. This index can be determined as an exponent or absolute norm of an error. Two algorithms for determination of the approximation coefficients are considered, a batch processing one and a recursive scheme, based on the well-known on-line identification algorithm. The proposed approach is not sensitive to local outliers present in the original frequency response. Application of the approach and its features are presented on examples of two simple dynamic systems.

References

Deschrijver, D., Gustavsen, B. and Dhaene, T. (2007). Advancements in iterative methods for rational approximation in the frequency domain, IEEE Transactionson Power Delivery 22(3): 1633-1642.10.1109/TPWRD.2007.899584
Search in Google Scholar
Deschrijver, D., Knockaert, L. and Dhaene, T. (2010). Improving robustness of vector fitting to outliers in data, IEEE ElectronicsLetters 46(17): 1200-1201.10.1049/el.2010.1364
Search in Google Scholar
Deschrijver, D., Knockaert, L. and Dhaene, T. (2011). Robust macromodeling of frequency responses with outliers, 15thIEEE Workshop on Signal Propagation on Interconnects(SPI), Naples, Italy, pp. 21-24.
Search in Google Scholar
Fiodorov, E. (1994). Least absolute values estimation: Computational aspects, IEEE Transactions on AutomaticControl 39(3): 626-630.10.1109/9.280775
Search in Google Scholar
Grivet-Talocia, S., Bandinu, M. and Canavero, F. (2005). An automatic algorithm for equivalent circuit extraction from noisy frequency responses, 2005 International Symposiumon Electromagnetic Compatibility, EMC 2005, Zurich,Switzerland, Vol. 1, pp. 163-168.
Search in Google Scholar
Gustavsen, B. (2004). Wide band modeling of power transformers, IEEE Transactions on Power Delivery19(1): 414-422.10.1109/TPWRD.2003.820197
Search in Google Scholar
Gustavsen, B. (2006). Relaxed vector fitting algorithm for rational approximation of frequency domain responses, IEEEWorkshop on Signal Propagation on Interconnects,Berlin, Germany, pp. 97-100.
Search in Google Scholar
Gustavsen, B. and Mo, O. (2007). Interfacing convolution based linear models to an electromagnetic transients program, Conference on Power Systems Transients, Lyon, France, pp. 4-7.
Search in Google Scholar
Gustavsen, B. and Semlyen, A. (1999). Rational approximation of frequency domain responses by vector fitting, IEEETransactions on Power Delivery 14(3): 1052-1061.10.1109/61.772353
Search in Google Scholar
Janiszowski, K. (1998). Towards least sum of absolute errors estimation, IFAC Symposium on Large Scale SystemsLSS’98, Patras, Greece, pp. 613-619.
Search in Google Scholar
Kowalczuk, Z. and Kozłowski, J. (2011). Non-quadratic quality criteria in parameter estimation of continuous-time models, IET Control Theory & Applications5(13): 1494-1508.10.1049/iet-cta.2010.0310
Search in Google Scholar
Kozłowski, J. (2003). Nonquadratic quality indices in estimation, approximation and control, IEEE ConferenceMMAR’2003, Mi˛edzyzdroje, Poland, pp. 277-282.
Search in Google Scholar
Levy, E.C. (1959). Complex-curve fitting, IRE Transactions onAutomatic Control AC-4(1): 37-43.10.1109/TAC.1959.6429401
Search in Google Scholar
Lima, A.C.S., Fernandes, A. and Carneiro, S., J. (2005). Rational approximation of frequency domain responses in the s and z planes, IEEE Power Engineering Society General Meeting,San Francisco, CA, USA, Vol. 1, pp. 126-131
Search in Google Scholar
Ljung, L. and Söderström, T. (1987). Theory and Practice ofRecursive Identification, MIT Press, Cambridge, MA.
Search in Google Scholar
Mohan, R., Choi, M.J., Mick, S., Hart, F., Chandrasekar, K., Cangellaris, A., Franzon, P. and Steer, M. (2004). Causal reduced-order modeling of distributed structures in a transient circuit simulator, IEEE Transactions on MicrowaveTheory and Techniques 52(9): 2207-2214.10.1109/TMTT.2004.834588
Search in Google Scholar
Pintelon, R. and Schoukens, J. (2004). System Identification:A Frequency Domain Approach, John Wiley & Sons, New York, NY.
Search in Google Scholar
Sreeram, V. and Agatokhlis, P. (1991). Model reduction of linear discrete-time systems via impulse response Gramians, InternationalJournal on Control 53(1): 129-144.10.1080/00207179108953613
Search in Google Scholar
Unbehauen, H. and Rao, G. (1997). Identification of continuous-time systems: A tutorial, 11th IFAC Symposiumon System Identification, Kitakyushu, Japan, pp. 1023-1049.
Search in Google Scholar
Varricchio, S., Gomes, S. and Martins, N. (2004). Modal analysis of industrial system harmonics using the s-domain approach, IEEE Transactions on Power Delivery19(3): 1232-1237. 10.1109/TPWRD.2004.829943
Search in Google Scholar
Wahlberg, B. and Mäkilä, P. (1996). On approximation of stable linear dynamical systems using Laguerre and Kautz functions, Automatica 32(5): 693-708.10.1016/0005-1098(95)00198-0
Search in Google Scholar
Young, P.C. (1966). Process parameter estimation and self adaptive control, in P.H. Hammnod (Ed.), Theory of SelfAdaptive Control Systems, Vol. 1, Plenum Press, New York, NY, p. 118. 10.1007/978-1-4899-6289-8_14
Search in Google Scholar

Approximation of a linear dynamic process model using the frequency approach and a non-quadratic measure of the model error

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