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.
@article{bwmeta1.element.bwnjournal-article-amcv24i1p99bwm,
author = {Krzysztof B. Janiszowski},
title = {Approximation of a linear dynamic process model using the frequency approach and a non-quadratic measure of the model error},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {24},
year = {2014},
pages = {99-109},
zbl = {1292.93085},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv24i1p99bwm}
}
Krzysztof B. Janiszowski. Approximation of a linear dynamic process model using the frequency approach and a non-quadratic measure of the model error. International Journal of Applied Mathematics and Computer Science, Tome 24 (2014) pp. 99-109. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv24i1p99bwm/
[000] Deschrijver, D., Gustavsen, B. and Dhaene, T. (2007). Advancements in iterative methods for rational approximation in the frequency domain, IEEE Transactions on Power Delivery 22(3): 1633-1642.
[001] Deschrijver, D., Knockaert, L. and Dhaene, T. (2010). Improving robustness of vector fitting to outliers in data, IEEE Electronics Letters 46(17): 1200-1201.
[002] Deschrijver, D., Knockaert, L. and Dhaene, T. (2011). Robust macromodeling of frequency responses with outliers, 15th IEEE Workshop on Signal Propagation on Interconnects (SPI), Naples, Italy, pp. 21-24.
[003] Fiodorov, E. (1994). Least absolute values estimation: Computational aspects, IEEE Transactions on Automatic Control 39(3): 626-630. | Zbl 0815.93023
[004] Grivet-Talocia, S., Bandinu, M. and Canavero, F. (2005). An automatic algorithm for equivalent circuit extraction from noisy frequency responses, 2005 International Symposium on Electromagnetic Compatibility, EMC 2005, Zurich, Switzerland, Vol. 1, pp. 163-168.
[005] Gustavsen, B. (2004). Wide band modeling of power transformers, IEEE Transactions on Power Delivery 19(1): 414-422.
[006] Gustavsen, B. (2006). Relaxed vector fitting algorithm for rational approximation of frequency domain responses, IEEE Workshop on Signal Propagation on Interconnects, Berlin, Germany, pp. 97-100.
[007] 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.
[008] Gustavsen, B. and Semlyen, A. (1999). Rational approximation of frequency domain responses by vector fitting, IEEE Transactions on Power Delivery 14(3): 1052-1061.
[009] Janiszowski, K. (1998). Towards least sum of absolute errors estimation, IFAC Symposium on Large Scale Systems LSS'98, Patras, Greece, pp. 613-619.
[010] Kowalczuk, Z. and Kozłowski, J. (2011). Non-quadratic quality criteria in parameter estimation of continuous-time models, IET Control Theory & Applications 5(13): 1494-1508.
[011] Kozłowski, J. (2003). Nonquadratic quality indices in estimation, approximation and control, IEEE Conference MMAR'2003, Mi˛edzyzdroje, Poland, pp. 277-282.
[012] Levy, E.C. (1959). Complex-curve fitting, IRE Transactions on Automatic Control AC-4(1): 37-43.
[013] 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
[014] Ljung, L. and Söderström, T. (1987). Theory and Practice of Recursive Identification, MIT Press, Cambridge, MA. | Zbl 0548.93075
[015] 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 Microwave Theory and Techniques 52(9): 2207-2214.
[016] Pintelon, R. and Schoukens, J. (2004). System Identification: A Frequency Domain Approach, John Wiley & Sons, New York, NY. | Zbl 1293.93221
[017] Sreeram, V. and Agatokhlis, P. (1991). Model reduction of linear discrete-time systems via impulse response Gramians, International Journal on Control 53(1): 129-144. | Zbl 0723.93010
[018] Unbehauen, H. and Rao, G. (1997). Identification of continuous-time systems: A tutorial, 11th IFAC Symposium on System Identification, Kitakyushu, Japan, pp. 1023-1049.
[019] Varricchio, S., Gomes, S. and Martins, N. (2004). Modal analysis of industrial system harmonics using the s-domain approach, IEEE Transactions on Power Delivery 19(3): 1232-1237.
[020] Wahlberg, B. and Mäkilä, P. (1996). On approximation of stable linear dynamical systems using Laguerre and Kautz functions, Automatica 32(5): 693-708. | Zbl 0856.93017
[021] Young, P.C. (1966). Process parameter estimation and self adaptive control, in P.H. Hammnod (Ed.), Theory of Self Adaptive Control Systems, Vol. 1, Plenum Press, New York, NY, p. 118.