Pole identification using discrete Laguerre expansion and variable projection

Dózsa, Tamás and Szabari, Mátyás and Soumelidis, Alexandros and Kovács, Péter (2023) Pole identification using discrete Laguerre expansion and variable projection. In: 22nd IFAC World Congress, 2023.07.09-2023.07.14, Yokohama, Japan. (In Press)

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Abstract

We propose a novel algorithm for identifying the poles of transfer functions describing SISO-LTI (single input single output, linear time invariant) systems. Our identification method works in the frequency domain and consists of two parts. In the first part, we extend a discrete Laguerre expansion based method with an automatic parameter selection scheme. This allows us to find an initial estimate of the poles of SISO-LTI transfer functions without the need for human intuition. Then, in the second part, we propose a novel optimization problem to improve our initial estimates. The proposed optimization aims to reduce the least squared error of a parameterized model, which can be interpreted as an orthogonal projection of the system’s frequency response onto a subspace spanned by Generalized Orthogonal Rational Basis functions (GOBFs). We solve the corresponding nonlinear optimization task using gradient based methods, where we can analytically calculate the gradient of the error functional. Through robust numerical experiments, we investigate the behavior of the developed methods and show that they work even in scenarios, when the transfer function has a high number of poles.

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