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On optimal input signal design for frequency response estimation
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. (System Identification Group)ORCID iD: 0000-0002-1927-1690
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-9368-3079
Uppsala University.
2010 (English)In: 49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC), IEEE , 2010, 302-307 p.Conference paper (Refereed)
Abstract [en]

This paper studies optimal input excitation design for parametric frequency response estimation. The objective is to minimize the uncertainty of functions of the frequency response estimate at a specified frequency ω while limiting the power of the input signal. We focus on least-squares estimation of Finite Impulse Response (FIR) models and minimum variance input design. The optimal input problem is formulated as a convex optimization problem (semi-definite program) in the second order statistics of the input signal. We analytically characterize the optimal solution for first order FIR systems with two parameters, and perform a numerical study to obtain insights in the optimal solution for higher order models. The optimal solution is compared to the case when a sinusoidal input signal, with frequency ω and amplitude that gives the same accuracy as the optimal input, is used as excitation signal. For first order FIR models with two parameters the input signal power can be reduced at best by a factor of two by using the optimal input signal compared with such a sinusoidal input signal. Numerical studies show that less is in general gained for higher order systems, for which a sinusoidal input signal with frequency ω often is optimal. We consider estimation of the ℋ ∞-norm of a stable linear system, that is the maximum of the absolute value of the corresponding frequency response. An asymptotic error variance expression for ℋ∞-norm estimates is derived.

Place, publisher, year, edition, pages
IEEE , 2010. 302-307 p.
Keyword [en]
Absolute values, Convex optimization problems, Error variance, Excitation signals, Finite-impulse response, FIR model, FIR systems, First order, Frequency response estimation, Higher order, Higher-order systems, Input design, Input problem, Input signal, Input signal design, Input signal power, Least-squares estimation, Minimum variance, Norm estimates, Numerical studies, Optimal solutions, Second order statistics, Semidefinite programs, Sinusoidal input signals, Stable linear systems, Two parameter, Convex optimization, Design, Estimation, FIR filters, Frequency estimation, Impulse response, Linear systems, Optimal systems, Optimization, Parameter estimation, Quadratic programming, Uncertainty analysis, Frequency response
National Category
Control Engineering
URN: urn:nbn:se:kth:diva-55387DOI: 10.1109/CDC.2010.5717921ISI: 000295049100050ScopusID: 2-s2.0-79953141924ISBN: 978-1-4244-7746-3OAI: diva2:471654
49th IEEE Conference on Decision and Control (CDC). Atlanta, GA. DEC 15-17, 2010
© 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. QC 20120104Available from: 2012-01-31 Created: 2012-01-02 Last updated: 2013-09-05Bibliographically approved

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Wahlberg, BoHjalmarsson, Håkan
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