Frequency-Domain Subspace Identification of Linear Time-Periodic (LTP) Systems

Uyanik, Ismail; Saranlı, Uluç; Ankaralı, Mustafa Mert; Cowan, Noah J.; Morgül, Ömer

doi:10.1109/tac.2018.2867360

Cited by 29 publications

(25 citation statements)

References 34 publications

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“…Note that the formulation for κ given in Eq. (19) includes N unknown Fourier series coefficients for each system and input matrices. However, we assume that the internal switching subsystems are respectively smooth time-periodic functions and the number of unknown Fourier series coefficients is limited.…”

Section: Remarkmentioning

confidence: 99%

“…For example, the truncated unknown Fourier series coefficients vectors, which will replace the ones in Eq. (19), for ( A i k , B i k ) can now be written as…”

Section: Remarkmentioning

confidence: 99%

“…At this point, one can compute an estimate for the original time periodic system by back-substitutingκ † into Eqs. (25), (19), (17), (14), (9), and (3).…”

Section: Remarkmentioning

confidence: 99%

“…The fact that an LTP system can be lifted to a multiinput multioutput linear time-invariant (LTI) system equivalent allows using LTI system identification tools (with some extensions) for LTP systems as well [18][19][20]. However, the hybrid nature of the class of systems we are interested in introduces "instant jumps" between different vector fields and is thus open to developing new tools that explicitly take the time-dependent (and possibly nonsmooth) changes in system dynamics into account.…”

Section: Introductionmentioning

confidence: 99%

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State-space identification of switching linear discrete time-periodic systems with known scheduling signals

Uyanik

Hamzaçebi

Ankaralı

2019

Turk J Elec Eng & Comp Sci

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In this paper, we propose a novel frequency domain state-space identification method for switching linear discrete time-periodic (LDTP) systems with known scheduling signals. The state-space identification problem of linear time-invariant (LTI) systems has been widely studied both in the time and frequency domains. Indeed, there have been several studies that also concentrated on state-space identification of both continuous and discrete linear time-periodic (LTP) systems. The focus in this study is the family of LDTP systems that switch among a finite set of subsystems triggered by known periodic scheduling signals. We address the state-space identification of such systems in frequency domain using input-output data. We also assume that full state measurements are available for the identification process.The major difference of our study is that we explicitly model the known scheduling signals responsible for switching, which greatly reduces the parametric complexity as well as potentially increases the estimation accuracy by avoiding overfitting. In our identification framework, we gather the Fourier transformations of input-output data, known periodic scheduling signals, and state-space system dimensions and fuse them in a linear regression framework. Later, we estimate the Fourier series coefficients of the time-periodic system and input matrices using a least-squares solution. Finally, we illustrate the effectiveness of our method using a switching LDTP system that is based on the damped Mathieu equation.

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Section: Remarkmentioning

confidence: 99%

“…For example, the truncated unknown Fourier series coefficients vectors, which will replace the ones in Eq. (19), for ( A i k , B i k ) can now be written as…”

Section: Remarkmentioning

confidence: 99%

“…At this point, one can compute an estimate for the original time periodic system by back-substitutingκ † into Eqs. (25), (19), (17), (14), (9), and (3).…”

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

State-space identification of switching linear discrete time-periodic systems with known scheduling signals

Uyanik

Hamzaçebi

Ankaralı

2019

Turk J Elec Eng & Comp Sci

Self Cite

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“…These methods mostly use chirp type (or single-sinusoid) input signals for system identification. On the other hand, there are also some methods that consider estimating a direct statespace model for LTP systems using subspace identification techniques (Goos and Pintelon, 2016;Uyanik et al, 2017Uyanik et al, , 2016bVerhaegen and Yu, 1995).…”

Section: Introductionmentioning

confidence: 99%

Harmonic transfer functions based controllers for linear time-periodic systems

Hıdır

Uyanik

Morgül

2018

Transactions of the Institute of Measurement and Control

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The analysis, identification and control of periodic systems has gained increasing interest during the last few decades due to the increased use of dynamical systems that exhibit periodic motion. The vast majority of these studies focus on the analysis and control problem for a known state-space formulation of the linear time-periodic (LTP) system. On the other hand, there are also some studies that focus on data-driven identification of LTP systems with unknown state-space formulations. However, most of these methods provide numerical estimates for the harmonic transfer functions (HTFs) of an LTP system that are extremely difficult to work with during controller design. The goal of this paper is to provide a simple controller design methodology for unknown LTP systems by utilizing so-called HTFs estimates. To this end, we first build a mathematical basis of LTP controller design for known LTP systems using the Nyquist diagrams and analytically derived HTFs. We propose a new methodology to design P-, PD-and PIDtype controllers for LTP systems using Nyquist diagrams and the eigenlocus of the HTFs. Having established the HTF-based controller design procedure, we extend our methodology to unknown LTP systems by presenting a new sum-of-cosine signal-based data-driven system identification method. We show that the proposed data-driven controller design method allows estimation of the HTFs and it provides simple tools for optimizing certain time-domain performance metrics. We provide numerical examples for both known and unknown LTP system cases to illustrate the performance of the proposed controller design methodology.

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Singular value decomposition based learning identification for linear time‐varying systems: From recursion to iteration

Song

Liu

et al. 2023

Intl J Robust & Nonlinear

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System identification is a critical task in various engineering applications such as motion control, signal processing and robotics. In this article, the identification of linear time-varying (LTV) systems that perform tasks repetitively over a finite-time interval is investigated. Traditional LTV system identification typically adopts recursive algorithms in the time domain, which are incapable of tracking drastic-varying parameters and are subject to estimation lag and numerical instability. To address these issues, this article proposes the utilization of an iteration axis in addition to the time axis for estimating repetitive time-varying parameters. Specifically, the proposed approach involves an estimation algorithm for the time-varying parameters based on a recursive least squares (RLS) method along the iteration axis, as well as an update algorithm for the covariance matrix based on singular value decomposition (SVD) to enhance numerical stability. Additionally, a bias compensation method based on noise variance estimation is introduced for the sake of eliminating estimation error induced by measurement noise. Numerical comparisons with existing methods are conducted to demonstrate the effectiveness and superiority of the proposed method.

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Frequency-Domain Subspace Identification of Linear Time-Periodic (LTP) Systems

Cited by 29 publications

References 34 publications

State-space identification of switching linear discrete time-periodic systems with known scheduling signals

State-space identification of switching linear discrete time-periodic systems with known scheduling signals

Harmonic transfer functions based controllers for linear time-periodic systems

Singular value decomposition based learning identification for linear time‐varying systems: From recursion to iteration

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