Method for identifying models of nonlinear systems using linear time periodic approximations

Sracic, Michael W.; Allen, Matthew S.

doi:10.1016/j.ymssp.2011.03.004

Cited by 25 publications

(9 citation statements)

References 17 publications

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“…Now, by using the new variables defined in Eqs. (16) and (17), we obtain a simpler form for Eq. (15) as…”

Section: Identification Of State-space Structurementioning

confidence: 99%

“…However, a vast majority of the system identification studies for such systems focus on their local behavior around a periodic orbit. Hence, linearization of such nonlinear hybrid dynamics around a limit cycle yields a linear time-periodic (LTP) system, where the state-dependent switching functions can also be approximated as time-or phase-dependent periodic scheduling signals [12,16,17].…”

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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“…Now, by using the new variables defined in Eqs. (16) and (17), we obtain a simpler form for Eq. (15) as…”

Section: Identification Of State-space Structurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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“…The source of the time-variation can be rotating parts in mechanical systems Bittanti and Colaneri (2008); hearth beat and/or breathing in biomedical applications Ionescu et al (2010); Sanchez et al (2013); and seasonality in econometrics Ghysels (1996); Osborn (2001). Linear periodically time-varying systems also appear when a nonlinear system is linearized about a periodic trajectory Sracic and Allen (2011).…”

Section: Overview Of the Literaturementioning

confidence: 99%

Realization and identification of autonomous linear periodically time-varying systems

et al. 2014

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Subsampling of a linear periodically time-varying system results in a collection of linear time-invariant systems with common poles. This key fact, known as "lifting", is used in a two step realization method. The first step is the realization of the time-invariant dynamics (the lifted system). Computationally, this step is a rank-revealing factorization of a block-Hankel matrix. The second step derives a state space representation of the periodic time-varying system. It is shown that no extra computations are required in the second step. The computational complexity of the overall method is therefore equal to the complexity for the realization of the lifted system. A modification of the realization method is proposed, which makes the complexity independent of the parameter variation period. Replacing the rankrevealing factorization in the realization algorithm by structured low-rank approximation yields a maximum likelihood identification method. Existing methods for structured low-rank approximation are used to identify efficiently linear periodically time-varying system. These methods can deal with missing data.

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“…The increased interest in periodic motion has also increased the necessity to develop novel tools for the analysis, identification and control of periodic systems (Farkas, 2013; Sandberg et al, 2005). Some examples of such periodic systems are wind turbines (Allen et al, 2011; Bottasso and Cacciola, 2015), helicopter rotors (Hwang, 1997; Siddiqi, 2001), power systems (Kwon et al, 2017; Mollerstedt and Bernhardsson, 2000a) and some nonlinear systems that exhibit periodic behavior around a stable limit cycle (Logan et al, 2016; Sracic and Allen, 2011; Uyanik, 2017). Note that standard linear time-invariant (LTI) analysis tools cannot capture the periodic nature of the system dynamics for these examples.…”

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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Method for identifying models of nonlinear systems using linear time periodic approximations

Cited by 25 publications

References 17 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

Realization and identification of autonomous linear periodically time-varying systems

Harmonic transfer functions based controllers for linear time-periodic systems

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