Optimal least squares model approximation for large-scale linear discrete-time systems

Vasu, Ganji; Kumar, Mahendra; Ramalingaraju, M

doi:10.1177/0142331216649023

Cited by 7 publications

(3 citation statements)

References 24 publications

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“…The least squares fitting algorithm (Chen et al, 2013; Giarnetti et al, 2015; Vasu et al, 2016) is a math optimization method. It searches for the optimal matching function of the data by minimizing the error of sum of square.…”

Section: Digital Phase Shift Methods Based On Least Squares Fitting Almentioning

confidence: 99%

A digital phase shift method for phase compensation of electronic transformer

Wei

Cheng

et al. 2017

Transactions of the Institute of Measurement and Control

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When sampling analog signal, the electronic transformer generally produces a fixed phase error that will compromise the measurement accuracy and require a phase shift method for correction. In this paper, we propose a digital phase shift method based on least squares fitting algorithm and derive the recursion formula of digital phase shift. The simulation has also been done to analysis its performance. The result shows that the method has high phase shift resolution and precision. By applying the method to an electronic transformer based on Rogowski coil, we have experimentally verified the feasibility and validity of the method.

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Section: Digital Phase Shift Methods Based On Least Squares Fitting Almentioning

confidence: 99%

A digital phase shift method for phase compensation of electronic transformer

Wei

Cheng

et al. 2017

Transactions of the Institute of Measurement and Control

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“…Therefore, model order reduction becomes important and popular. So far, many effective methods have emerged to reduce the large-scale linear time invariant (LTI) models, such as Krylov subspace method (Grimme, 1997; Yuan et al, 2018), balanced truncation method (Haider et al, 2017; Yang and Jiang, 2020; Zhou et al, 2001), orthogonal decomposition method (Yuan et al, 2018), optimal model order reduction method (Jiang and Xu, 2017; Sato and Sato, 2017; Vasu et al, 2018), and so on.…”

Section: Introductionmentioning

confidence: 99%

Model order reduction based on discrete-time Laguerre functions for discrete linear periodic time-varying systems

Sun

Jiang

2020

Transactions of the Institute of Measurement and Control

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Many engineering problems can be modelled as linear periodic time-varying (LPTV) systems, which naturally leads to the need for model order reduction of LPTV systems. This paper investigates a new model order reduction method for discrete LPTV systems. First, the state-space realization in the Fourier-lifted form of discrete LPTV system is constructed by representing periodic matrices in exponentially modulated periodic (EMP) Fourier series. By using Laguerre functions to expand the transfer function of the resulting Fourier-lifted system, the corresponding model order reduction algorithm is developed. Furthermore, the proposed algorithm is used to reduce the discrete LPTV system in the standard-lifted form. Theoretical analysis indicates that the transfer functions of both reduced order systems can match a certain number of moments. Finally, two numerical examples are given to verify the effectiveness of the proposed method.

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“…But, the Routh approximation method fails to give well approximate at the low frequency level of the higher-order system. Several methods [4]- [7] have been given to improve the Routh approximation method for obtaining a reduced order model. All these methods are available for systems with fixed coefficients only.…”

Section: Introductionmentioning

confidence: 99%

Design of Robust Controller for Higher Order Interval System using Differential Evolutionary Algorithm

Rao¹,

Kumar²,

Raju³

2018

IJRA

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This paper describes the design of the robust PI/PID controller for the higher order interval system via its reduced order model using the differential evolution (DE) algorithm. A stable reduced interval model is generated from a higher order interval system using the DE in order to minimize the cost and reduce the complexity of the system. This reduced order interval numerator and denominator polynomials are determined by minimizing the Integral Squared Error (ISE) using the DE. Then, using reduced order interval model, a robust PI/PID controller is designed based on the stability conditions for determining robust stability of interval system. Finally, using these stability conditions, a set of inequalities in terms of controller parameters is obtained from the reduced order closed loop characteristic polynomial. Then these inequalities are solved to obtain robust controller parameters with the help of a DE algorithm. The designed, robust controller from the reduced order interval model will be attributed to the higher order interval system. The designed PI/PID controller from our proposed method not only stabilizes the reduced order model, but also stabilizes the original higher order system. The viability of the proposed methodology is illustrated through the numerical example of its successful implementation. The efficacy of the proposed methodology is also evaluated against the available approaches presented in the literature and the results were successfully implemented.

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Optimal least squares model approximation for large-scale linear discrete-time systems

Cited by 7 publications

References 24 publications

A digital phase shift method for phase compensation of electronic transformer

A digital phase shift method for phase compensation of electronic transformer

Model order reduction based on discrete-time Laguerre functions for discrete linear periodic time-varying systems

Design of Robust Controller for Higher Order Interval System using Differential Evolutionary Algorithm

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