A new frequency weighted Fourier-based method for model order reduction

Rydel, Marek; Stanisławski, Rafał

doi:10.1016/j.automatica.2017.11.016

Cited by 19 publications

(9 citation statements)

References 17 publications

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“…For this reason, research works which aim to obtain a balanced system in a numerically efficient way have still been carried out (see e.g. [44][45][46][47][48][49][50][51][52]). The preliminary results of approximation of a fractional-order system by use of the expanded state space model and the BT method have been presented in [33].…”

Section: Resultsmentioning

confidence: 99%

Computation of controllability and observability Gramians in modeling of discrete‐time noncommensurate fractional‐order systems

Rydel

Stanisławski

2019

Asian Journal of Control

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This paper presents a new algorithm for computation of controllability and observability Gramians for an expanded state space form of integer-order approximator to linear time-invariant discrete-time noncommensurate fractional-order systems. The introduced methodology can significantly reduce the time complexity of the Gramians' calculation, being the main computational burden in modeling of discrete-time fractional-order systems by means of a high integer-order expanded state space approximator and the balanced truncation reduction method. Simulation experiments illustrate an efficiency of the introduced methodology, in particular for low-dimension fractional-order systems and high implementation lengths.

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Section: Resultsmentioning

confidence: 99%

Computation of controllability and observability Gramians in modeling of discrete‐time noncommensurate fractional‐order systems

Rydel

Stanisławski

2019

Asian Journal of Control

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“…Transformation (or projection) matrix T and its inverse are not unique. Nevertheless, the majority of algorithms determine its form based on the controllability P and observability Q Gramians of the system [23,29,37,38,49,60,63,66]. Consider a SISO FIR-based approximation of the NCFO system as in Eqn.…”

Section: Cross Gramian-based Model Order Reductionmentioning

confidence: 99%

“…It is worth mentioning that the reduction process, in particular determination of Gramians for very high order systems, is highly time-consuming. This problem can be solved through the Fourier Model Reduction (FMR) method, which uses discrete-time Fourier coefficients to develop an intermediate order approximation of the original model [49,60,67]. Controllability and observability Gramians can be calculated in an analytical way, which significantly reduces time complexity of the reduction process [49,60].…”

Section: Introductionmentioning

confidence: 99%

“…This problem can be solved through the Fourier Model Reduction (FMR) method, which uses discrete-time Fourier coefficients to develop an intermediate order approximation of the original model [49,60,67]. Controllability and observability Gramians can be calculated in an analytical way, which significantly reduces time complexity of the reduction process [49,60]. In this paper, new model order reduction methods combining the FIR-based approximation of a non-commensurate fractional-order system with BT and FW model order reduction methods based on the cross Gramian are proposed.…”

Section: Introductionmentioning

confidence: 99%

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New integer-order approximations of discrete-time non-commensurate fractional-order systems using the cross Gramian

Rydel

2018

Adv Comput Math

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This paper presents a new approach to modeling of linear time-invariant discrete-time non-commensurate fractional-order single-input single-output state space systems by means of the Balanced Truncation and Frequency Weighted model order reduction methods based on the cross Gramian. These reduction methods are applied to the specific rational (integer-order) FIR-based approximation to the fractional-order system, which enables to introduce simple, analytical formulae for determination of the cross Gramian of the system. This leads to significant decrease of computational burden in the reduction algorithm. As a result, a rational and relatively low-order state space approximator for the fractional-order system is obtained. A simulation experiment illustrates an efficiency of the introduced methodology in terms of high approximation accuracy and low time complexity of the proposed method.

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“…Such an approach allows for larger errors outside these specified intervals, without negative impact on the usefulness of the obtained reduced model. The time and frequency boundaries can be applied either by using frequency-and time-limited controllability and observability Gramians [16][17][18][19] or by frequency-weighted functions connected to the model which are the subject to the reduction process [20][21][22][23][24][25][26]. In this paper, we focus on the generalization of such approaches to reduction and an accurate approximation in given frequency and time intervals for the discrete-time commensurate fractional-order systems.…”

Section: Introductionmentioning

confidence: 99%

Balanced Truncation Model Order Reduction in Limited Frequency and Time Intervals for Discrete-Time Commensurate Fractional-Order Systems

2019

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In this paper we investigate an implementation of new model order reduction techniques to linear time-invariant discrete-time commensurate fractional-order state space systems to obtain lower dimensional fractional-order models. Since the models of physical systems correctly approximate the physical phenomena of the modeled systems for restricted time and frequency ranges only, a special attention is given to time- and frequency-limited balanced truncation and frequency-weighted methods. Mathematical formulas for calculation of the time- and frequency-limited, as well as frequency-weighted controllability and observability Gramians, are extended to fractional-order systems. An instructive simulation experiment corroborates the potential of the introduced methodology.

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A new frequency weighted Fourier-based method for model order reduction

Cited by 19 publications

References 17 publications

Computation of controllability and observability Gramians in modeling of discrete‐time noncommensurate fractional‐order systems

Computation of controllability and observability Gramians in modeling of discrete‐time noncommensurate fractional‐order systems

New integer-order approximations of discrete-time non-commensurate fractional-order systems using the cross Gramian

Balanced Truncation Model Order Reduction in Limited Frequency and Time Intervals for Discrete-Time Commensurate Fractional-Order Systems

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