A generalised partial-fraction-expansion based frequency weighted balanced truncation technique

Sreeram, Victor; Sahlan, Shafishuhaza; Muda, Wan Mariam Wan; Fernando, Tyrone; Iu, Herbert Ho-Ching

doi:10.1080/00207179.2013.764017

Cited by 21 publications

(29 citation statements)

References 12 publications

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“…The infinity norm of the approximation error ||W (z) − W r (z)|| ∞ obtained using existing FWMR methods [10][11][12][13] are at best equal to or slightly lower than Enns Method. Furthermore more recent theoretical developments for FWMR techniques are still relatively less compared to unweighted model reduction techniques [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 92%

“…(7). Upon solving the double sided FWMR problem with the double sided weights as described in (13) and obtaining the reduced order controller -K rc (z), this reduced order controller -K rc (z) is replaced into (7) to establish the frequency weighted approximation error which corresponds to the variation of the parameter c denoted as E c which is a function of the free parameter matrix C = cI as follows:…”

Section: Derivation Of New Double Sided Frequency Weightsmentioning

confidence: 99%

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An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation

Ahmad

Houlis

Sreeram

et al. 2017

Asian Journal of Control

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In this paper, an improved parameterized controller reduction technique via a new frequency weighted model reduction formulation is developed for the feedback control of MIMO discrete time systems particularly for non-unity feedback control system configurations which have the controller located in the feedback path. New frequency weights which are a function of a free parameter matrix are derived based on a set of equivalent block diagrams and this leads to a generalized double sided frequency weighted model reduction formulation. Solving this generalized double sided frequency weighted model reduction problem for various values of the free parameter results in obtaining controllers which correspond to each value of the free parameter. It is shown that the proposed formulation has a useful characteristic such that selecting a controller which corresponds to a large value of the free parameter results in obtaining an optimal reduced order controller and using this optimal reduced order controller in a closed loop system results in significant reduction in the infinity norm of the approximation error between the original closed loop system and the closed loop system which uses an optimal reduced order controller (when compared to existing frequency weighted model reduction methods).

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Section: Introductionmentioning

confidence: 92%

Section: Derivation Of New Double Sided Frequency Weightsmentioning

confidence: 99%

An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation

Ahmad

Houlis

Sreeram

et al. 2017

Asian Journal of Control

Self Cite

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“…Therefore, to handle the instability problem, several methods [18][19][20][21][22][23][24][25] are proposed. [18] Sreeram et al [17] implemented the diagonalization of modified weighted Gramians P lc and Q lc in place of P 11 and Q 11 .The weighted Gramians P lc and Q lc are given by …”

Section: Introductionmentioning

confidence: 99%

Frequency weighted square-root optimal Hankel norm model reduction

Kumar

Nagar

2015

2015 10th Asian Control Conference (ASCC)

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In this paper a square-root balanced approach based frequency weighted optimal Hankel norm model reduction algorithm is developed as an extension of [21] and [25]. The proposed algorithm generates stable reduced order models with single and double-sided weighting functions. A numerical example is included and the results are compared with the existing techniques as a validation of developed algorithm. Keywords-balanced realization; frequency weighted model reduction; optimal hankel norm approximation; square-root approach.978-1-4799-7862-5/15/$31.00

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“…Various partial fraction based techniques appear in the literature [31][32][33][34][35] that works for continuous as well as discrete time systems. Unfortunately, most of these techniques yield large frequency response error [30] as compared to Enns technique.…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, most of these techniques yield large frequency response error [30] as compared to Enns technique. However, [35] incorporates free parameters to reduce the approximation error.…”

Section: Introductionmentioning

confidence: 99%

Frequency Weighted Model Order Reduction Technique and Error Bounds for Discrete Time Systems

Imran¹,

Ghafoor

Sreeram³

2014

Mathematical Problems in Engineering

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Model reduction is a process of approximating higher order original models by comparatively lower order models with reasonable accuracy in order to provide ease in design, modeling and simulation for large complex systems. Generally, model reduction techniques approximate the higher order systems for whole frequency range. However, certain applications (like controller reduction) require frequency weighted approximation, which introduce the concept of using frequency weights in model reduction techniques. Limitations of some existing frequency weighted model reduction techniques include lack of stability of reduced order models (for two sided weighting case) and frequency response error bounds. A new frequency weighted technique for balanced model reduction for discrete time systems is proposed. The proposed technique guarantees stable reduced order models even for the case when two sided weightings are present. Efficient technique for frequency weighted Gramians is also proposed. Results are compared with other existing frequency weighted model reduction techniques for discrete time systems. Moreover, the proposed technique yields frequency response error bounds.

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A generalised partial-fraction-expansion based frequency weighted balanced truncation technique

Cited by 21 publications

References 12 publications

An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation

An Improved Parameterized Controller Reduction Technique via New Frequency Weighted Model Reduction Formulation

Frequency weighted square-root optimal Hankel norm model reduction

Frequency Weighted Model Order Reduction Technique and Error Bounds for Discrete Time Systems

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