Frequency Interval Gramians Based Structure Preserving Model Order Reduction for Second Order Systems

Haider, Shafiq; Ghafoor, Abdul; Imran, Muhammad; Malik, Fahad Mumtaz

doi:10.1002/asjc.1598

Cited by 16 publications

(17 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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“…where ln(M) denotes the principle branch of the matrix logarithm of M. Even though originally constructed for the first-order case, the method can be extended to second-order systems (7) by considering the general method in Section 3.3. A discussion of this extension for some versions of the second-order balanced truncation method can be found in [66], but has only been applied to small systems so far. The application to the large-scale system case can be done using projection methods [23].…”

Section: Frequency-limited Balanced Truncationmentioning

confidence: 99%

A comparison of second-order model order reduction methods for an artificial fishtail

Saak

Siebelts

Werner

2019

At - Automatisierungstechnik

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In order to apply control theory in small autonomous vehicles, mathematical models with small numbers of states are required for using the limited computational power in embedded programming. In this paper, we consider an artificial fishtail as an example for a complex mechanical system with a second-order large-scale model, which is derived by using the finite element method. To meet the above limitations, the several hundreds of thousands of degrees of freedom need to be reduced to merely a handful of surrogate degrees of freedom. We seek to achieve this task by various second-order model order reduction methods. All methods are applied on the fishtail’s matrices and their results are evaluated and compared in the frequency domain as well as in the time domain.

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“…Besides, the framework for frequency limited model reduction of continuous‐time stable SOSs has been provided in Ref. [15], while framework for frequency limited model reduction of discrete‐time stable SOSs has been discussed in Ref. [16] and technique for time‐limited MOR for continuous SOSs has been presented in Ref.…”

Section: Introductionmentioning

confidence: 99%

Model Reduction Techniques for Unstable Second Order‐Form Systems

Ali

Mohd‐Mokhtar

Haider

et al. 2021

IEEJ Transactions Elec Engng

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In the present work, multiple non existing model order reduction (MOR) techniques for unstable second‐order form systems (SOSs) are proposed. For unstable SOSs, continuous‐time algebraic Lyapunov equations get unsolvable that halt the reduction process. To avoid this problem, unstable SOS is first decomposed into stable and unstable portions and balanced truncation is applied to the stable part. The obtained reduced order model (ROM) for the stable portion is augmented with the unstable portion to obtain the overall reduced system. It is observed that the second‐order structure in ROM for the first technique gets lost as well as augmented unstable dynamics degrade the ROM performance. To cater to these constraints, two structure‐preserving second‐order balanced truncation techniques for unstable SOSs are proposed in second part. System is first stabilized using the Bernoulli feedback stabilization procedure and then gramians are computed for the stabilized system. Further, gramians are partitioned into position and velocity portions to achieve structure preservation in ROM and balanced truncation is applied. As second technique retains second‐order structure as well as involves stabilized system dynamics, this technique far closely approximates original system behavior. Proposed techniques are tested on multiple systems and results certify the correct development of proposed techniques that can be utilized for MOR applications of unstable SOSs. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

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Frequency Interval Gramians Based Structure Preserving Model Order Reduction for Second Order Systems

Cited by 16 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

A comparison of second-order model order reduction methods for an artificial fishtail

Model Reduction Techniques for Unstable Second Order‐Form Systems

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