Linear System of Order Reduction Using a Modified Balanced Truncation Method

Suman, Shankar; Kumar, Awadhesh

doi:10.1007/s00034-020-01596-3

Cited by 15 publications

(12 citation statements)

References 113 publications

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“…ROM should not lose both the SOSS structure and physical exposition of (1), but a converse suggestion was found in previously suggested techniques for SOSSs [5,6]. Afterwards, contrivances like modified Arnoldi, second order balanced truncation (SOBT) and moment matching (based on Krylov‐subspaces) [3,5,7–13] etc. retain second order structure in ROM.…”

Section: Introductionmentioning

confidence: 89%

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Discrete Time Limited Gramians Model Order Curtailment for Unstable Second Orderly‐Structured Systems

Ali,

Haider,

Mokhtar

et al. 2024

IEEJ Transactions Elec Engng

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In this manuscript, sundry model order Curtailment (MOC) techniques for discrete time frequency limited applications of unstable second orderly‐structured systems (SOSSs) are suggested. Discrete‐time limited frequency gramians (DLFGs) for generalized SOSSs and limited frequency discrete time algebraic Lyapunov equations (LFDALEs) are developed. For unstable SOSS, LFDALEs are unsolvable and the Curtailment process is halted. First technique fragments discrete time unstable SOSS into stable and unstable snippets and balanced truncation process is solicited to stable fragment. The acquired reduced order model (ROM) for stable snippet is added with unstable one. Second order structure in ROM gets lost as well as added unstable dynamics degrade the ROM performance using this approach. Then, two structure retaining limited frequency second order balanced truncation (SOBT) techniques for unstable SOSSs are suggested. Bernoulli feedback stabilization stratagem is adopted and then DLFGs are found for stabilized system from LFDALEs. Furthermore, gramians are fragmented in to position and velocity snippets which give rise to structure retention in ROM. Finally, ROM in desired frequency hiatus is gleaned by solicitation of SOBT. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

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Section: Introductionmentioning

confidence: 89%

“…In curtailment process of stable subsystem H s , LF controllability and observability gramians W csδ and W osδ are obtained for stable snippet H s by solving LFDALEs (10) and (11). To obtain the balanced X-formation, contemplate the singular value decomposition of gramians:…”

Section: Curtailment Of Stable Snippetmentioning

confidence: 99%

Discrete Time Limited Gramians Model Order Curtailment for Unstable Second Orderly‐Structured Systems

Ali,

Haider,

Mokhtar

et al. 2024

IEEJ Transactions Elec Engng

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“…The balanced system derived above is then partitioned into strong and weak sub-systems. To get the balanced truncated model, the weak sub-systems are truncated as they contribute significantly very less to the overall response of the system (Suman & Kumar, 2021). In the proposed methodology, the coefficients of numerator and denominator which are found by using the balanced truncation method are used as base values to work for the moth flame optimization.…”

Section: Balanced Truncation Methodsmentioning

confidence: 99%

“…The reduced-order LTI system derived in equation ( 23) may exhibit steady-state errors requiring further correction. Suman & Kumar (2021) introduced a gain adjustment concept in the conventional balanced truncation approach. The proposed methodology employs the gain adjustment factor after optimization of the numerator & denominator coefficients.…”

Section: (I) Generation Of Initial Populationmentioning

confidence: 99%

“…Moreover, the applicability of balanced truncation to power system models has been discussed in Ghosh and Senroy (2013). Recently, the problem of steady-state error in balanced truncation methods is addressed in Suman & Kumar (2021), wherein a simple methodology using a gain adjustment factor is used to match the steady-state response. In the present proposed methodology, the method of Suman & Kumar (2021) is used as one of the mathematical tools to match the steady-state gain.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Boundary Conditions based Optimization Approach for Efficient Model Order Reduction of Complex Systems

Goel,

Manocha

2024

Preprint

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This paper proposed a new methodology to address the key problem in model order reduction methods of setting random values of lower & upper bounds and initial values of the parameters in optimization-based approaches. The moth flame optimization (MFO) method is utilized for the model order reduction process wherein the search space boundaries are found using a novel strategy with the classical balanced truncation technique. Both the numerator and denominator coefficients of the desired reduced-order system are found using the proposed optimization approach. The integral square error (ISE) is employed as the objective function in the optimization of SISO systems while a novel objective function is framed using ISE for the MIMO systems. The key advantage of using balanced truncation-based search space boundaries ensures targeted search with potential solutions and stability of the reduced order model. Further, the disadvantage of steady-state error of the balanced truncation is overcome using a gain adjustment factor. The overall methodology takes very less simulation time while keeping all the necessary parameters of the reduced-system close to those of the original system. To test the efficacy of the proposed methodology, five real-world high-order systems with two SISO systems, two MIMO systems and one discrete-time system are considered and compared with existing methods through several error indices and time and frequency-domain specifications. It has been found that the proposed methodology results in significant reduction of ISE and improvement in matching of step responses, preserving stability of the reduced-order models.

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Approximation of Fractional-Order Systems Using Balanced Truncation with Assured Steady-State Gain

Duddeti

2023

Circuits Syst Signal Process

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Linear System of Order Reduction Using a Modified Balanced Truncation Method

Cited by 15 publications

References 113 publications

Discrete Time Limited Gramians Model Order Curtailment for Unstable Second Orderly‐Structured Systems

Discrete Time Limited Gramians Model Order Curtailment for Unstable Second Orderly‐Structured Systems

Dynamic Boundary Conditions based Optimization Approach for Efficient Model Order Reduction of Complex Systems

Approximation of Fractional-Order Systems Using Balanced Truncation with Assured Steady-State Gain

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