Reducing order of large-scale systems by extended balanced singular perturbation approximation

Kumar, Deepak; Tiwari, Jayesh; Nagar, Shyam Krishna

doi:10.1504/ijaac.2012.045438

Cited by 21 publications

(8 citation statements)

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“…This figure demonstrates that the lower order model (39) acquired by the proposed technique precisely retains the characteristics of the original system (34). In Table 2, it is shown that the performance error indices values of the proposed method are the lowest values compared with some standard methods (Chen et al, 1979; Gu, 2005; Krishnamurthy and Seshadri, 1978; Moore, 1981; Wan, 1981), recently proposed methods (Kranthi et al, 2013; Kumar et al, 2012; Prajapati et al, 2020; Prajapati and Prasad, 2018c) and optimization methods (Desai and Prasad, 2013; Vishwakarma and Prasad, 2009). The accuracy and effectiveness of the proposed scheme to the other popular diminution schemes present in the literature are tabulated in Table 2 by comparing various performance error indices.…”

Section: Controller Design Algorithmmentioning

confidence: 96%

A novel order reduction method for linear dynamic systems and its application for designing of PID and lead/lag compensators

Prajapati

Prasad

2020

Transactions of the Institute of Measurement and Control

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This paper proposes a new model order reduction technology for the simplification of the complexity of large scale models. The proposed technique is focused on the Mihailov stability approach that guarantees the stability of the reduced model constrained that the complex system is stable. In this scheme, the denominator coefficients of the approximated simplified system are computed by using the Mihailov stability algorithm and the truncation method is used for the determination of coefficients of the numerator polynomial. The effectiveness and efficiency of the proposed approach are illustrated by comparing the step responses of the given system and approximated lower order models. The error indices such as integral square error (ISE), relative integral square error (RISE), integral absolute error (IAE) and integral time weighted absolute error (ITAE) are used as performance indices for comparing the proposed scheme with other existing standard reduced order modeling methods. The obtained reduced model is used for the designing of controllers for the original complex system. A new scheme for the determination of controllers is also proposed for the large scale models with help of reduced order modeling. The proposed technique is validated by applying it to an eighth order flexible-missile control system and a third order fuel control system. The simulation results show the dominance of the proposed methodologies over the latest model diminution techniques available in the literature.

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Section: Controller Design Algorithmmentioning

confidence: 96%

A novel order reduction method for linear dynamic systems and its application for designing of PID and lead/lag compensators

Prajapati

Prasad

2020

Transactions of the Institute of Measurement and Control

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“…In the model BT 'r' are kept balanced, strongly controlled and observed and even weakly controllable and/or observed. The weakly truncated state is used to (preserve) maintain the original system DC gain using SPA in the model (Safonov et al, 1989;Kumar et al, 2012).…”

Section: Lemma (Pernebo and Silverman 1982)mentioning

confidence: 99%

“…Based on the concept of the Singular perturbation approach (Kumar et al, 2012). We set the derivative of the approximate…”

Section: Lemma (Pernebo and Silverman 1982)mentioning

confidence: 99%

“…for all States to zero The rth -Order BSPA of the balanced system can be identified by comparing the derivate of the state of the weaker subsystem with zero. Finally, reduced model matrices which maintain DC gain and steady-state values of the original system ( Liu et al, 1989;Kumar et al, 2012;Guiver, 2019), Now, after implementation of the above steps to partition the balanced system ( , which is discussed in the numerical example section.…”

Section: Lemma (Pernebo and Silverman 1982)mentioning

confidence: 99%

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Model Order Reduction by Using Improved Approximation Techniques

Suman¹,

Kumar²

2020

SJKFU

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A simplified approach for model order reduction (MOR) is presented in this article using the balanced singular perturbation approximation (BSPA) approach applicable to large-scale linear dynamical (LSLD) systems. The reduced system was so designed to preserve complete parameters of the original system with reasonable accuracy, employing MOR. The approach is based on the retention of the dominant states of the system and comparatively less important once. The reduced system comes from the preservation of the dominant States (say "desirable states") of the original system and thus from stability to preservation. The key demerit of the Balanced Truncation approach is that the ROM steady-state values do not correspond with the higher-order systems. This drawback has been eliminated in the proposed approach, which leads to hybridization of balanced truncation and singular perturbation approximation into a novel reduction method without the loss of retaining its dynamic behaviour. The proposed approach has been tested on LSLD systems and the results obtained show the efficacy of the approach. The methodology presented has been tested on two typical numerical examples taken from the literature review, to examine the performance, precision and comparison with other available standard order reduction methods. both the quality and the presentation of the manuscript. I would like to thank my supervisor, Dr. Awadhesh Kumar, for the patience guidance, encouragement and advice, he has provided throughout my time as his student. I have been extremely lucky to have a supervisor who cared so much about my work and who responded to my questions and queries so promptly.

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“…The idea was further developed in [18] where it was shown that direct truncation of a balanced system and the slow singular perturbation approximation both yield minimal, stable, and balanced reduced‐order systems. Recent research involving combination of both methods has focused on order reduction in large‐scale systems [19], approximation of bounded balanced and stochastically balanced transfer matrices [20], balancing of non‐linear singularly perturbed systems [21, 22], and the effects that the balancing realisation has on singular perturbations [23, 24].…”

Section: Introductionmentioning

confidence: 99%

Finding Hankel singular values for singularly perturbed linear continuous‐time systems

Kodra¹,

Skataric

Gajić³

2017

IET Control Theory & Applications

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Reducing order of large-scale systems by extended balanced singular perturbation approximation

Cited by 21 publications

References 0 publications

A novel order reduction method for linear dynamic systems and its application for designing of PID and lead/lag compensators

A novel order reduction method for linear dynamic systems and its application for designing of PID and lead/lag compensators

Model Order Reduction by Using Improved Approximation Techniques

Finding Hankel singular values for singularly perturbed linear continuous‐time systems

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