Model reduction using the stability-equation method and the Padé approximation method

Chen, T.C.; Chang, Chao‐Yuan; Han, Kuang-Wei

doi:10.1016/0016-0032(80)90096-4

Cited by 88 publications

(14 citation statements)

References 12 publications

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“…In other words, it retains the stability of the original system and also nullifies the steady state response matching issues. A composite method, making use of the advantages of SE method and the Pade approximation method for reducing high-order transfer functions of single-input/single-output systems and multivariable systems is presented in Chen, Chang, and Han (1980). Similarly, Panda, Tomar, Prasad, and Ardil (2009) and Vishwakarma and Prasad (2009) have dealt with performing MOR using heuristic techniques and are successful.…”

Section: Se Methodsmentioning

confidence: 99%

A new approach to order reduction using stability equation and big bang big crunch optimization

Desai

Prasad

2013

Systems Science & Control Engineering

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A new method of model order reduction is introduced by combining the merits of big bang big crunch (BBBC) optimization technique and stability equation (SE) method. A linear-continuous single-input single-output system of higher order is considered and reduced to a lower order system. The denominator polynomial of the reduced system is obtained by SE method, whereas the numerator terms are generated using BBBC optimization. Furthermore, step and frequency responses of the original reduced system are plotted. The superiority of the proposed method is justified by solving numerical examples from the available literature and comparing the reduced systems in terms of error indices.

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Section: Se Methodsmentioning

confidence: 99%

A new approach to order reduction using stability equation and big bang big crunch optimization

Desai

Prasad

2013

Systems Science & Control Engineering

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“…The Routh approximation and the stability equation method are used to guarantee the stability of the reduced model. Research works proposed by Chen et al (1980a,b), Gupta et al (2002), Pal et al (1995) and Shamash (1975) proves the quality of the reduction process. Most of the model order reduction techniques are concerned with preserving stability and matching initial time moments between the full and reduced systems.…”

Section: Introductionmentioning

confidence: 91%

Order reduction of linear systems with an improved pole clustering

Komarasamy¹,

Albhonso²,

Gurusamy³

2011

Journal of Vibration and Control

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A new model order reduction technique for the reduction of the linear time invariant system has been proposed in this paper. An improved clustering algorithm is employed in the proposed method to obtain the reduced order denominator polynomial. The reduced order numerator polynomial is obtained with a simple mathematical calculation as mentioned in the proposed scenario. The validity of the proposed method has been illustrated through some numerical examples. The improved clustering algorithm guaranteed the stability in the reduced model and also preserves the characteristics of the original system in the approximated one. The method is extended to the higher order multivariable system described by its matrix transfer function.

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“…Example 1: Consider a transfer function of a flexible-missile control system (28) given in Chen et al (1980a, 1980b)…”

Section: Controller Design Algorithmmentioning

confidence: 99%

“…However, this methodology fails to keep the stability of some class of large scale original models into its equivalent reduced model (Ashoor and Singh, 1982; Prajapati et al, 2018). In order to circumvent this drawback several mixed model diminution techniques exist in the literature (Chen et al, 1980; Pal, 1979; Prasad, 2000; Vishwakarma and Prasad, 2008; Wan, 1981). Routh stability (Krishnamurthy and Seshadri, 1978) is another methodology for the diminution of complex linear systems and it is a convenient scheme for the resembling of the transient behavior of the complex system and its equivalent simplified model (Ashoor and Singh, 1982; Prajapati et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

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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Model reduction using the stability-equation method and the Padé approximation method

Cited by 88 publications

References 12 publications

A new approach to order reduction using stability equation and big bang big crunch optimization

A new approach to order reduction using stability equation and big bang big crunch optimization

Order reduction of linear systems with an improved pole clustering

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

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