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Jaya optimization-based approximation of LTI systems using stability equations | IEEE Conference Publication | IEEE Xplore

Jaya optimization-based approximation of LTI systems using stability equations


Abstract:

This article presents a novel hybrid approach by integrating Jaya optimization and stability equations (SEs) benefits for simplifying complex and high-order linear time-i...Show More

Abstract:

This article presents a novel hybrid approach by integrating Jaya optimization and stability equations (SEs) benefits for simplifying complex and high-order linear time-invariant (LTI) systems. The proposed method employs SEs to compute the coefficients of the reduced-order denominator polynomial while the numerator polynomial of the reduced model is calculated by Jaya optimization via minimizing the fitness function. Three test systems are examined to assess the performance of the proposed approach over existing approaches. Both continuous and discrete time LTI systems are considered in this work for completeness. Furthermore, a performance indices-based numerical analysis is included to demonstrate the superiority of the proposed method.
Date of Conference: 10-12 February 2023
Date Added to IEEE Xplore: 04 April 2023
ISBN Information:
Conference Location: Aligarh, India

I. Introduction

In general, large-scale physical systems are represented by complex higher-order models (HOM) in the real world. The complexity of such systems is a significant concern in analysis, synthesis, simulations, and controller design. Hence, a reduced-order model (ROM) is desired to preserve the essential characteristics of the original HOM. Some conventional model order reduction (MOR) methods are continued fraction expansion methods [1], Routh approximation [2], [10], Padé approximation [3], Hurwitz polynomial approximation [4], stability equation method (SEM) [5], balanced truncation [11], etc. The main disadvantage of the Padé approximation [3] is that occasionally, the approximants computed by this method become unstable as this method does not use any stability criterion. Therefore, stability preservation techniques (SPT) [4] are employed to overcome this issue by considering a specific stability criterion. Subsequently, several mixed methods [5] –[9] are proposed in which an SPT obtains the denominator polynomials of the ROM. At the same time, classical or optimization techniques are used to compute the coefficients of numerator polynomials in these mixed methods. Appiah [5] used the Hurwitz polynomial with Padé to obtain a ROM. Similarly, Singh et al. [6] utilized an improved Routh-Padé approach-based model reduction using optimization. Later, Parmar et al. [7]–[8] implemented Eigen spectrum analysis-based MOR techniques using the factor division [7] and Padé approach [8]. Another SPT is presented by Sikander et al. [9], where factor division and SEM are used. Pole clustering-based model reduction is also one of the SPT used in many works such as [15], [16]. Later, Prajapati et al. [18] proposed another method using balanced truncation [11] and factor division and showed a comparative analysis of various methods. A time-moment matching-based method [18] has been presented recently. However, this method fails to ensure the stability of a ROM due to the instability issue of Padé-based methods. Over the last few decades, many researchers have developed several nature-inspired metaheuristics optimization algorithms. Many of these algorithms are successfully implemented for MOR of LTI systems [19] –[24] such as Parmar et al. [19] presented SEM and genetic algorithm-based model reduction methods. Gupta et al. [20] developed the Eigen permutation and Jaya optimization-based technique to reduce LTI systems. The order reduction of HOM by these optimization algorithms is based on minimizing a specific performance criterion.

References

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