Computing Dominant Poles of High-Dimensional Transfer Functions Using the Modified Clustering Method

Abstract

Model order reduction (MOR) solves a high-dimensional problem to its compact representation and plays a key role in the fields where complex simulation studies are always a challenge in terms of simulation time. A new criterion for the dominance of poles has been set out in this paper and its effect on the reduced-order model (ROM) has been observed. Considering the conventional as well as dominant pole-based solutions to ROM, the original system has been reduced to a lower-dimensional state-space and compared with each other. A dominant pole-based strategy incorporated into the modified pole clustering technique has been developed which leads to a proposed novel methodology as a dominant pole-based modified pole clustering method (DPMPCM). The paper also reveals that having applied DPMPCM, an improved approximation to the original system has been achieved as compared to other methods reported to the best of my knowledge in the literature. This method ensures the stability of the ROM with the original system considered as stable. A time delay model has also been presented to approximate the original system well in frequency and time domain. Also, the advantage of the method is that it maintains both transient and steady-state performance. The method proposed has been successfully applied to the linear systems and the results obtained indicate the methodology’s effectiveness. The proposed method, which proves to be an excellent match, efficient and superior as compared to the responses obtained by other methods in the literature concerning the same original system, validating the proposed technique.

KEYWORDS:

• Dominant pole
• High-dimensional system
• Padé approximation
• Pole clustering
• Reduced-order model

Additional information

Notes on contributors

Santosh Kumar Suman

Santosh Kumar Suman was born in Chandauli (Varanasi), India on 24 July 1990. He graduated from the Azad IET, Lucknow, Uttar Pradesh, India with BTech degree in electrical engineering in 2013 & MTech (Control & Instrumentation) from Electrical Engineering Department of Madan Mohan Malaviya University of Technology (MMMUT), Gorakhpur, currently; He is Pursuing PhD in Electrical Engineering Department, MMMUT. His research interests include intelligent & optimization techniques, control system, model order reduction. He has published numbers of research papers in national/international conference and SCI/SCImago referred journals. He is a member of IEEE and member of ACDOS, India. He has a total experience of 3 years in teaching and research.

Awadhesh Kumar

Awadhesh Kumar is currently working as an assistant professor in the Department of Electrical Engineering at Madan Mohan Malviya University of Technology, Gorakhpur, India. He obtained his PhD in electrical engineering from Motilal Nehru National Institute of Technology, Allahabad, India. He did his ME degree from National Institute of Technical Teachers' Training and Research, Chandigarh, Punjab, India and BE from Birla Institute of Technology, Mesra, Ranchi, India. His research interests include control systems, model order reduction, applications of optimization and artificial intelligence techniques to control design etc. He has published numbers of research papers in national/international conference and referred journals. He has a total experience of 15 years in teaching and research. He is a Member of IEEE, Member of IE(I) and Executive Member of ACDOS, India. Email: [email protected]