Model Reduction Using the Balanced Truncation Method and the Padé Approximation Method

Abstract

The objective of this article is the construction of a new model reduction method for the simplification of large-scale linear dynamical plants. In this method, the denominator of the lower order plant is determined by using the balanced truncation technique and the numerator is obtained by the Padé approximation method. This technique is given for the removal of existing limitations of the Padé approximation and the balanced truncation method. In this proposed method, it is ensured the stability and steady-state value of the original system are preserved in the reduced model. Thus the instability problem of the Padé approximation method and the steady-state error limitation of the balanced truncation method are circumvented. The advantages of the Padé approximation and the balanced truncation method are retained in the reduced model. For showing the accuracy and simplicity of the proposed method, standard numerical examples are simplified. This method is also compared to the recent and standard methods of the model diminution with the help of MATLAB.

KEYWORDS:

• Controllability and observability Gramians
• Lyapunov equation
• Model order reduction
• Routh stability
• Time moments

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Arvind Kumar Prajapati

Arvind Kumar Prajapati was born in Jaunpur (Uttar Pradesh), India, in 1990. He received the BTech degree with Gold Medal in electrical engineering from VBS Purvanchal University, Jaunpur, in 2013. He received the MTech degree in electrical engineering from National Institute of Technology, Silchar, India, in 2015. He received the PhD degree in electrical engineering from Indian Institute of Technology, Roorkee, India, in 2019. He served as a guest lecturer in Electrical Engineering department of VBS Purvanchal University Jaunpur in 2015 and a senior assistant professor in Electrical and Electronics Engineering department of Madanapalle Institute of Technology and Science Madanapalle Andhra Pradesh in 2019. Currently, he is a senior assistant professor in the School of Electronics Engineering, VIT AP University, Amaravati, Andhra Pradesh. His area of interest includes model order reduction, fault detection and accommodation of dynamic system, and integrated vehicle health management system. Email: [email protected], [email protected]

Rajendra Prasad

Rajendra Prasad was born in Hangawali (Saharanpur), India, in 1953. He received BSc (Hons) degree from Meerut University, India, in 1973. He received BE, ME and PhD degrees in electrical engineering from the University of Roorkee, India, in 1977, 1979 and 1990, respectively. He has served as assistant engineer in Madhya Pradesh Electricity Board (MPEB) from 1979 to 1983. He served as lecturer in Electrical Engineering department, University of Roorkee, India, from 1983 to 1996. He worked as an assistant professor during 1996–2001, an associate professor from 2001 to 2009 and he is a professor in the Department of Electrical Engineering, Indian Institute of Technology Roorkee, Roorkee (India), from 2009 to 2019. He has published around 300 papers in various journals/conferences and received 15 awards on his publications in various national/international journals/conferences proceeding papers. He has guided 18 PhD scholars, and presently one PhD student is pursuing the programme. His main research interests include model order reduction, data analysis, robotics and its applications, control, optimization and system engineering. Email: [email protected]