Qualitative Analysis of Stable Reduced Order Models for Interval Systems Using Mixed Methods

ABSTRACT

A large number of problems are available for complex higher order systems. These systems are difficult to analyze and synthesize. Therefore it is needful to approximate higher order models to lower order models. Interval systems have constant coefficients which are uncertain within a finite range. In this paper, the frequency domain reduction methods are applied for reducing the order of interval systems. The three mixed methods are considered for reducing the linear dynamic interval systems. In these mixed methods, denominators of the reduced models are obtained by using differentiation method while the numerators of the reduced models are obtained by using differentiation, factor division, and pade approximation methods. The novel feature of the proposed methods is that it guarantees the stability of reduced order models if the original interval systems are stable. In addition, the mixed methods are compared qualitatively in terms of integral square error and integral absolute error to know about the best method among three mixed methods. Numerical examples are given to show the effectiveness of the mixed methods.

KEYWORDS:

• Differentiation method
• Factor division algorithm
• IAE
• Interval systems
• ISE
• Order reduction
• Pade approximation

Additional information

Funding

This work was supported by the Ministry of Human Resource Development [grant number 14914021].

Notes on contributors

Sudharsana Rao Potturu

Sudharsana Rao Potturu was born in Guntur, Andhra Pradesh, India, in 1988. He received the BTech degree in electronics and instrumentation engineering from JNTU Kakinada, A.P, India, in 2010, and M.Tech degree in control system engineering, from Indian Institute of Technology Kharagpur, West Bengal, India, in 2013 and presently he is pursuing PhD from the Department of Electrical Engineering, Indian Institute of Technology Roorkee, Roorkee-247667, Uttarakhand, India. His area of interest includes control system, model order reduction, biomedical engineering, and controller design.

Rajendra Prasad

Dr Rajendra Prasad was born in Hangawali (Saharanpur), India, in 1953. He received the 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 served as an Assistant Engineer in MPEB from 1979 to 1983. From 1983 to 1996, he was a Lecturer in the Electrical Engineering Department of the University of Roorkee, Roorkee (India) and from 1996 to 2001, he was an Assistant Professor. He served as an Associate Professor from 2001 to 2009. Presently, he is Professor w.e.f. 2009 in the Department of Electrical Engineering at the Indian Institute of Technology Roorkee (India). His research interests include control, optimization, system engineering and model order reduction. Email: [email protected]