Integral-Square-Error Based Normalized Relative Gain Array for the Input-Output Pairing and Equivalent Transfer Function Design of MIMO Processes

Abstract

Input-output pairing effectively minimizes the loop interaction in MIMO processes and avoids integral instability. In this article, a modified Relative Normalized Gain Array is proposed for the Input-Output Pairing and design of the First-order and Second-order Equivalent Transfer function. The proposed modified Relative Gain Array (mRNGA) matrix is derived by Normalizing the Relative Gain Array matrix with a normalization factor, which is calculated by minimizing the Integral Square Error of the given MIMO process. After that, the first order and second order Equivalent Transfer function is design by the derived mRNGA matrix, which offers an improved estimation of the Effective open-loop transfer function of the given MIMO process. The proposed method is corroborated with the help of the Input-Output pairing examples up to the 5 × 5 MIMO processes and three ETF design example.

Keywords:

• Equivalent Transfer function
• Integral Square Error
• MIMO process
• Relative Gain Array
• RNGA

ACKNOWLEDGEMENT

This publication is an outcome of the R&D work undertaken project under the Visvesvaraya PhD Scheme of Ministry of Electronics & Information Technology, Government of India, being implemented by Digital India Corporation.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Bharat Verma

Bharat Verma was born in Agra, India. He received the BTech degree in electronics and instrumentation engineering from Gautam Buddh Technical University, Lucknow, India, in 2010, the M.E. degree in measurement and control from the Madhav Institute of Technology and Science, Gwalior, India, in 2015, and the PhD degree in control system from the Pandit Dwarka Prasad Mishra Indian Institute of Infor-mation Technology Design and Manufacturing (PDPM IIITDM), Jabalpur, India, in 2019. He is currently an assistant professor with the Electronics and Communication Department, The LNM Institute of Information Technology, Jaipur India. His research interests include indirect design approach, optimal control, intelligent control, proportional-integral-derivative controller, and biomedical signal processing. Email: [email protected]

Prabin Kumar Padhy

Prabin Kumar Padhy received the master’s degree in electrical egineering-control system from the Electrical Engineering Department, Indian Institute of Technology (IIT) Banaras Hindu University, Varanasi, India, in 2001, and the doctoral degree in control system from the Electrical Engineering Department, IIT Guwahati, Guwahati, Assam, India, in 2007. He is currently an associate professor with the Electronics and Communication Department, PDPM Indian Institute of Information Technology, Design and Manufacturing, Jabalpur, India. His research interests include proportional-integral-derivative controller, adaptive control, system identification, control of processes and time-delayed systems.