A Novel Order Abatement Technique for Linear Dynamic Systems and Design of PID Controller

Abstract

AbstractThis article proposes a novel hybrid technique of order abatement for large-scale models that combines the Mihailov stability method (MSM) and the stability equation method (SEM). In this approach, the denominator coefficients of the higher-order system (HOS) are estimated using the MSM, while the numerator coefficients are computed using the SEM. The suggested approach is based on the MSM, which guarantees the stability of the estimated model if the actual model is stable. The MSM also makes sure that important factors of the original plant, such as dominant poles and stability, are retained in the reduced order system (ROS). The suggested approach is compared to several current conventional reduction methods using error indicators, and the smallest performance error indices values reflect the supremacy of the method. The transfer function (TF) of the ROS is then used to design controllers by employing the moment matching technique. When the controller designed with the approximated model is applied to the real HOS, it indicates that the response of the closed-loop system of the real model entirely overlaps with the response of the reference plant. To further demonstrate the efficiency of the proposed schemes, time-domain specifications are produced and time responses are plotted.KEYWORDS: Controller designHigher order modelMihailov stability methodModel order reductionReduced order modelStability equation method Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementThe authors confirm that the data supporting the findings of this study are available within the article.Additional informationNotes on contributorsSunil Kumar GautamSunil Kumar Gautam received the Btech degree in electrical engineering from Uttar Pradesh Technical University, Uttar Pradesh, India, in 2013, and the Mtech degree in control and instrumentation from Motilal Nehru National Institute of Technology, Allahabad, Uttar Pradesh, India, in 2019. He is currently pursuing a PhD in control systems from the Maulana Azad National Institute of Technology, Bhopal, Madhya Pradesh, India. His current research interests include mathematical modelling of electrical systems, model order reduction, and controller design. Corresponding author. Email: sunilgautam827@gmail.comSavita NemaSavita Nema was born in Jabalpur, Madhya Pradesh, India. She is currently a professor in the Department of Electrical Engineering at the Maulana Azad National Institute of Technology (MANIT), Bhopal, India. She received her B.E. degree in electrical engineering and her M.E. degree in control systems from Jabalpur Engineering College, Madhya Pradesh, India, in 1990 and 1993, respectively. She received her PhD degree from Rajiv Gandhi Proudyogiki Vishwavidyalaya (RGPV) Bhopal, India, in 2011. She has 30 years’ experience in teaching and research. She has published more than 100 research papers in national and international journals and conferences, and she has co-authored four books. Her current research interests include renewable energy, photovoltaics, control systems, electric drives, and electric vehicles. Email: s_nema@yahoo.comR.K. NemaRajesh Kumar Nema was born in Jabalpur, Madhya Pradesh, India, in 1963. He received his Btech and Mtech degrees in electrical engineering from Bhopal University in 1986 and 1992, respectively. He obtained a PhD degree in electrical engineering from Barkatullah University, Bhopal, in 2004. He has been working as a professor in the Electrical Engineering Department at MANIT Bhopal. He is the author of more than 150 articles. His current research interests include multilevel inverters, solar PV controllers, hybrid energy systems, control systems, and power electronics converters for renewable energy applications. Email: rk_nema@yahoo.com