A modified functional observer-based EID estimator for unknown sampled-data singular systems

Abstract

This paper presents both an observer/Kalman filter identification (OKID) method-based linear quadratic digital tracker (LQDT) and a new functional observer-based discrete equivalent input disturbance (EID) estimator, for unknown square/non-square singular sampled-data systems with unknown input and output disturbances. Initially, it is shown that even if the solution of the impulsive mode-free singular linear quadratic tracker problem exists, under some quite general conditions the tracker-based generalised algebraic Riccati equation (GARE) might have no solution. To overcome this issue, an innovative methodology that involves an introduced reduced-order equivalent proper regular model (EPRM) of the singular system is presented, to make the tracker-based GARE solvable for a wide class of servo control problems for a singular system. Furthermore, a new functional observer-based design methodology for the discrete EID estimator of the discrete EPRM is proposed in this paper, for a proper sampled-data system with unknown matched/mismatched input and output disturbances. Finally, a discrete-time EPRM of the unknown singular sampled-data system is constructed using the off-line OKID method and the robust prediction-based state-estimate optimal LQDT, associated with the (plug-in) discrete EID estimator, is developed for the singular sampled-data system.

KEYWORDS:

• Optimal linear quadratic digital tracker
• disturbance estimator
• functional observer
• observer/Kalman filter identification
• singular system
• equivalent input disturbance estimator

Additional information

Notes on contributors

Jason Sheng-Hong Tsai

Jason Sheng-Hong Tsai received both M.S. and Ph.D. in Electrical Engineering from University of Houston, Texas, U.S.A. in 1985 and 1988, respectively. Since August 1988, he has been an associate professor in Department of Electrical Engineering at National Cheng-Kung University, Taiwan, R.O.C. He has been a full professor since August 1992 and a distinguished professor since Aug. 2002. His research interests include state-space self-tuning control, chaotic system control, partial differential system control, numerical analysis and robotics. He was (Executive) Editor for Science Development, published by National Science Council, R.O.C., Editor for Journal of the Chinese Institute of Electrical Engineering during, Associate Editor for International Journal of Systems Science, and Associate Editor for The Journal of The Franklin Institute.

Chia-Yuan Chang

Chia-Yuan Chang received B.S. degree from National Taiwan Ocean University of Electrical Engineering, Taiwan in 2013 and received M.S. degree from National Cheng Kung University, Taiwan in 2018. His research interests include singular systems, the extended equivalent input disturbance and generalised linear quadratic digital tracker.

Yang-Fang Chen

Yang-Fang Chen received B.S. degree from National Chiao Tung University, Taiwan in 2016 and received M.S. degree from National Cheng Kung University, Taiwan in 2018. Her research interests include singular system, Observer/Kalman filter identification and linear functional observer.

Shu-Mei Guo

Shu-Mei Guo received the M.S. degree from the Department of Computer and Information Science, New Jersey Institute of Technology, Newark, in 1987 and the Ph.D. degree in Computer and Systems Engineering from University of Houston, Houston, TX, in May 2000. Since June 2000, she has been an assistant professor with the Department of Computer System and Information Engineering, National Cheng-Kung University, Tainan, Taiwan, and since August 2010, she has been a full professor. Her research interests include various applications on evolutionary programming, chaos systems, Kalman filtering, fuzzy methodology, neural network, sampled-data systems, and computer and systems engineering.

Leang-San Shieh

Leang-San Shieh received his B.S. degree from National Taiwan University, Taiwan, in 1958, and his M.S. and Ph.D. degrees from the University of Houston, Houston, Texas, U.S.A., in 1968 and 1970, respectively. He was a professor in the Department of Electrical and Computer Engineering from 1971 to 2011 and a director of the Program of Computer and Systems Engineering from 1988 to 2011. Since 2011, he has been a professor emeritus of the Department of Electrical and Computer Engineering, University of Houston. He was the recipient of more than 10 College Outstanding Teacher Awards, the 1973 and 1997 College Teaching Excellence Awards, the 1988 College Senior Faculty Research Excellence Award and the 2003–2004 Fluor Daniel Faculty Excellence Award, the highest award given in the College, from the Cullen College of Engineering. In addition, he was the recipient of the 1976 University Teaching Excellence Award and the 2001–2002 El Paso Faculty Achievement Award in Teaching and Scholarship from the University of Houston. Furthermore, he received the Honor of Merit from Instituto Universitario Politecnico, Republic of Venezuela in 1978. He has co-authored more than 300 peer-reviewed journal articles. His fields of interest are hybrid control of linear and non-linear systems.

Jose I. Canelon

Jose I. Canelon received a BS degree in Electrical Engineering in 1994 and an MS degree in Applied Computing in 1997, both from the University of Zulia in Maracaibo, Venezuela, and a Ph.D. degree in Electrical Engineering in 2004 from the University of Houston, Houston, Texas, U.S.A. He has been a professor of the Electrical Engineering School of the University of Zulia from 1994. In the same university he was the coordinator of the Master of Engineering Program in Process Control from 2009 to 2016, and the Director of the Research Institute in Applied Calculus from 2013 to 2018. His main research areas of interest include: design of advanced control strategies, identification, control and optimisation of systems with complex dynamics (with recent applications in oil recovery processes and artificial lift systems) and digital control of continuous-time systems. He has been involved in funded research projects, being the principal researcher in some of them. He has co-authored more than 20 papers in peer-reviewed journals and more than 15 conference presentations. He was co-recipient of the Venezuelan National Award to the best scientific, technological and innovation work, given by the Ministry of Science and Technology, in 2003 and 2014.