Design of Optimal Linear Reduced-Order Observers for Suppressing Transient Estimation Error

Abstract

By exploiting the idea of orthogonal functions and evolutionary optimization, a new approach is proposed in this paper to design a coordinate-change-based linear reduced-order observer such that (i) the eigenvalues of the reduced order observer are specified to satisfy desired convergence performance, and (ii) a quadratic performance measurement of the state estimation error is minimized so as to suppress the transient estimation error. The proposed optimal design method can be used to uniquely determine the observer gain matrix when the number of the output is greater than the number of states to be estimated, whereas existing approaches fail to do so. Two illustrative examples are also given to demonstrate the effectiveness and efficiency of the proposed optimization method for state estimations.

KEYWORDS:

• Evolutionary optimization
• Luenberger state observer
• Optimal design
• Orthogonal functions approach
• Reduced-order observer

Acknowledgement

The authors thank the Reviewers, Editor and Editor-in-Chief for their constructive comments, suggestions and evaluations, which helped us to improve the quality of this article.

Additional information

Notes on contributors

Fu-I Chou

Fu-I Chou received the BS degree from National University of Kaohsiung,Taiwan, in 2010, and the MS degree from National Dong Hwa University, Taiwan, in 2012, all in electrical engineering. He is currently pursuing his PhD degree in electrical engineering from the National Cheng Kung University, Taiwan. Since 2012, he has been an engineer of Metal Industries Research and Development Centre, Taiwan. His research interests include state observer design, automation and machine vision.

Ming-Yang Cheng

Ming-Yang Cheng received the BS degree in control engineering from National Chiao Tung University, Hsinchu, Taiwan, in 1986, and MS and PhD degrees in electrical engineering from the University of Missouri, Columbia, in 1991 and 1996, respectively. From 1997 to 2002, he held several teaching positions at Kao Yuan Institute of Technology, Kaohsiung, Taiwan; Dayeh University, Changhua, Taiwan; and National Kaohsiung First University of Science and Technology, Kaohsiung, Taiwan. Since 2002, he has been with the Department of Electrical Engineering, National Cheng Kung University, Tainan, Taiwan, where he is currently a professor. His research interests include motion control, motor drives, visual servoing, and robot control.