Implications of the degree of controllability of controlled plants in the sense of LQR optimal control

ABSTRACT

In this paper, the relationship between the degree of controllability (DOC) of controlled plants and the corresponding quadratic optimal performance index in LQR control is investigated for the electro-hydraulic synchronising servo control systems and wind turbine systems, respectively. It is shown that for these two types of systems, the higher the DOC of a controlled plant is, the better the quadratic optimal performance index is. It implies that in some LQR controller designs, the measure of the DOC of a controlled plant can be used as an index for the optimisation of adjustable plant parameters, by which the plant can be controlled more effectively.

KEYWORDS:

• Degree of controllability
• optimal control
• quadratic optimal performance
• electro-hydraulic, wind turbines

Acknowledgments

The authors thank the editors and anonymous reviewers for their helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant number 61174038], [grant number 61673213], [grant number 51507080]; the Fundamental Research Funds for the Central Universities [grant number 30915011104], [grant number 30920140112005]; the Perspective Research Foundation of Production Study and Research Alliance of Jiangsu Province of China [grant number By2016004-13].

Notes on contributors

Yaping Xia

Yaping Xia received her Ph.D. degree in control theory and control engineering from Nanjing University of Science and Technology, Nanjing, China. She is a lecturer in the College of Information and Engineering, Xiangtan University. Her research interests include control theory and application, wind power conversion system.

Minghui Yin

Minghui Yin received the B.S. and M.S. degrees in electrical power engineering and Ph.D. degree in automatic control engineering from the Nanjing University of Science and Technology, Nanjing, China, in 1999, 2001, and 2009, respectively. From 2007 to 2008, he worked as a Research Assistant in the Department of Electrical Engineering, The Hong Kong Polytechnic University, Hong Kong, China. Currently, he is an Associate Professor in the School of Automation, Nanjing University of Science and Technology. His major research interests include wind power conversion system and transient stability of power systems.

Yun Zou

Yun Zou received the B.S. degree in mathematics from the Northwestern University, Xian, China, in 1983 and the M.S. and Ph.D. degrees in control theory and control engineering from Nanjing University of Science and Technology, Nanjing, China, in 1987 and 1990, respectively. He is currently a Professor in the School of Automation, Nanjing University of Science and Technology. His current research interests include differential-algebraic equation systems, two-dimensional systems, singular perturbations, transient stability of power systems, and power market. Prof. Zou is a Mathematical Reviewer of the journal Mathematical Reviews and a Member of the American Mathematical Society.