Optimal damping stabilisation based on LQR synthesis

Abstract

Significant attention is currently being paid to the synthesis of stabilising controllers for nonlinear and non-autonomous plants. We aimed to present a new method for nonlinear time-dependent control law design based on the application of Zubov’s optimal damping concept. This theory is used to reduce significant computational costs in solving optimal stabilisation problems. The main contribution is the proposition of a new methodology for selecting the functional to be damped. The central idea is to perform parameterisation of a set of admissible items for the mentioned functional. As a particular case, a new method of this parameterisation has been developed, which can be used for constructing an approximate solution of the classical optimisation problem. The emphasis is on the specific choice of the functional to be damped using LQR control to provide the desirable stability and performance features of the closed-loop connection. The applicability and effectiveness of the proposed approach are confirmed using a practical numerical example of the convey-crane control.

KEYWORDS:

• Feedback
• stability
• damping control
• functional
• optimisation

Acknowledgements

This work was supported by the Russian Foundation for Basic Research (RFBR) [research project number 20-07-00531] controlled by the Government of Russian Federation.

Disclosure statement

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

Additional information

Funding

This work was supported by the Russian Foundation for Basic Research (RFBR) [research project number 20-07-00531] controlled by the Government of Russian Federation.

Notes on contributors

Evgeny I. Veremey

Evgeny I. Veremey received the M. Eng. degree of electrical and mechanical engineering in control and systems from the Physical and Technical Faculty, Dnipropetrovsk State University, Dnipropetrovsk, Ukraine, in 1973 and then received the Ph.D. degree (candidate of technical science) and D.Sc. degree (doctor of physical and mathematical science) from the Applied Mathematics and Control Processes Faculty, Saint Petersburg State University, Saint Petersburg, Russia, in 1980, and 1995, respectively. Between March 1973 and February 1975, he served as an officer in the Soviet Army. From March 1975 before January 1981 he held the position of Scientific Researcher with the Faculty of Applied Mathematics and Control Processes, Saint Petersburg University. Since January 1981 until December 1989, he was a Senior Researcher: since January 1990, he has been an Associate Professor, and in 1996 he obtained the Professor position. He is currently a Professor, Head of the Computer Applications and Systems Department, Saint Petersburg University. He is the author or co-author of more than 200 scientific publications (mostly, in Russian). His research interests include control theory, optimisation approaches, computer modelling, and theirs applications to shipbuilding, robotics, and tokomaks plasma control. Professor Veremey is an honoured worker of the Higher Educational System of Russia. Since 2004, he has been a member of the International Public Association ‘Academy of Navigation and Motion Control'. Since 2019, he has been an Honorary Professor of Saint Petersburg State University.