Disturbance attenuation in observer design for linear systems – a new parametric approach

Abstract

In this paper, a new parametric approach is developed for disturbance attenuation in observer design of linear time-invariant systems. First, based on the general solution to a type of generalised Sylvester equations, a complete parametric form of the observer gain matrix is established. Secondly, a new disturbance attenuation index is introduced, and the parameters are further optimised to minimise the index. Under certain conditions, the optimal solution of this optimisation problem is obtained. Finally, the proposed method is used to design the robust observer for the yaw/roll channel attitude control system of a nonrotating missile. It is verified from the simulation results that the proposed method shows a stronger tolerance to disturbances compared with the traditional robust pole assignment method.

Keywords:

• Observer design
• disturbance attenuation
• disturbance decoupling
• parametric control system design
• eigenstructure assignment

Acknowledgments

The authors are very grateful to the associate editor and reviewers for their meaningful suggestions and comments.

Disclosure statement

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

Additional information

Funding

This work was supported by the Major Program of National Natural Science Foundation of China [grant numbers 61690210 and 61690212], Self-Planned Task of State Key Laboratory of Robotics and System (HIT) [grant number SKLRS201716A] and the National Natural Science Foundation of China [grant number 61333003].

Notes on contributors

Tianyi Zhao

Tianyi Zhao received his B.S. degree in Control Science and Engineering from Harbin Institute of Technology in 2018. In the same year, he was qualified to pursue a doctoral degree directly. He is currently pursuing the Ph.D. degree in Navigation, Guidance and Control from Harbin Institute of Technology, Harbin, China. His current research interests include robust control, eigenstructure and spacecraft control.

Guangren Duan

Guangren Duan received his Ph.D. degree in Control Systems Science and Engineering from Harbin Institute of Technology in 1989. After that he worked as a post-doctoral researcher at Harbin Institute of Technology, where he became professor of control systems theory in 1991. Prof. Duan visited the University of Hull, UK, and the University of Sheffield, UK from December 1996 to October 1998 and worked at the Queen's University of Belfast, UK from October 1998 to October 2002. He has been the Director of the Center for Control Theory and Guidance Technology at Harbin Institute of Technology since 2001, and is the author and co-author of over 400 publications. His main research interests include robust control, eigenstructure assignment, descriptor systems, spacecraft control and magnetic bearing control. Prof. Duan is a Chartered Engineer in the UK, Fellow of the IEEE, IET and CAA, and an Academician of the Chinese Academy of Sciences.