New observer-based boundary control approaches to vibration reduction and disturbance attenuation of a flexible arm

Abstract

This paper addresses the vibration reduction and disturbance attenuation problems of a flexible arm, which is modelled as a fourth-order partial differential equation. The main control objectives lie in reducing the influence of the disturbance, steering the flexible arm to the desired angular position and suppressing the vibration, simultaneously. To achieve the objectives, firstly, two different disturbance observers are designed. Secondly, we construct boundary controllers based on the two designed disturbance observers and boundary measurable signals. Then, with the two disturbance observers, the boundary disturbance compensation is achieved, and with the designed boundary controllers, the uniform boundedness of the flexible arm is guaranteed. Moreover, the well-posedness of the closed-loop system under the designed boundary controllers is discussed by means of the operator semigroup theory. Finally, the effectiveness and advantages of the proposed controllers are demonstrated through simulations and physical experiments.

Keywords:

• Flexible arm
• boundary control
• disturbance observer
• partial differential equation
• uniform boundedness

Acknowledgements

The authors would like to thank the editors and the anonymous referees for their valuable comments and suggestions, which substantially improved the original manuscript.

Disclosure statement

The authors declare that they have no potential conflict of interest concerning the publication of this manuscript.

Additional information

Funding

This work was supported by Natural Science Foundation of Jiangsu Province [grant number BK20201340] and 333 High-level Talents Training Project of Jiangsu Province.