Boundary feedback stabilisation of a flexible robotic manipulator with constraint

ABSTRACT

In this paper, the flexible robotic manipulator is modelled as a distributed parameter system, represented by a group of partial differential equations and ordinary differential equations. Control is designed at the boundary of the robotic manipulator based on integral-barrier Lyapunov function to suppress the vibration of the elastic deflection and track the desired angular position. With the proposed boundary control, the manipulator can be driven to the desired set-point with angular position and elastic deflection stay under the former setting constraint. Uniformed boundedness of the closed-loop system under the unknown time-varying disturbance is achieved. Stability analysis of the closed-loop system is given by employing the Lyapunov stability theory. Simulation results illustrate the effectiveness of the proposed boundary controller for ensuring output constraint and suppressing vibrations.

KEYWORDS:

• Flexible robotic manipulator
• distributed parameter system
• vibration control
• boundary control
• flexible structure

Acknowledgments

The authors would like to sincerely extend their appreciation to the editor-in-chief, the associate editor, and the anonymous reviewers for their constructive comments which helped improve the quality and presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61522302], [grant number 61203057]; the National Basic Research Program of China (973 Program) [grant number 2014CB744206] and the Foundation of Shanghai Key Laboratory of Deep Space Exploration Technology [grant number DS201504-001].