Distributed control of a class of flexible mechanical systems with global constraint

Abstract

In this paper, the constrained problem is investigated for both flexible string model and Euler–Bernoulli beam model with the tip payload, based on an infinite dimensional generalisation of a distributed control method. The control objectives are to develop the control law so that the motion of flexible mechanical systems can track a desired reference signal, and ensure that the string or beam remain in a constrained space. We prove that, with the proposed control, the tracking error is exponentially stable without violation of the constraint. The proof of convergence is based on an Integral-Barrier Lyapunov Function (IBLF), and extensive simulations are provided to illustrate the performance of the control system.

Keywords:

• distributed control
• flexible structures
• distributed parameter system
• integral-Barrier Lyapunov function
• global constraint

Acknowledgements

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 61203057], [grant number 61125306]; and the National Basic Research Program of China (973 Program) [grant number 2014CB744206].