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.
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.