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

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.