Abstract

In this paper we determine the general control laws for point-wise controllers that dissipate energies of vibration of translating strings and beams with an arbitrarily varying length. Special domain and boundary control laws that can be easily implemented result as a special case. Sufficient conditions for uniform and uniform exponential stability of controlled systems are established via Lyapunov stability criteria. Numerical simulations demonstrate the effectiveness of active controllers in stabilizing translating media during both extension and retraction. Optimal gains leading to the fastest rates of decay of energies of vibration of controlled systems are identified. It is shown that under the optimal control gains, translating media can be completely stabilized during extension and retraction.

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