Active control of translating media with arbitrarily varying length

The general control laws for pointwise controllers to dissipate vibratory e nergies of translating beams and strings with arbitrarily varying length ar e presented. Special domain and boundary control laws that can be easily im plemented result as a special case. Sufficient conditions for uniform stabi lity and uniform exponential stability of controlled systems are establishe d via Lyapunov stability criteria. Numerical simulations demonstrate the ef fectiveness of the active controllers in stabilizing, translating media dur ing both extension and retraction. Optimal gains leading to the fastest rat es of decay of vibratory energies of controlled systems are identified. It is shown that under the optimal control gains, translating media can be com pletely stabilized during extension and retraction.