Backstepping stabilization of a clamped string with actuation inside the domain
Résumé
In this paper, we consider the stabilization of a clamped string with actuation located inside the domain. Such a model can represent the simplified dynamics of a microendoscope. Inspired by the Port Hamiltonian framework, we use the Riemann invariants of the energy states to reformulate this problem as stabilizing a chain of two coupled hyperbolic subsystems with actuation at the in-between boundary. After applying successive transforms, it is shown to be equivalent to stabilizing a neutral-type delay-differential equation. A suitable controller is derived using the backstepping methodology with a Fredholm integral transform. Some simulations illustrate this approach.
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