Exponentially stabilizing boundary control of string-mass systems

Exponentially stabilizing controllers are derived for the transverse vibrat ion of a string-mass system modeled by the one-dimensional wave equation wi th a pinned and a controlled boundary condition. Lyapunov's theory for dist ributed parameter systems, the Meyer-Kalman-Yakubovitch Lemma, and integral inequalities prove that a class of boundary controllers provide strong exp onential stability. These controllers are designed so that the transfer fun ction between boundary slope and velocity satisfies a restricted strictly p ositive real condition. An example controller, consisting of boundary posit ion, velocity, slope, slope rate, and integrated slope feedback, is impleme nted on a laboratory test stand. In experimental impulse response tests, th e controlled response decays six times faster than the open-loop response a nd has half the response amplitude.