Input shaping techniques reduce the residual vibration in flexible structur
es by convolving the command input with a sequence of impulses. The exact c
ancellation of the residual structural vibration I ia input shaping is depe
ndent on the amplitudes and instances of impulse application. A majority of
the current input shaping schemes are instances are inherently open-loop w
here impulse application at inaccurate instances can lead to system perform
ance degradation. In this paper, ne develop, a closed-loop control design f
ramework for input shaped systems. This framework is based on the realizati
on that the dynamics of input shaped systems give rise to time delays in th
e input. Thus, we exploit the feedback control theory of time delay systems
for the closed-loop control of input shaped flexible structures. A Riccati
equation-based and a linear matrix inequality-based frameworks are develop
ed for the stabilization of systems with uncertain, multiple input delays.
Next, the aforementioned framework is applied to two input shaped flexible
structures systems. This framework guarantees closed-loop system stability
and performance when the impulse train is applied at inaccurate instances.
Two illustrative numerical examples demonstrate the efficacy of the propose
d closed-loop input shaping controller.