Closed-loop input shaping for flexible structures using time-delay control

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.