Optimal input shaping filters for non-zero initial states

Authors:
Abhishek Dhanda;Joshua Vaughan;William Singhose
Affiliations:
Department of Mechanical Engineering, Stanford University, Stanford, CA;George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia;George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia
Venue:
ACC'09 Proceedings of the 2009 conference on American Control Conference
Year:
2009

Citing 6
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Abstract

This paper presents an approach to design optimal vibration reduction input shapers for systems with non-zero initial conditions. The problem is first formulated as an optimal control problem and the optimal solution is shown to be bang-bang. Once the structure of the optimal shaper is known, a parametric problem formulation is presented for the computation of the switching times. For digital implementation, discrete time approximate solutions are derived by solving a quasi convex Linear Program. Simulation results are shown for closed-form implementation of these filters on flexible structures. The digital solutions are experimentally verified on a portable bridge crane.