This paper introduces a novel methodology to embed desired reference trajectories into the modal dynamics of an underactuated system through eigenstructure assignment. A unique characteristic of the method is that it decomposes the control input into two parts: an open loop, periodic excitation signal, and a closed loop feedback signal. The periodic excitation causes the system’s natural modes to resonate in a fashion that matches the desired trajectory; modal dynamics, determined by the system’s eigenstates (eigenvectors and their corresponding eigenvalues), are shaped by tuning physical and control parameters concurrently. The method requires the solution of a dual-domain eigenstate factorization problem, in which it is necessary to compute certain unknown elements of a matrix and of its eigenvectors at the same time.
Embedding Desired Eigenstates into Active and Passive Dynamics of a Linear, Underactuated Feedback System
Medford, MA 02155
Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 8, 2013; final manuscript received August 21, 2013; published online April 28, 2014. Assoc. Editor: Michael Kokkolaras.
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Saunders, F., and Rife, J. (April 28, 2014). "Embedding Desired Eigenstates into Active and Passive Dynamics of a Linear, Underactuated Feedback System." ASME. J. Mech. Des. July 2014; 136(7): 071005. https://doi.org/10.1115/1.4025295
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