Embedding Desired Eigenstates into Active and Passive Dynamics of a Linear, Underactuated Feedback System

Abstract

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 dualdomain eigenstate factorization problem, in which it is necessary to compute certain unknown elements of a matrix and of its eigenvectors at the same time.