Exciting Nonlinear Modes of Conservative Mechanical Systems by Operating a Master Variable Decoupling

Abstract

Eigenmanifolds extend eigenspaces to nonlinear mechanical systems with possibly non-Euclidean metric. Recent work has shown that hyper-efficient oscillations can be excited by simple controllers, which simultaneously stabilize an Eigenmanifold and regulate the total energy. Yet, existing techniques require imposing assumptions on the system dynamics that may not be fulfilled by the controlled system. This paper overcomes these limitations, by allowing for a partial dynamic compensation, which produces an advantageous decoupling of the system's dynamics. This decoupling happens in a convenient set of coordinates, which are induced by the modal characterization of the mechanical system. Two control algorithms taking advantage of this property are proposed and validated in simulation