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

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