Uncontrollable Singularities in Nonlinear Systems

The problem of tracking through singular sub-manifolds is extended to include regions of uncontrollability. A special, pragmatic class of nonlinear systems with uncontrollable, singular points is analyzed. The unique behavior of these systems is compared to systems with controllable, input singularities such as the well-known ball and beam system that has enjoyed considerable attention throughout the literature. Analysis reveals the deficiency of existing control solutions to properly handle an input singularity that is also uncontrollable. A sufficient condition for successfully maneuvering through an uncontrollable, singular submanifold is derived providing a basis for reference trajectory design. An illustrative example of practical applicability is presented for a disk drive, commutational ramp load actuator