Auto-resonance control of a nonlinear, parametrically excited system - application to nano-scale topography sensing

A closed-loop control scheme of a parametrically excited nonlinear structure is described. By locking onto the relative phase, the open-loop unstable, non-unique solution branches are stabilized in closed-loop under a 2:1 excitation. The closed-loop automatically locks onto any desired point on the solution branches exploiting the uniqueness of phase values. The method is utilized to actuate axially driven slender beams, representing a nanowire-based sensor. Automatic excitation is carried out utilizing a relay-based Autoresonance scheme fed by automatic gain control and a tunable phase shifter. By inducing parametric excitation, the nonlinear response is exploited to obtain high sensitivity to small changes in potential forces (e.g. Van der Waals) and thus enabling the detection of minute topographic features. The paper briefly outlines the mathematical model, asymptotic analysis, numerical simulations and large-scale experiments, all validate the proposed method where several modes of vibrations are excited to sense the potential forces.