Parametric Control of Flexible Systems

One position sensor, a bilinear observer, and quadratic, observer-based feedback to a parametric actuator asymptotically stabilize n-modes of a flexible system. Using a perturbation approach, the transient and forced response of a controlled mode are approximated. The decay rate and resonance amplitude are related to the control gains, initial conditions, and forcing amplitude. A forced spillover instability is discovered that can destabilize uncontrolled modes with insufficient damping. A control bound is determined, based on the damping coefficients and frequencies of the modes, that prevents this instability. Experiments on a tension-controlled, pinned-pinned beam demonstrate that parametric control provides substantially faster transient decay and constrained response at resonance.