PARAMETRIC CONTROL OF FLEXIBLE SYSTEMS

One position sensor, a bilinear observer, and quadratic, observer-base d feedback to a parametric actuator asymptotically stabilize n-modes o f 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 cond itions, and forcing amplitude. A forced spillover instability is disco vered that can destabilize uncontrolled modes with insufficient dampin g. A control bound is determined, based on the damping coefficients an d frequencies of the modes, that prevents this instability. Experiment s on a tension-controlled, pinned-pinned beam demonstrate that paramet ric control provides substantially faster transient decay and constrai ned response at resonance.