Partial feedback linearization on a harmonically excited beam with one-sided spring

Partial feedback linearization is applied to a harmonically excited beam with one-sided spring to reduce vibration amplitudes while keeping the control effort small. Vibration amplitudes are reduced by globally stabilizing the small amplitude 1-periodic solution which is one of the coexisting solutions. As the 1-periodic solution represents a natural solution of the uncontrolled system, no control effort will be needed once the system vibrates in the 1-periodic response. To control the multi-degree-of-freedom (d.o.f.) beam system to the 1-periodic solution, only one actuator is used that controls one (d.o.f.). The behaviour of the other d.o.f.s is eventually described by the zero dynamics. Whether these d.o.f.s converge to the 1-periodic solution depends on the stability of the zero dynamics. The global asymptotic stability of the non-autonomous zero dynamics can be partially determined by a frequency domain technique known as the circle criterion. However, the circle criterion does not guarantee stability at all actuator positions along the beam