Stabilization of periodic solutions of nonlinear mechanical systems : controllability and stability

In nonlinear mechanical systems, which show stable (sub)harmonic, quasi-periodic and/or chaotic responses, together with coexisting (unstable) harmonic solutions, a large reduction of maximum subharmonic, quasi-periodic, or chaotic displacement might be established if the coexisting unstable harmonic solution could be made stable. The control effort to obtain this goal can be very small. In this article, a method is presented for determining the controllability of periodically excited nonlinear mechanical systems. This method determines if an unstable periodic solution can be stabilized using control. Furthermore, a method for calculating the local stability of an earlier developed control method (i.e., sliding computed torque control) for the above-mentioned goal is presented. Simulation results are presented for a periodically excited beam system supported by a one-sided spring to demonstrate the capabilities of the above-presented methods