Scalar Modal Control of a Nonlinear System Using Time Varying Gain

摘要

A nonlinear system inhibited some relationship between system stability and controller off-time. An increase in the off-time of the controller from 6.5% to 78.0% resulted in the nonlinear system maintaining stability over 50 time periods. A nonlinear system was controlled using feedback based on the unstable system parameters. The Henon and Heiles model was used to provide an unstable periodic orbit. The linearized equations of motion, using Floquet Theory, were developed into variational equations. A controller was derived based on a system characteristic: the controllability matrix. Together with the nonlinear system the controller was integrated for many time periods using zero initial displacement. Stability was achieved for about 50 time periods of the zero displacement conditions.