A nonlinear dual-mode active vibration controller for hardening systems and its experimental application to a beam

The control of nonlinear vibrations, such as those arising from geometric nonlinearities and large amplitude, has often been limited to the first natural mode. In this work, a novel nonlinear dual-mode multiple-input multiple-output (MIMO) positive position feedback (PPF) controller is presented and tested experimentally on a clamped composite sandwich beam subject to a stepped-sine-excitation with increasing force excitation levels in the frequency neighbourhood of the first and second natural frequencies. This nonlinear controller contains two linear PPF controllers, targeting the first and second natural frequencies, each one augmented with a cubic term designed to counter the hardening behaviour of the test structure. Control parameters were chosen by optimizing the vibration reduction observed at low excitation amplitudes. The nonlinear dual-mode MIMO controller was compared to a single-input single-output version, and to a linear version in which the cubic terms were removed. The nonlinear dual-mode MIMO was shown to outperform both. A linear dual-mode MIMO controller was compared to two linear single-mode MIMO controllers, targeting the first and second mode respectively, and was found to outperform both when applied to the first mode. The effect of varying the nonlinear cubic term of the nonlinear dual-mode MIMO controller was also investigated, indicating better vibration reduction for higher cubic terms, up to some values. Overall, this study shows that a nonlinear dual-mode MIMO PPF controller is the preferred option for controlling the first two modes of the beam under study.