An experimental approach to multi-input multi-output nonlinear active vibration control of a clamped sandwich beam

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Large amplitude vibrations are often associated with geometric nonlinearity. These nonlinear systems are usually controlled using linear controllers, such as positive position feedback (PPF). Nonlinear control has also often been limited to single-input single-output (SISO) architectures. The present study develops a nonlinear PPF controller implemented with both a SISO and a multiple-input multiple-output (MIMO) architecture on a real experimental set-up, consisting of a clamped composite sandwich beam. The controller aimed to reduce the vibration amplitude observed when the structure was subject to a stepped-sine excitation in the frequency neighborhood of the first natural frequency for different force excitation levels. The developed nonlinear controller is based on a linear PPF controller to which a cubic term was added since the system under study is of hardening type. The control parameters were selected by optimization of the reduction of the vibration at low excitation amplitude. The nonlinear MIMO and SISO versions of the controller were compared to linear MIMO and SISO versions, which omitted the cubic term but maintained the other parameters. The nonlinear controllers were found to outperform the linear ones, and the MIMO versions of each controller also outperformed the SISO ones. Overall, the experimental evidence shows that a nonlinear MIMO PPF controller should be preferred for the application under study.