Nonlinear time delay saturation-based controller for suppression of nonlinear beam vibrations

In the present paper, time delay is considered in active suppression of nonlinear vibrations applying saturation-based controller. Its effect on the system behavior is studied. Time delay inherently exists in many active control systems as a result of transport delay, on-line computation, measurements of the system states, executing the control algorithms and processing of the errors and control signals. The 1:2 internal resonance cases between the main system and the nonlinear saturation-based controller is studied when the main system is excited at a frequency near its natural frequency. The method of multiple scales is applied to obtain approximate solution for the system response. With the time delay varying for fixed controller parameters, it is seen that the vibration can be suppressed at some values of time delay. These values form a so called “vibration suppression region” which we found as a periodic function of time delay. However, the vibration suppression is invalid at some values of time delay. The effects of the gains γ,λ and the excitation amplitude f on the vibration suppression are investigated. The analyses showed that, all predictions from analytical solutions are in good agreement with the numerical simulation. A comparison with the available published work is included.