On nonlinear dynamics of a parametrically excited pendulum using both active control and passive rotational (MR) damper

Abstract

This paper presents two control strategies for a parametrically excited pendulum with chaotic behavior. One of them considers active control obtained by nonlinear saturation control (NSC) and the other a passive rotational magnetorheological (MR) damper. Firstly, the active control problem was formulated in order to design the external torque for the pendulum, considering the NSC. Numerical simulations were carried out in order to show the effectiveness of this method for the active control of the pendulum oscillation. The ability of the control of the proposed NSC in suppression of the chaotic behavior, considering the proposed parameters, was tested by a sensitivity analysis to parametric uncertainties. In the case of the passive rotational MR damper, firstly the influence of the introduction of the MR in a pendulum was performed considering the 0-1 test. Different electric currents are applied to suppress the chaotic behavior of the system. The numerical results showed that the simple introduction of a passive rotational MR damper without electric current did not change the chaotic behavior of the system. However, it is possible to keep the pendulum oscillating with periodic behavior using the rotational MR damper with energizing discontinuity.