Control of a Delayed Limit Cycle Using the Tilt Angle of a Fast Excitation

We investigate the tilting effect of a fast excitation on self-excited vibrations in a delayed van der Pol pendulum. Specifically, we analyze the simultaneous effects of fast excitation and time delay in controlling self-excited oscillations taking into account the influence of the incline angle of the fast excitation. We use an averaging technique to reduce the original oscillator to a slow flow system. Analysis of stationary solutions of this slow flow provides analytical approximations of regions in parameter space where self-excited vibrations can be controlled. We have shown that in the case where the delay and the fast excitation are both imposed in the system, the incline of the fast excitation can be an alternative to control self-excited vibrations.