THE CRITERION OF HIGHER PERIOD ON CONTROLLING CHAOS IN A VIBRO-IMPACT SYSTEM

The main contribution of this paper lies in the design of a dynamic intermittent feedback control strategy and the determination of higher period by combining Poincaré map and power spectrum technique. The controlling methods can save great energy and transmit the chaos in a vibro-impact system into different nP higher periodic and nH quasiperiodic orbits. A desired unstable periodic orbit, which is embedded in the chaotic attractor, is stabilized and the controlled system can maintain its stable dynamical behaviors in large windows of parameter space. The number of higher periodic orbits and quasi-periodic orbits represented by attracting invariant circles can be identified accurately. Some typical control results are given by numerical analysis, which are helpful for designing, vibration control and safety operating of vibro-impact systems.