Adaptive sliding mode control of nonlinear gyro chaotic vibration

In this paper, we investigate the control of chaos in nonlinear gyros. The model system which we study is the gyroscopes which has attributes of great utility to navigational, aeronautical and space engineering and have been widely studied. This Gyro has a chaotic vibration for some range of parameters. To control the chaotic vibration of this system, a switching surface is adopted so that it becomes easy to ensure the stability of the error dynamics in the sliding mode. Then an adaptive sliding mode controller (ASMC) is derived to guarantee the occurrence of the sliding motion. The adaptive laws are derived in the Lyapunov sense to guarantee the stability and tracking of the controlled system. Two different desired responses are considered in this study and the effectiveness of the proposed method is shown for both cases.