Chaos controlling and anticontrolling problems for the mechanical centrifugal flywheel governor systems

摘要

The complex dynamics characters of the mechanical centrifugal flywheel governor system are studied. The dynamical equation and the state equation of the mechanical centrifugal flywheel governor system are established according to Lagrangian equations. By the phase portraits, the motions of the nonautonomous system are studied under the definite parameters. And by Poincare map, the route from periodic motion to chaos is studied under the presented system parameters. An adaptive differential feedback is constructed to control the chaos of the mechanical centrifugal flywheel governor system. The chaos of the system is controlled via x |x|, too. And the periodic motion of the system is anticontrolled to chaotic motion by add a linear feedback item. The phase portraits of the controlled and anticontrolled system are obtained. The advantages of the two controlled methods are that the collect of the control signals are simple and can put on any time and the chaotic system can be asymptotically stabilized to equilibriums with small control, and the control disturbance will tend to zero at the same time. Chaos anticontrolling is helpful to make a non-chaotic dynamical system chaotic. The orbits of the system can be controlled by these three methods according to our target.