Linear and nonlinear feedback control of chaos in a thermal convection loop

In this paper, the linear and nonlinear active feedback controls of chaos in thermal convection loop are studied theoretically. The one-dimensional partial differential equations consisting of mass, momentum, and energy balances are expanded to an infinite set of ordinary differential equations. The first mode of this set of equations is three equations which are similar to the celebrated Lorenz equations. These equations can be decoupled from the rest of the set and can be solved independently of other equations without need of truncation. The temperature difference as the controlling signal and the power input as the controlled signal are used. The linear and nonlinear active feedback control are used to adjust the wall temperature. It is found that the linear and nonlinear active feedback control can change the flow structure in a thermal convection loop. The chaos suppression or enhancement can be realized and some unstable periodic orbits can be stabilized by nonlinear feedback control successfully.