For an underactuated translational oscillators with rotating actuator（ TORA）

whose dynamics model is converted into the linear model with matching uncertainties and the modeling errors of zero dynamics

and put forward a certain constraints to the modeling errors of zero dynamics. In system design

linear controller and adaptive controller are respectively used to calm your system of linear part and matching uncertainties

using the observer to obtain state estimation

through feedback system to adjust neural network weights by the on- line way. Simulation results show that the proposed method is simple and effective.