A nonlinear vibration controller is proposed for the translational oscillators with rotating actuator (TORA) system with the recursive technology. A composite state variable (CSV) is defined for the TORA system to start the recursive process. The design procedure treats the some state variables as virtual control inputs to design the virtual controllers step by step until the nonlinear vibration controller is obtained. The system stability is studied via a stability theorem and simulation results show the validity of the proposed controller
