Design of a nonlinear oscillator using a nonlinear feedback

Resonances induced without periodic excitation are called self-excited oscillation. In the self-excited linear system, the amplitude grows with time. However, the existence of nonlinear damping produces the steady state. In this paper, we propose a method in order to realize the desired steady state amplitudes by using a nonlinear feedback in the self-excited system. Furthermore, it is theoretically clarified in the case of small initial disturbance that the Coulomb friction can avoid the occurrence of the self-excited oscillation in the system with negative damping.