<p>Recently, artificial self-excited oscillations by external forces based on positive velocity feedback and other methods have been applied in a variety of systems, and the range of applications of these oscillations is expected to expand. The steady-state response of self-excited oscillations is generally dependent on the system’s nonlinearity. Previous studies have mainly focused on system modeling and analysis by considering nonlinearity up to the cubic order. To extend the usefulness of self-excited oscillations further, more accurate modeling and higher-order nonlinear analysis will be required. In this study, we derive a mathematical model that considers quintic nonlinearity and, using the method of multiple scales, perform a fifth-order nonlinear analysis of artificial self-excited oscillations with both linear and nonlinear feedback. As an essential model, we consider a cantilever beam that is subjected to feedback excitation by a piezoelectric actuator. The equations of motion, which consider the quintic nonlinear inertial and restoring forces of the beam when subjected to linear and nonlinear damping effects, are presented. The fifth-order nonlinear analysis shows that the cubic nonlinear inertial and restoring forces fundamentally affect the bifurcation of the response amplitudes, such as the newly produced saddle-node bifurcation, which cannot be predicted by the analysis when it is considered up to the cubic nonlinearity. Additionally, we demonstrate that the cubic nonlinear feedback can control the saddle-node bifurcation point and also eliminate it. Furthermore, the theoretically predicted quintic nonlinear characteristics of the self-excited cantilever beam and the controllability of the bifurcation phenomena are investigated experimentally using simple apparatus.</p>