The main resonance of a nonlinear oscillator under semi-active control is investigated, where the bifurcation and singularity are also included. The Main resonance is obtained analytically at first, and then all the bifurcation diagrams are researched and classified in the space composed of the amplitude of excitation and the detuning parameter through singularity theory. It could be proved that the response is the universal unfolding of the winged cusp bifurcation, and all of the bifurcation diagrams of the system are verified through numerical method. It is shown that this analytical method could not only analyze the response of the semi-active control oscillator, but also research the global dynamic behavior.

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