The classical single-iron suspension model linearizes the electromagnetic force for further research, ignoring the influence of the nonlinear characteristics of the electromagnetic force on the system structure stability and control effect. In this paper, a single iron suspension model considering nonlinear electromagnetic force is established, and the state feedback method with displacement-velocity-acceleration as feedback parameters is used to control. The harmonic balance method is used to solve the amplitude-frequency response of the main resonance of the system and analyze the influence of each feedback parameter on the amplitude-frequency response of the system. The singularity theory is used to study the static bifurcation phenomenon of the system, and the dynamic bifurcation phenomenon of each feedback parameter in the state feedback method is studied. The global bifurcation characteristics of the system are studied by using cell mapping theory. The results show that the displacement and acceleration feedback parameters will change the resonance frequency domain and the resonance peak value of the system, and the velocity feedback parameters only change the resonance peak value of the system. The transition set of the system divides the unfolding parameter interface into three regions, and the corresponding bifurcation topology can be obtained in different parameter regions. In a certain range, when the feedback parameters of displacement, velocity and acceleration change, the motion state of the system will appear the situation of chaotic motion and period doubling motion alternating with each other. Under certain parameter conditions, the external excitation frequency and the feedback parameters of the system change, and the number and area of the attractor and its domain of attraction of the system will change.
