Chaotic motion in the cantilever of an atomic force microscopy and its bifurcation properties were investigated by the method of numerical simulation, and the range of the control parameter was examined for two control methods, respectively, i.e., timedelayed feedback control and periodic signal control. Furthermore, the ranges of different control parameters for periodic orbits with the same period were also considered. The research results provide significant theoretical reference for the analysis of the nonlinear dynamical behavior in complex systems and the control of chaotic motion. Simultaneously our results are valuable in engineering applications for controlling the motion of main component of an atomic force microscopy and improving its measurement accuracy.