Nonlinear behavior analysis and control of the atomic force microscope and circuit implementation

In this paper an analysis of the nonlinear dynamic behavior and control of an atomic force microscope system is described. Phase plane trajectories, spectrum analysis, bifurcation analysis, the Poincare cross-section, the maximal Lyapunov exponent, and other numerical analysis methods were used to observe and verify the dynamic characteristics and the differential equations for the system. The results showed that at specific excitation frequencies, the system will exhibit nonlinear behavior that may be cyclic, multi-cyclic or acyclic. A Psim circuit simulation using the same parameters showed the same nonlinear behavior, as did laboratory circuit implementations. The results also showed than an understanding and control of the dynamic characteristics would not be an easy task. However, they could be used as a basis for the suppression and control of nonlinear behavior and vibration in atomic force microscope systems. A proportional-derivative system was also used, with particle swarm optimization, to find the control parameters K-p and K-D and a fuzzy controller was used to compare the results. The controller simulation and hardware implementation both effectively inhibited the nonlinear behavior and were most helpful for the control and enhancement of measurement accuracy.