Particle swarm optimization used with proportional–derivative control to analyze nonlinear behavior in the atomic force microscope

Abstract

An investigation of nonlinear probe behavior in an atomic force microscope, caused by different excitation frequencies, was carried out as well as an analysis and subsequent regulation using particle swarm optimization in combination with proportional–derivative control. The dynamic behavior was resolved by numerical analysis using the atomic force microscope probe governing equations and the properties were examined using phase portrait, bifurcation diagrams, Poincaré maps, and the maximum Lyapunov exponent. The results show that excitation frequency ratio can actuate periodic, sub-harmonic, and chaotic behavior in the system under certain conditions. A proportional–derivative controller was employed to control the chaos, and particle swarm optimization was used to find the proportional–derivative parameters. Integral absolute error was used to evaluate the quality of the parameters for the performance indicator. The generation of nonlinear behavior and a chaotic state may be effectively suppressed to improve the stability and performance of an atomic force microscope system.