Chaos control in AFM system using sliding mode control by backstepping design

This paper presents a robust algorithm to control the chaotic atomic force microscope system (AFMs) by backstepping design procedure. The proposed feedback controller is composed by a sliding mode control (SMC) and a backstepping feedback, so its implementation is quite simple and can be made on the basis of the measured signal. The developed control scheme allows chaos suppression despite uncertainties in the model as well as system external disturbances. The concept of extended system is used such that a continuous sliding mode control effort is generated using backstepping scheme. It is guaranteed that under the proposed control law, uncertain AFMs can asymptotically track target orbits. The converging speed of error states can be arbitrary turned by assigning the corresponding dynamics of the sliding surfaces. Numerical simulations demonstrate its advantages by stabilizing the unstable periodic orbits of the AFMs and this method can also be easily extended to elimination chaotic motion in any types of chaotic AFMs.