TM-AFM nonlinear motion control with robustness analysis to parametric errors in the control signal determination

Nonlinear motion of the microcantilever probe in the Atomic Force Microscope (AFM) has been extensively studied considering mainly the van der Waals forces. Since the behavior of the microcantilever is vital to quality of generated images, the study of control strategies that force the probe to avoid undesired behavior such as chaotic motion, is also of significant importance. A number of published works has shown that the microcantilever is subject to chaotic motion for a certain combination of parameters. For such a parameter combination, the control system must suppress the chaotic motion. Here, an study of the AFM mathematical model is presented, aiming to find a region of operation of the AFM where the motion is chaotic. In order to suppress the chaotic motion, a periodic orbit of the system is obtained, and the controller forces the system to that periodic orbit. Two control strategies are used, namely: The State Dependent Riccati Equation (SDRE) and the Optimal Linear Feedback Control (OLFC). Both control strategies consider the complete nonlinearities of the system, and the OLFC guarantees the global stability. The numerical simulations carried out showed the efficiency of the control methods as well as the sensitivity of each control strategy to parametric errors. Without the parametric errors, both control strategies were effective in maintaining the system into the desired orbit. On the other hand, in the presence of parametric errors, the SDRE technique was more robust than the OLFC.