Advanced Negative-Derivative Feedback Control for Nonlinear Resonance Suppression in 2-DOF AFM Systems

A Negative Derivative Feedback (NDF) controller is designed for vibrations suppression of an atomic force microscope (AFM) model. The controlled system is modeled as a two-degree-of-freedom (2-DOF) closed-loop dynamic system. The average method was used to derive approximate analytical solutions. All possible resonance conditions were identified, with particular attention given to the simultaneous resonance case Ω=ω1, Ω1=2ω1, ω2=ω1, identified as the most critical. For validation and proper insights, the system was also solved numerically using the fourth-order Rung–Kutta method. The time response of the AFM system in contact mode was analyzed before and after applying the NDF controller under the worst-case resonance conditions. A comprehensive parametric study was conducted to evaluate the controller’s robustness and effectiveness. The results demonstrate a high degree of agreement between the numerical simulations and the analytical approximations, confirming the reliability of the approach.