Output feedback near-optimal control of atomic force microscope

This is the authors' abstract. We don't add key points for this paper.

This paper presents a compact atomic force microscope (AFM) model based on a singular perturbation approach tailored for systems with relatively high cantilever stiffness. This method simplifies the model, allowing for a faster response to the Van der Waals interaction forces between the measurement sample and the cantilever tip. For scenarios where the tip-sample interaction force is unknown, the proposed model serves as the basis for designing a nonlinear, near-optimal feedback control technique. This control approach guides the cantilever tip along a desired trajectory while maintaining it vertically aligned at the balance point of attraction and repulsion forces. Additionally, a cascaded high-gain observer is designed to estimate AFM dynamics using only the measured piezo tube position. Combined with the near-optimal feedback control, this observer addresses the output feedback control problem. The proposed controller is validated through a simulation example.