A super-twisting observer for atomic-force reconstruction in a probe microscope

Abstract

This paper presents a new methodology employing a super-twisting sliding mode observer to reconstruct un-measureable atomic-forces at nano-Newton precision in a Vertically Oriented Probe Microscope (VOPM). The VOPM senses the deflection of a vertically oriented cantilever, caused by shear-force interaction with a confined water layer above the sample-substrate. The paper describes the development of a model and the subsequent experimental process for computing its parameters. This forms the basis for the design of a super-twisting observer to estimate the unknown shear-forces. The reconstructed force can be decomposed into elastic and viscous components, which are important in biological research.

Digital implementation of sliding‐mode control via the implicit method: A tutorial

“…The big challenge is the analysis of implicitly discretized differentiators in closed-loop systems. The case of closed-loop systems incorporating super-twisting state observers [133], may also be worth investigating.…”

“…A basic assumption is for some known constant M . As is known, the dynamics in (55) also corresponds to that of a supertwisting observer for a dimension two system, 26,93,101 where the two states are the observation errors.…”

“…The big challenge is the analysis of implicitly discretized differentiators in closed‐loop systems. The case of closed‐loop systems incorporating supertwisting state observers, 101 may also be worth investigating. Higher order sliding‐mode controllers, other than twisting and supertwisting. Infinite dimensional homogeneous systems 113 (would maximal monotone operators as used for the first time in sliding‐mode control in References 31‐33,78, be useful in this context? ). Improve the robustness with respect to noise on the sliding variable (despite of the fact that modern SMC possess good robustness properties in that respect, even enhanced by the use of proper differentiators). Backstepping control with nested controllers for uncertain triangular systems of dimension n ≥ 3 (Section 3.4).…”

Real-Time Force Reconstruction in a Transverse Dynamic Force Microscope

“…the water buffer in this work. For example, this coefficient can be chosen following the damping coefficient tuning method given in [34]. Then, the scaling factor can be tuned (as suggested in [19]) by adjusting the magnitude of the theoretical model to fit the measured Y (s)/U (s) response in the low frequency range, where the phase values are close to zero.…”

Adaptive Nonlinear Control for the Stabilized Platform With Disturbance and Input Saturation

“…And the algorithm does not have the problem of chattering phenomena and has better ability to suppress noise. Supertwisting observer (STO) [13] is used in many applications [14,15]. Considering the characteristics of STO and ESO, super-twisting extended state observer (STESO) [16] is designed to estimate states and disturbances.…”