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This article investigates the properties, from a nonlinear control system standpoint, of atomic force microscope (AFM) systems, whenever operated in contact mode and controlled in the vertical direction by proportional-integral control law. By modeling the AFM as a system in which a piezo-electric actuator and a cantilever mutually interact in order to produce the sample topography, ensuing distortions affecting the quality of the yielded topography measurement are naturally cast and analyzed. The proposed investigation considers distortions due to the inception of hysteresis and vibrational dynamics within the piezo-actuator or provoked by system saturation. Both hysteresis and saturation are inherently nonlinear phenomena and are modeled as such. In spite of the inherently nonlinear nature of the AFM dynamics, investigations of the contact mode case from a nonlinear standpoint are lacking within the AFM literature. As the topography yielded by the AFM completely relies on its control algorithm, to the point that the measurement itself corresponds to the control action v(t), it becomes of paramount importance to understand how v(t) relates to the actual topography, and how such a relationship is affected by the aforementioned distortions. This article hence intends to contribute to the AFM literature, by providing a study in which the very meaning of the image measurement yielded by the AFM is investigated, in the light of distortions due to nonlinear phenomena. The AFM is considered to be operated in contact mode with a PI algorithm. Furthermore, as a byproduct of the derived nonlinear stability analysis, a novel, model-based algorithm for tuning the PI control gains is provided. Finally, experimental results are presented and analyzed in view of the derived theory.

Traffic congestion, energy efficiency and environmental issues are fueling the interest in Light Electric Vehicles (LEV's). Electric Human-Powered Hybrid vehicles show a great potential: they are cost effective, safe, easy to use and have a small footprint. In this paper, we discuss an electrically assisted kick scooter. Electric scooters are common on the market but, being throttle-controlled, they sit in a legislative gray area between human powered vehicles and electric vehicles. The proposed design solves this issue by designing a genuine electrically assisted scooter. The proposed design does not have any human machine interface but controls the electric assistance in a transparent way. The user only needs to kick the scooter as she would do with a normal scooter and the control system smoothly delivers the assistance. The proposed solution is based on a kick detection algorithm and a closed-loop control of the vehicle velocity. The details of the control system are discussed in the paper and an extensive experimental validation shows that the electric assistance cuts in half the effort necessary to operate the vehicle with a battery consumption of 4 Wh/km (half that of an electrically assisted bicycle)