Enhancing fixed-point control robustness for experimental non-contact scans with the Transverse-dynamic Force Microscope

The Transverse Dynamic Force Microscope (TDFM) is unique as it uses a vertical cantilever, and genuinely permits scans without physical interaction with a specimen. Recently, we suggested a simple control scheme for true non-contact scans using the TDFM. This control scheme implemented in FPGA-systems (Field-Programmable Gate Arrays) was developed for a non-contact control task at specific points above a given specimen, but dynamic specimen placement requirements in the horizontal plane through an x-y stage were neglected. Considering the large range of the specimen, a practical approach has been developed which reconfigures the fixed-point-arithmetic control implementation and permits a dynamic scan in true non-contact mode. For this, an off-line numerical optimization has been developed which establishes the most suitable fixed-point ranges of the control algorithm, avoiding algorithm overflow. This creates an implementation robust to plant and sensor non-linearities and dynamic changes during non-contact scans. Experimental non-contact scanning results, for nano-spheres in water, demonstrate the imaging capacity of the TDFM.