This Report covers the initial research into modeling the Scanning Electrochemical Microscopy (SECM) system for the purposes of high precision control. The SECM system is a microscope based around electro-chemical effects. It operates in several modes relating on degrees of conductivity of the involved elements. The control is to be based on the observed additional damping the system experiences in control critical conditions. The improvement of this control is necessary to improve the precision and resolution of the system as well as gaining insight in its physical function.
Experiments where conducted using an industry setup of the system. This time with the system was used gather data important for model generation as well as requiring intuition on the intricacies of using the system and what type of precision can be used.
Next, mathematical descriptions are developed for all elements of the \ac{SECM} system. First of the electrical components involved in the measurement and subsequently of the physics effecting the system. The approximations are picked with the goal of developing a state space model and maintaining a link to the physical world in its parameters. The most complex and relevant being the effect of hydrodynamic damping which is critical in the observed damping process.
It is modeled in the Lagrangian Energy approach, which captures only a part of the dynamics. Some additional factors are still missing. A departure from the homogeneous nature of the model is suggested. Experience with the system has led to increased insight into the systems behavior under various conditions and has provided a stepping stone towards more intricate future modeling attempts. While also providing inspiration for possible model free approaches.