To improve the model quality and thus also the control, detailed modeling, in particular of hysteresis phenomena, is required in comparison with measured data. Operator-based or differential (also fractional) approaches must be compared with respect to their structure, complexity and real-time capability. Furthermore, sensor quantizations, which have so far been simplistically regarded as disturbances, have to be included, since they become relevant for the targeted accuracies. So far, standard controllers can only bring the system dynamics to a stable limit cycle. Adapted designs [23] are able to reduce the extent of this limit set so that the accuracy is increased. For state estimation, quantization with hybrid observers or oversampling can be considered. For this purpose, the sampling time must be chosen as small as possible, which requires a near-hardware implementation. For a highly dynamic control of tip- and laser-based machining processes, not only the distance but also the current between cantilever and substrate (A1, A2) or the laser power has to be actively controlled in case of unknown surface properties. For this purpose, observer approaches from past measurement points must be used to make predictions about the (future) geometry still to be processed. If the unknown geometry is modeled as a perturbation, fractional approaches can help here to extend the possible perturbation class. Multidimensional approaches are required to account for directionality. Subsequently, the control of the cantilever current or the laser power should be operated coupled with the subordinate position control.
Project leader: Prof. Reger, Dr. Schäffel