Application of derivative-free adaptive control to a nanopositioning machine

Abstract

Nanopositioning and nanomeasuring machines are playing an increasingly important role in the evolution of modern technologies in various fields. The Institute of Process Measure ment and Sensor Technology at Ilmenau University of Technology has been researching for more tan one decade high precisión machines. In this direction, the general objective of this master tesis is the development of aderivative-free model reference adaptive control (DFMRAC) algorithm for the vertical axisofa nanopositioning and nanomeasuring machine. Firstly, a nonlinear unknown friction term is included in the adaptation process of a standard model reference adaptive control (MRAC) and the DFMRAC. Then, the MRAC and DFMRAC algorithms are developed theoretically, in which the DFMRAC stability análisis requiresa Lyapunov-Krasovskii functional to prove that the error signal and the weightpa- rameters are uniformly ultimately bounded (UUB). Thanks to this characteristic, the DFMRAC algorithm does not have the problema of the weight drifting parameters, as MRAC does. Overall, the new adaptive controllers have significantly better results and fine-tuning in the machine. Regarding the sine reference experimental tests with afixed amplitude of 1mm and a frequency from 0.25 Hz to 2 Hz, a reduction of the máximum error and root mean square error (RMSE) of about 95% is achieved in comparison to a simple PI state-feed back controller and the previously applied MRAC with an adaptation weight matrix of lower order. Referring to the step reference tests, with a step height of 10mm and different transition times (which are related to the máximum reached velocity from 1mm/s to 5mm/s) the máximum error and the RMSE are reduced approximately by 60% and 75%, respectively. Furthermore, the corresponding extensions to the unknown input matrix case are developed for the adaptive proposals, however it does not significantly improve the experimental results. The new controllers out performed the previous ones with DFMRAC being the best one because it does not have the drifting weight parameters problem and it is easier to implement (no need to implement any projection method). Finally, eventhough, the new adaptive algorithms have extended the size of the weight matrix and added nonlinearities to the computer calculations, the execution time is only increased by around 1 μs.