Budgeting of Systematic Versus Stochastic Errors in Sensor Fusion for Piezo Electric Transducers

Inherent non-linearity of piezo electric transducers, used in atomic force microscopy limits the position accuracy. In order to improve linearity, the elongation can be estimated by charge measurements. To extend the frequency range to DC, strain gauges are added by means of sensor fusion. This paper addresses the challenge of choosing the filter parameters for a first order complimentary filter used for sensor fusion. After identifying stochastic and systematic errors of charge and strain gauge measurements, the optimal parameters of a first order complimentary filter is computed. Depending on the application different filter parameters are found for the same nano-positioning system, by minimizing either stochastic errors, systematic errors or a combination of both. By this method the positioning uncertainty of charge monitoring (234.1 nm) and strain gauge measurement (347.1 nm) is reduced to 140.6 nm for a commercial tube piezo.