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The control strategy of multi-stroke repetitive driving is often required in the micro–nano-system. However, the current research only focuses on the modeling algorithm of a single stroke; thus, it is difficult to realize the hysteresis compensation at any stroke of the piezoelectric actuator. This paper proposes a multi-stroke compensation algorithm combined with the inverse model: through the analysis of the hysteresis model, the rising trajectory with better linearity is defined as the target line to find a mathematical expression with fewer parameters to describe the falling trajectory, then to find the relationship between maximum stroke voltage and the above parameters to establish a mathematical model that can describe any stroke, and finally, to verify that the above model applies to any unknown stroke, thereby realizing multi-stroke compensation. The experimental results show that the hysteresis corrected rate after the above algorithm compensation is mostly over 85%, of which the maximum hysteresis corrected rate is 93.81% and the hysteresis error is less than 2.5%. Experiments prove the effectiveness of the above multi-stroke compensation algorithm based on the inverse model and extend the research on piezoelectric hysteresis characteristics to multi-stroke compensation. [ABSTRACT FROM AUTHOR]

As a three-dimensional measuring instrument, the laser tracker is widely used in industrial measurement. To avoid the influence of angle measurement error on the overall measurement accuracy, the multi-station and time-sharing measurement with a laser tracker is introduced on the basis of the global positioning system (GPS) principle in this paper. For the proposed method, how to accurately determine the coordinates of each measuring point by using a large amount of measured data is a critical issue. Taking detecting motion error of a numerical control machine tool, for example, the corresponding measurement algorithms are investigated thoroughly. By establishing the mathematical model of detecting motion error of a machine tool with this method, the analytical algorithm concerning on base station calibration and measuring point determination is deduced without selecting the initial iterative value in calculation. However, when the motion area of the machine tool is in a 2D plane, the coefficient matrix of base station calibration is singular, which generates a distortion result. In order to overcome the limitation of the original algorithm, an improved analytical algorithm is also derived. Meanwhile, the calibration accuracy of the base station with the improved algorithm is compared with that with the original analytical algorithm and some iterative algorithms, such as the Gauss-Newton algorithm and Levenberg-Marquardt algorithm. The experiment further verifies the feasibility and effectiveness of the improved algorithm. In addition, the different motion areas of the machine tool have certain influence on the calibration accuracy of the base station, and the corresponding influence of measurement error on the calibration result of the base station depending on the condition number of coefficient matrix are analyzed. [ABSTRACT FROM AUTHOR]

Several computational methods are presented for the rapid extraction of decay time constants from discrete exponential data. Two methods are found to be comparably fast and highly accurate. They are corrected successive integration and a method involving the Fourier transform (FT) of the data and the application of an expression that does not assume continuous data. FT methods in the literature are found to introduce significant systematic error owing to the assumption that data are continuous. Corrected successive integration methods in the literature are correct, but we offer a more direct way of applying them which we call linear regression of the sum. We recommend the use of the latter over FT-based methods, as the FT methods are more affected by noise in the original data. [ABSTRACT FROM AUTHOR]