**5. Conclusions**

The MSPI model e ffectively solves the problem of low description accuracy of reciprocating linear voltage hysteresis of the classical PI model. In this paper, the experimental data can be used to find the hysteresis regulation when the hysteresis rate tangent is defined. With a defined segmented basis, the slope characteristics are analyzed to propose a mark-segmented point, which carries out a theoretical solution to segmented modeling. It has been verified that the further segmented modeling can not only compensate for the nonlinear characteristics of the external hysteresis loop under various linear voltages, but can also e ffectively identify the segmentation of features generated by the intrinsic microscopic mechanism.

The MSPI model hysteresis compensation method does not introduce a new operator. The hysteresis characteristic parameters are completely based on the experimental data. The two types of mark-segmented point recognition methods are simple and evident. Hence, the segmented basis makes the MSPI model reliable. The model construction is easy to implement as well. This paper also provides su fficient theoretical preparation for further study of the more complex hysteresis characteristics of the nanopositioning stage under the nonlinear voltage.

**Author Contributions:** Data curation, M.S. and J.S.; methodology, Y.Y. and Y.X.; writing—original draft, D.A.; writing—review and editing, G.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was supported by the National Science Foundation of China (51975130, 51705340); Natural Science Foundation of Liaoning Province (20180550002); Basic Research Projects for Colleges and Universities of Liaoning Province (LJZ2017035); and the Key Research and Development Project of Liaoning Province (2017225016).

**Conflicts of Interest:** The authors declare no conflict of interest.
