**4. Results**

This section presents the experimental results of this study. In the first part of this section, the two typical examples of the MSPI model presented in the third section of this study, namely the single-ring linear voltage hysteresis and the reciprocating linear voltage hysteresis, whose compensation control voltages are obtained by the inverse models, are verified and the errors are analyzed. The second part of this section carries out two verification experiments. One of them studies the effects of different frequency voltages on the MSPI model. The other one tests the MSPI model for another type of nanopositioning stage and observes the modeling effect. All of the above experiments demonstrate the contribution of the MSPI model to improving the nanopositioning accuracy of the stage.
