Modeling of dynamic characteristics and μ-synthesis control of piezoelectric positioning platform

The dynamic hysteresis nonlinearity and various uncertainties of the piezoelectric positioning platform are critical factors limiting its high-precision applications. To address this, the dynamic characteristics of the piezoelectric positioning platform under various loads are identified based on the linearization of the Prandtl-Ishlinskii inverse model. The inverse compensation error and load disturbances are attributed to model uncertainties, which are modeled in the frequency domain. A mu-synthesis controller is designed to improve the tracking accuracy of the piezoelectric positioning platform under uncertainty disturbances. The experimental results of sine wave tracking indicate that with the mu-synthesis controller, the piezoelectric positioning platform achieves a relative error (RE) of less than 2.71% when unloaded. The RE is less than 6.03% for load disturbances of 100 g, 200 g, and 300 g, respectively. These results demonstrate that the designed controller meets the high-precision positioning performance requirements under various load disturbance conditions.