A modified generalized Prandtl-Ishlinskii model and its inverse for hysteresis compensation

Hysteresis nonlinearities are inherently exhibited in smart material based actuators. Many hysteresis models have been proposed in the literature to describe such hysteresis nonlinearities. Therein, the Prandtl-Ishlinskii (PI) model is getting more and more popular due to its unique analytical invertibility for the construction of its feedforward compensator. However, the Prandtl-Ishlinskii (PI) model suffers some limits and can only describe a certain class of hystereses. To extend to a more general class, a generalized Prandtl-Ishlinskii (GPI) model was developed. When the smart actuators are cascaded with plants, they usually generate the undesirable oscillations. In order to mitigate the hysteresis effects, its inverse is commonly constructed to compensate such effects. Though, the analytic inverse of the PI is well documented in the literature, the inverse for the GPI has only been listed. As the further development, the GPI is re-defined and a modified generalized Prandtl-Ishlinskii (MGPI) model is proposed which can still describe similar general class of hysteresis shapes. The benefit is that with the linear envelope function an analytical inverse hysteresis model can be derived for the purpose of compensation. The proposed approach is verified in both simulation and experiment.