Inverse control of a class of nonlinear systems with modified generalized Prandtl-Ishlinskii hysteresis

The exhibition of hysteresis effects in smart actuators highly affects the accuracy and stability of the control systems. In this work, a modified generalized PI (MGPI) model is proposed to describe a more general class of hysteresis shapes. Comparing to the previous works, the MGPI model not only enlarges the application of the PI model, but also makes it possible to derive the analytical inverse model. The inverse MGPI model can be used as a compensator to mitigate the hysteresis effect in the control systems. Furthermore, in order to minimize the inverse compensation error due to the modeling inaccuracy and to achieve the closed-loop stability and tracking precision, an adaptive variable structure controller is designed. The simulation results show that the proposed controller consisting of both the inverse compensator and adaptive controller has superior control performance comparing with the adaptive controller itself.