About the output of the inverse compensation of the Prandtl-Ishlinskii model

The inverse estimated Prandtl-Ishlinskii model is applied as a feedforward compensator to compensate for hysteresis nonlinearities modeled by the Prandtl-Ishlinskii model. We prove that the output of this inverse compensation is a Prandtl-Ishlinskii hysteresis nonlinearity. Since the output of the inverse compensation shows a hysteresis nonlinearity characterized by the Prandtl-Ishlinskii model, model-based hysteresis compensation methods can be used along with inverse-based hysteresis compensation methods to improve the tracking performance in the closed-loop control system. The simulation results suggest that a significantly improved tracking performance can be achieved in closed-loop control systems using the analytical expression for the output of the inverse compensation.