Identification of Prandtl-Ishlinskii Hysteresis Model and Its Inverse for Varying Hysteresis Nonlinearities

Abstract

Piezo actuators are used in positioning and control applications widely. They possess inherent nonlinearity due to hysteresis resulting in nonlinear relationship between input and output. In order to improve performance of systems using piezo actuator, hysteresis is modelled, and inverse of the model is used to control the system. Prandtl-Ishlinskii method of modeling hysteresis is widely used due to its ease of implementation and possibility of analytical inverse. In this paper, Prandtl-Ishlinskii model is used for identifying model and inverse of a time varying hysteresis. Experimentation is done on a system which uses electro pneumatic positioner having a piezo valve. The paper shows how identifying change in slopes can be used to determine weights and thresholds of play operators used to model varying hysteresis. MATLAB is used to find model and inverse of hysteresis. The results are verified using simulations.