Generalized Inverse Multiplicative Structure for Differential-Equation-Based Hysteresis Models

In this article, a generalized inverse multiplicative structure (GIMS) is developed for the purpose of compensating for the hysteresis effect represented by the differential-equation-based hysteresis model. The GIMS approach is an approximate inverse compensation approach, and it does not require the analytical solution of the differential equations. The novelty of the proposed GIMS is that it extends the classical inverse multiplicative structure and it can be applied to construct the inverse compensator for differential-equation-based hysteresis models that can be written into the proposed unified expression. The LuGre model and the backlash-like model are employed as examples in the simulations and experiments. Both results validate the effectiveness of the proposed compensation approach.