Model Reference Control including Adaptive Inverse Hysteresis for Systems with Unknown Input Hysteresis

Control of linear systems with unknown input hysteresis is a challenging task and is receiving increased attention in recent years. Many hysteresis models have been proposed in the literature, but the challenge is to determine how to integrate these models with available control techniques to ensure system stability. Such a possibility is by using the Krasnosel´skii-Pokrovkii (KP) hysteresis model. After establishing an off-line KP approximate model of the unknown hysteresis, an inverse KP hysteresis model can be constructed to partially eliminate the hysteresis effects. To combine the model reference control methodology with the inverse hysteresis model, the relationship between system tracking error and parameter errors of the modeled hysteresis is derived, and then an adaptive control algorithm is developed to update the model parameters to ensure that the tracking error asymptotically converges to zero. The approach is illustrated and verified through simulations performed on a linear plant.