Further Results on Hysteresis Compensation of Smart Micropositioning Systems With the Inverse Prandtl-Ishlinskii Compensator.

A formula that characterizes the output of the inverse compensation is derived when the inverse Prandtl–Ishlinskii hysteresis model is applied as a feedforward compensator. For that the composition property as well as the initial loading curve of the Prandtl–Ishlinskii model is used to obtain this formula. We demonstrate, therefore, that the output of the feedforward controlled system is linear versus the input reference with an additional nonlinear and bounded term. To illustrate the interest of this theoretical result, we propose an experimental application with a piezoelectric actuator (PEA). First, we apply the Prandtl–Ishlinskii feedforward technique to control the PEA. Then, the formula of the previous theoretical result is used to construct an $H_infty $ feedback control from the feedforward controlled actuator. The experimental results demonstrate the efficiency of the calculated controller and, therefore, the benefits of the formula concerning the output of the inverse compensation.