Further Results on Hysteresis Compensation of Smart Micro-Positioning Systems with the Inverse Prandtl-Ishlinskii Compensator.
Résumé
A formula that characterizes the output of the in-
verse 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 are 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. First, we apply the Prandtl-
Ishlinskii feedforward technique to control the piezoelectric
actuator. Then, the formula of the previous theoretical result is
used to construct an H ∞ 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.