Existence, Uniqueness and L∞-stability of the Prandtl-Ishlinskii Hysteresis and Creep Compensator *

The article presents a rigorous existence, uniqueness and stability proof for a hysteresis and creep compensator of Prandtl-Ishlinskii type which is used in practical applications to compensate the complex hysteretic and creep actuator characteristic of active materials (especially of piezoceramics) in large signal operation. The hysteresis and creep compensator consists of an inverse Prandtl- Ishlinskii hysteresis operator in the feedforward path and a Prandtl-Ishlinskii creep operator in the feedback path. The simple proof of existence, uniqueness and stability with the well-known small-gain theorem is based on the Lipschitzcontinuity of both operators and leads to an additional contraction condition which restricts the application range of the compensator from the theoretical point of view. The proof discussed in this contribution avoids this restrictive contraction condition and thus extends considerably the application range of the compensator.