Inverse control of systems with hysteresis and creep

TLDR

Hysteresis operators have been widely used since the 1990s to linearise hysteretic transducers, especially as solid‑state actuators such as magnetostrictive, piezoelectric, and shape‑memory alloys become common, all of which exhibit strong hysteresis and, for piezoelectric devices, significant creep. This paper extends the operator‑based approach to model systems exhibiting both hysteresis and creep. Creep operators are incorporated alongside hysteresis operators to form a composite system operator, and functional‑analytic methods establish the existence, uniqueness, Lipschitz continuity, and input–output stability of its inverse. A real‑time inverse feedforward controller based on this concept is implemented for piezoelectric actuators, reducing tracking errors from hysteresis and creep by roughly an order of magnitude.

Abstract

Since the beginning of the 1990s, hysteresis operators have been employed on a larger scale for the linearisation of hysteretic transducers. One reason for this is the increasing number of mechatronic applications that use solid-state actuators based on magnetostrictive or piezo-electric material or shape memory alloys. All of these actuator types show strong hysteretic effects. In addition to hysteresis, piezo-electric actuators show strong creep effects. Thus, the objective of the paper is to enlarge the operator-based methodology of hysteresis operators by elements that allow the description of systems with hysteresis and creep. To reach this objective, following the procedure used for hysteretic systems, creep operators are introduced to form, together with the hysteresis operators, a system operator for the simultaneous consideration of both phenomena. With regard to applications in control and measurement technology, the existence, uniqueness, Lipschitz continuity and thus input–output stability of its inverse operator are theoretically supported by functional analytical methods. Subsequently, the efficiency of this new concept is demonstrated, in practice, by a real-time inverse feedforward controller for piezo-electric actuators. Using this control concept, the tracking errors caused by hysteretic and creep effects are reduced by approximately one order of magnitude.