Inverse control of systems with hysteresis and creep

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 which use solid-state actuators based on magnetostrictive or piezoelectric material or shape memory alloys. All of these actuator types show strong hysteretic effects. In addition to hysteresis, piezoelectric actuators show strong creep effects. Thus, the objective of this article is to enlarge the operator-based methodology of the 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, the system operator for the simultaneous consideration of both phenomena. With regard to applications in control and measurement technology the existence, the uniqueness, the Lipschitz continuity and thus the 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 piezoelectric actuators. Using this control concept, the tracking errors caused by hysteretic and creep effects are reduced by approximately one order of magnitude.

Unified hysteresis and creep compensation in AFM tip positioning with an extended PI model

“…The proposed extended PI model in this study has a relatively simpler structure and less parameters than the compensation methods in [20], [21] , in which the creep model depends on the history of input signal and the creep effects are compensated through the whole process of PZT actuation. Therefore the hysteresis and creep compensation with the extended PI model will consume less time, which is especially meaningful for the AFM-based nanomanipulation requiring high speed actuation.…”

“…The inflexion creep can be modeled as the response of a first order linear system with a step function as input, which corresponds to the inflexion voltage [20], [21]. The magnitude of the creep depends on the inflexion voltage value.…”

“…[20], [21], in which the creep effects are described as a first order linear system. With these methods for hysteresis and creep compensation, the creep effects are considered for all the time during the whole PZT activation process and depend on the history of excitation voltage signal, which makes the computation of the inverse model difficult.…”

Recent Advances in the Control of Piezoelectric Actuators

“…Krejci and Kuhnen [45] expressed the inverse analytical expression of the traditional P-I model, which reduced the tracking error by one order of magnitude. Kuhnen [46] inserted an operator dead zone into the traditional P-I model in order to describe asymmetry hysteresis nonlinearity by eliminating the influence of asymmetry on the system. Based on this controller, Shen [47] designed a new synovial controller to further improve the accuracy.…”

Pick-and-place nanomanipulation with three-dimensional manipulation force microscopy

“…1 (a), one XYZ piezoelectric actuated nanostage (MCL Nano-Bio2M) with a maximum scan range of 50 µm × 50 µm × 50 µm and a XYZ piezotube (PI P-153.10H) with a scan range of 10 µm × 10 µm × 10 µm are used. Note that hysteresis of the piezotube are well compensated by PI operator [17,18]. The AFM cantilevers with protrudent tips (ATEC-FM), as shown in right inset of Fig.…”