TY - JOUR
T1 - Approximate inversion of the Preisach hysteresis operator with application to control of smart actuators
AU - Iyer, Ram Venkataraman
AU - Tan, Xiaobo
AU - Krishnaprasad, P. S.
N1 - Funding Information:
Manuscript received May 5, 2004; revised February 6, 2005. Recommended by Associate Editor J. M. Berg. This work was supported by the Army Research Office under the ODDR&E MURI97 Program Grant DAAG55-97-1-0114 to the Center for Dynamics and Control of Smart Structures (through Harvard University, Cambridge, MA).
PY - 2005/6
Y1 - 2005/6
N2 - Hysteresis poses a challenge for control of smart actuators. A fundamental approach to hysteresis control is inverse compensation. For practical implementation, it is desirable for the input function generated via inversion to have regularity properties stronger than continuity. In this paper, we consider the problem of constructing right inverses for the Preisach model for hysteresis. Under mild conditions on the density function, we show the existence and weak-star continuity of the right-inverse, when the Preisach operator is considered to act on Hölder continuous functions. Next, we introduce the concept of regularization to study the properties of approximate inverse schemes for the Preisach operator. Then, we present the fixed point and closest-match algorithms for approximately inverting the Preisach operator. The convergence and continuity properties of these two numerical schemes are studied. Finally, we present the results of an open-loop trajectory tracking experiment for a magnetostrictive actuator.
AB - Hysteresis poses a challenge for control of smart actuators. A fundamental approach to hysteresis control is inverse compensation. For practical implementation, it is desirable for the input function generated via inversion to have regularity properties stronger than continuity. In this paper, we consider the problem of constructing right inverses for the Preisach model for hysteresis. Under mild conditions on the density function, we show the existence and weak-star continuity of the right-inverse, when the Preisach operator is considered to act on Hölder continuous functions. Next, we introduce the concept of regularization to study the properties of approximate inverse schemes for the Preisach operator. Then, we present the fixed point and closest-match algorithms for approximately inverting the Preisach operator. The convergence and continuity properties of these two numerical schemes are studied. Finally, we present the results of an open-loop trajectory tracking experiment for a magnetostrictive actuator.
KW - Approximate inversion
KW - Closest-match algorithm
KW - Electro-active polymers
KW - Fixed point iteration algorithm
KW - Hysteresis
KW - Magnetostriction
KW - Piezoelectricity
KW - Preisach operator
KW - Regularization
KW - Shape memory alloys
KW - Smart actuators
UR - http://www.scopus.com/inward/record.url?scp=21344451372&partnerID=8YFLogxK
U2 - 10.1109/TAC.2005.849205
DO - 10.1109/TAC.2005.849205
M3 - Article
AN - SCOPUS:21344451372
SN - 0018-9286
VL - 50
SP - 798
EP - 810
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 6
ER -