Absolute stability analysis of linear systems with Duhem hysteresis operator

In this paper, we investigate the stability of positive and negative feedback interconnections of a linear system and a Duhem hysteresis operator. We provide sufficient conditions on the linear plant and on the Duhem operator which are based on the counterclockwise (CCW) or clockwise (CW) input-output property of the plant and hysteresis operator. We show the application of our main result in the design of a linear controller to stabilize a simple mechanical system driven by a hysteretic actuator, such as, piezo-actuator or smart material-based actuator.

[1]  Kirsten Morris,et al.  Dissipative controller designs for second-order dynamic systems , 1994, IEEE Trans. Autom. Control..

[2]  Alexander Lanzon,et al.  Feedback Control of Negative-Imaginary Systems , 2010, IEEE Control Systems.

[3]  Jacquelien M. A. Scherpen,et al.  PD control of a second-order system with hysteretic actuator , 2013, 52nd IEEE Conference on Decision and Control.

[4]  David W. L. Wang,et al.  Passivity-based stability and control of hysteresis in smart actuators , 2001, IEEE Trans. Control. Syst. Technol..

[5]  David J. Hill,et al.  Stability results for nonlinear feedback systems , 1977, Autom..

[6]  David Angeli,et al.  Systems with counterclockwise input-output dynamics , 2006, IEEE Transactions on Automatic Control.

[7]  Dennis S. Bernstein,et al.  Semilinear Duhem model for rate-independent and rate-dependent hysteresis , 2005, IEEE Transactions on Automatic Control.

[8]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[9]  Amir Khajepour,et al.  Stability and robust position control of hysteretic systems , 2010 .

[10]  Bayu Jayawardhana,et al.  On the robustness of hysteretic second-order systems with PID: iISS approach , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[11]  D. Jiles,et al.  Theory of ferromagnetic hysteresis , 1986 .

[12]  Chih-Jer Lin,et al.  Precise positioning of piezo-actuated stages using hysteresis-observer based control , 2006 .

[13]  Oriol Gomis-Bellmunt,et al.  A limit cycle approach for the parametric identification of hysteretic systems , 2008, Syst. Control. Lett..

[14]  S. Fassois,et al.  Duhem modeling of friction-induced hysteresis , 2008, IEEE Control Systems.

[15]  A. Visintin.  Differential models of hysteresis , 1994 .

[16]  José Rodellar,et al.  A linear controller for hysteretic systems , 2006, IEEE Transactions on Automatic Control.

[17]  Arjan van der Schaft,et al.  Positive feedback interconnection of Hamiltonian systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[18]  Bayu Jayawardhana,et al.  Stability of systems with the Duhem hysteresis operator: The dissipativity approach , 2012, Autom..

[19]  Takayoshi Kamada,et al.  Active vibration control of frame structures with smart structures using piezoelectric actuators (Vibration control by control of bending moments of columns) , 1997 .

[20]  I. Mayergoyz.  Mathematical models of hysteresis and their applications , 2003 .

[21]  Hartmut Logemann,et al.  PID control of second-order systems with hysteresis , 2008, Int. J. Control.

[22]  Ian R. Petersen,et al.  A negative-imaginary lemma without minimality assumptions and robust state-feedback synthesis for uncertain negative-imaginary systems , 2012, Syst. Control. Lett..

[23]  F. Ikhouane,et al.  Systems with Hysteresis: Analysis, Identification and Control Using the Bouc-Wen Model , 2007 .

[24]  Paolo Nistri,et al.  Mathematical Models for Hysteresis , 1993, SIAM Rev..

[25]  Gang Tao,et al.  Adaptive control of system with unknown output backlash , 1995 .

[26]  Ruiyue Ouyang,et al.  Stability analysis and controller design for a system with hysteresis , 2013 .

[27]  JinHyoung Oh,et al.  Counterclockwise Dynamics of a Rate-Independent Semilinear Duhem Model , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[28]  Isabelle Queinnec,et al.  Stability analysis for linear systems with input backlash through sufficient LMI conditions , 2010, Autom..

[29]  Bayu Jayawardhana,et al.  On the characterization of the Duhem hysteresis operator with clockwise input-output dynamics , 2012, Syst. Control. Lett..

[30]  B. D. Coleman,et al.  A constitutive relation for rate-independent hysteresis in ferromagnetically soft materials , 1986 .

[31]  J. Willems,et al.  Every storage function is a state function , 1997 .

[32]  J. S. Wang.  Statistical Theory of Superlattices with Long-Range Interaction. I. General Theory , 1938 .

[33]  M. Brokate,et al.  Hysteresis and Phase Transitions , 1996 .