Generalized dissipation in hysteretic systems

We give a formal definition of dissipative systems that is considerably more general than earlier definitions. The measured output is irrelevant in this formulation. The key component of dissipation is an appropriate work rate. We also define cycle-dissipation and show how it can be used to obtain a suitable work rate. Using this idea, we propose a new work rate for the Preisach hysteresis model, and demonstrate dissipativity with respect to this rate. The Preisach model describes the dynamics of many "smart materials" such as shape memory alloys. This new type of dissipativity will be beneficial in the design of position controllers for SMA.

[1]  David W. L. Wang,et al.  Stability of control for the Preisach hysteresis model , 1997, Proceedings of International Conference on Robotics and Automation.

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

[3]  P. Moylan,et al.  Stability criteria for large-scale systems , 1978 .

[4]  David W. L. Wang,et al.  Preisach model identification of a two-wire SMA actuator , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[5]  J. Wen,et al.  Preisach modeling of piezoceramic and shape memory alloy hysteresis , 1995, Proceedings of International Conference on Control Applications.

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

[7]  David Wang,et al.  Control of hysteretic systems: A state-space approach , 1999 .

[8]  Kazuhiro Yoshida,et al.  Response of Proportional Valve Using Shape-Memory-Alloy Array Actuators , 1996 .

[9]  Minoru Hashimoto,et al.  Application of shape memory alloy to robotic actuators , 1985 .

[10]  J. Willems.  Mechanisms for the stability and instability in feedback systems , 1976, Proceedings of the IEEE.