Feedforward controller of ill-conditioned hysteresis using singularity-free Prandtl-Ishlinskii model

U-Xuan Tan, Win Tun Latt, Cheng Yap Shee, Cameron Riviere, and Wei-Tech Ang
IEEE/ASME Transactions on Mechatronics, Vol. 14, No. 5, October, 2009, pp. 598-605.


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Abstract
Piezoelectric, magnetostrictive, and shape memory alloy actuators are gaining importance in high-frequency precision applications constrained by space. Their intrinsic hysteretic behavior makes control difficult. The Prandtl–Ishlinskii (PI) operator can model hysteresis well, albeit a major inadequacy: the inverse operator does not existwhen the hysteretic curve gradient is not positive definite, i.e., ill condition occurs when slope is negative. An inevitable tradeoff between modeling accuracy and inversion stability exists. The hysteretic modeling improves with increasing number of play operators. But as the piecewise continuous interval of each operator reduces, the model tends to be ill-conditioned, especially at the turning points. Similar ill-conditioned situation arises when these actuators move heavy loads or operate at high frequency. This paper proposes an extended PI operator to map hysteresis to a domain where inversion is well behaved. The inverse weights are then evaluated to determine the inverse hysteresis model for the feedforward controller. For illustration purpose, a piezoelectric actuator is used.

Keywords
Actuators, hysteresis, piezoelectric ceramics

Notes
Sponsor: National Institutes of Health
Associated Center(s) / Consortia: Medical Robotics Technology Center
Associated Lab(s) / Group(s): Surgical Mechatronics Laboratory
Associated Project(s): Micron: Intelligent Microsurgical Instruments

Text Reference
U-Xuan Tan, Win Tun Latt, Cheng Yap Shee, Cameron Riviere, and Wei-Tech Ang, "Feedforward controller of ill-conditioned hysteresis using singularity-free Prandtl-Ishlinskii model," IEEE/ASME Transactions on Mechatronics, Vol. 14, No. 5, October, 2009, pp. 598-605.

BibTeX Reference
@article{Riviere_2009_6693,
   author = "U-Xuan Tan and Win Tun Latt and Cheng Yap Shee and Cameron Riviere and Wei-Tech Ang",
   title = "Feedforward controller of ill-conditioned hysteresis using singularity-free Prandtl-Ishlinskii model",
   journal = "IEEE/ASME Transactions on Mechatronics",
   pages = "598-605",
   month = "October",
   year = "2009",
   volume = "14",
   number = "5",
}