Feedforward Controller of Ill-Conditioned Hysteresis Using Singularity-Free Prandtl-Ishlinskii Model.
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 exist when 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.
Tan
U-Xuan
UX
School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798.
Latt
Win Tun
WT
Shee
Cheng Yap
CY
Riviere
Cameron N
CN
Ang
Wei Tech
WT