High speed inverse model implementation for real-time control of ferroelectric and ferromagnetic transducers operating in nonlinear and hysteretic regimes

Ferroelectric (e.g., PZT), ferromagnetic, and ferroelastic (e.g., shape memory alloy) materials exhibit varying degrees of hysteresis and constitutive nonlinearities at all drive levels due to their inherent domain structure. At low drive levels, these nonlinear effects can be mitigated through feedback mechanisms or certain amplifier architectures (e.g., charge or current control for PZT) so that linear models and control designs provide sufficient accuracy. However, at the moderate to high drive levels where actuators and sensors utilizing these compounds often prove advantageous, hysteresis and constitutive nonlinearities must be incorporated into models and control designs to achieve high accuracy, high speed control specifications. In this paper, we employ a homogenized energy framework to characterize hysteresis in this combined class of ferroic compounds. We then use this framework to construct highly efficient inverse models that can be used to approximately linearize actuator dynamics for subsequent linear control design. For applications such as high speed tracking (e.g., kHz rates) or broadband vibration attenuation, the efficiency of the inverse construction proves crucial for realtime control implementation. We demonstrate aspects of the inverse model implementation in the context of rod models used to characterize PZT and magnetic actuators presently employed in applications ranging from nanopositioning to high speed milling of automotive components.