Modeling and Compensation of Hysteresis In Piezoelectric Actuators: A Physical Approach

A study in the polarization domain is conducted by probing the impedance of the piezoelectric actuator as it moves along its trajectory. A sensing signal is overlaid over a driving signal that is used to vary the position of the device. The electric polarisation is extracted from the capacitance measurement calculated from the impedance. These polarisation curves are then modelled using the Jiles-Atherton model and compensated for using the inverse model. These measurements give insight into the ferroelectric processes within the piezoelectric actuator, which operate on the polarisation state.

In addition, research has been conducted on the topic of parameter estimation of hysteresis models. This dissertation proposes a Monte Carlo study on a novel normalised Jiles-Atherton model to generate a statistical set of model solutions to compare area and remnant displacement characteristics for different parameter selections. Two parameters were found to be the most responsible for changes in these characteristics, and solutions near the desired values of the measured hysteresis curves were found to be densely distributed in certain areas of the parameter space. Different parameter estimation techniques are proposed for the Prandtl-Ishlinskii model. For this model, the parameters have geometrical significance in the slope of certain points of the hysteresis curve. A novel rescaling procedure is developed to scale a Prandtl-Ishlinskii model hysteresis curve area to a new value without requiring a refitting of the coefficients and a frequency-dependent Prandtl-Ishlinskii model is developed.

Finally, a temperature-dependent, asymmetric Prandtl-Ishlinskii (TAPI) model is developed to account for the changes in hysteresis due to the external temperature. These effects are modelled in the charge domain as an extra bound charge that appears as a result of domain reorientation effects. The temperature effectively changes the amount of energy required to break pinning sites in the actuator which changes the shape of the curve. The TAPI model is then implemented on a Fabry-Perot interferometer system consisting of three piezoelectric actuators controlling the placement of a mirror forming the etalon. A decoupled inverse TAPI model is shown to effectively linearise the output of this system at different temperatures.