Document Type


Date of Award

Fall 1994

Degree Name

Master of Science in Electrical Engineering - (M.S.)


Electrical and Computer Engineering

First Advisor

Timothy Nam Chang

Second Advisor

Andrew Ulrich Meyer

Third Advisor

Edwin Hou


In this thesis, a mathematical model of a piezoelectric stack actuator is presented to describe its voltage versus displacement hysteresis characteristices. This model can accommodate a wide range of piezoelectric materials, including the PZT (lead zirconate-lead titanate) type which is most popular in industrial applications.

Besides describing the conventional "single-loop" hysteresis, this model also accounts for the off-axis minor loops by augmenting the algorithm with loop indexing.

It is shown that the PZT hysteresis possesses certain "weak scalability" that enables the use of spectral analysis to measure the level of nonlinearity.

After a suitable mathematical model has been obtained, a dither is injected into the model to weaken the nonlinearity of hysteresis loop. An integral controller and a harmonic ratio comparator are used in an adaptive system to determine suitable dither amplitude to meet the requirement of the reference distortion lever. The dither effectively "linearizes" the hysteresis nonlinearity, thus rendering it more suitable for application to precision control.

Extensive numerical simulations are carried out and simulation results are presented.



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