A general modeling scheme is proposed for precision positioning of piezoelectrically-driven flexural systems. To
describe the nonlinear behavior of the structure while also considering the system dynamics, a second order linear
dynamic model subjected to nonlinear hysteretic input is first adopted. Using the memory-dependent properties of
hysteresis nonlinearity, a new mathematical framework is then proposed for describing this phenomenon. More
specifically, a nonlinear mapping strategy is proposed for the approximation of each of the ascending and descending
multiple-loop hysteresis curves based on the shape of hysteresis reference curves. The trace of internal hysteresis
trajectory is, however, obtained based on the locations of the past turning points, corresponding to the input extrema.
Experimental tests are carried out on a dual-axis piezoelectrically-driven flexural stage to demonstrate the contribution
of dynamic and hysteresis models, individually and combined together, on the improvement of the model response.
Results indicate that the proposed hysteresis model can effectively predict the nonlinear response of the system, while
the influence of dynamic model is more apparent for high rate inputs.
Complex structural nonlinearities of piezoelectric materials drastically degrade their performance in variety of micro-
and nano-positioning applications. From the precision positioning and control perspective, the multi-path time-history dependent hysteresis phenomenon is the most concerned nonlinearity in piezoelectric actuators to be analyzed. To realize the underlying physics of this phenomenon and to develop an efficient compensation strategy, the intelligent properties of hysteresis with the effects of non-local memories are discussed. Through performing a set of experiments on a piezoelectrically-driven nanostager with high resolution capacitive position sensor, it is shown that for the precise prediction of hysteresis path, certain memory units are required to store the previous hysteresis trajectory data. Based on the experimental observations, a constitutive memory-based mathematical modeling framework is developed and trained for the precise prediction of hysteresis path for arbitrarily assigned input profiles. Using the inverse hysteresis model, a feedforward control strategy is then developed and implemented on the nanostager to compensate for the system everpresent nonlinearity. Experimental results demonstrate that the controller remarkably eliminates the nonlinear effect if memory units are sufficiently chosen for the inverse model.