Complex hysteretic nonlinearity

However, even in quasi-static operation the actual displacement and desired displacement usually do not correspond. Internal imperfections such as complex hysteretic nonlinearities described by the operator Ia in Fig. 6.6 and external influences such as load reactions via the surrounding mechanical... 

The next step to extend the validity of the system model is carried out by the modeling of complex hysteretic nonlinearities by the so called complex hysteresis operators. These complex hysteretic nonlinearities are present in varying degrees in virtually all sohd-state actuators provided that they are driven with sufEciently high amphtudes [349],... 

Unfortunately, in addition to complex hysteretic nonlinearities, actuators and sensors based on the technologically important piezoelectric ceramics contain also log(t)-type creep dynamics to a degree which is not neglectable in wideband applications like positioning systems. 

The self-sensing actuator concept requires the powerful mathematical machinery of complex hysteresis operators - first for reconstructing the mechanical quantities by means of the measured values of electrical quantities and second for compensating the hysteretic nonlinearities and the load dependency. Whereas robust software tools exist for modeling, identifying and compensating scalar complex hysteretic nonlinearities in practical applications, a considerable amount of research activities is necessary in the field of vectorial hysteresis phenomena to obtain a similar status. 

Kuhnen, K. Janocha, H. Inverse feedforward controller for complex hysteretic nonlinearities in smart material systems. Control and Intel . Sys. 29, 3 (2001), pp. 74-83... 

Kuhnen, K. Modeling, Identification and Compensation of complex hysteretic Nonlinearities - A modified Prandtl-Ishlinskii approach. Eur. J. of Control 9, 4 (2003), pp. 407-418... 

Using a model with lumped masses at two characteristic levels (top and level 1), a nonlinear dynamic analysis was performed with a complex hysteretic (IZIIS) model (Fig. 8.5, Shendova 1998). To calibrate the computations in defining the capacity degradation in hysteretic models, the results from seismic shaking table testing of the model were used. With this, an attempt was made to model the dynamic response in a simple way, suitable for everyday analyses, resulting however in satisfactory final results on the behavior at individual levels. 

In order to conduct nonlinear analysis, the force-displacement relationships corresponding to the equivalent strut model must be adequately defined. The modeling of hysteretic behavior increases not only the computational complexity but also the uncertainties of the problem. 

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