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Piezo actuator close up11/11/2023 A small shift of the working point after each loop can be observed, the so-called wipe-out, reported by. Results substantiate that the hysteresis’ width much more depends on amplitude than on frequency. 4 illustrates one measurement with input signal U over time and the measured actuators displacement y m over input voltage U. Therefore, a sinusoidal input signal with rising amplitude is chosen to cover a large number of minor loops, which are homogeneously distributed.įig. It is vital to cover a wide range of minor loops too. When identifying the hysteresis, it is not sufficient to measure the major loop. However, the influence is minor and experiments in this work have shown that avoiding the aforementioned parasitic effects in measurements is more important. It shall be noted though, that there is no common consent regarding frequency dependence. In even smaller frequency ranges, creeping of the piezo would interfere. As pointed out by, the hysteresis itself does not depend on frequency, so in order to safely avoid other effects, input signals only span 5 Hz to 40 Hz. Thus, one has to prevent other effects from contributing to the measurements, since it is not possible to distinguish between nonlinearity caused by hysteresis or other influences, such as negative phase of the plant or possible delays caused by the measurement system. The focus lies on the identification of the hysteresis exhibited by the piezo. Hysteresis identification and forward model This simplifies or even enables the usage in later application since there are no means for measuring the actuators displacement directly within the final clamping device for active vibration cancellation.ĥ. The approach is open-loop, which means there is no feedback necessary. amplifier) to yield a more linear relation between voltage applied and displacement of the actuator. When evaluating the inverse model compensation, configuration (B) is employed, where U i n v equals the reshaped input signal for the piezo (i.e. For identifying the hysteresis of the actuator and to parameterize the forward model, configuration (A) is used, where the desired displacement is linearly approximated into a desired control signal U c o n t r o l. The setup and control scheme is illustrated in Fig. In the scope of this study, two kinds of experiments are carried out. The developed hysteresis model is realized within Matlab/Simulink. The vibrometer is calibrated to measure displacements from this set point. For the experiments though, the set point U W P = 0 V is chosen to allow for large hysteresis loops in one direction. By this, the piezo is allowed to exhibit displacement in both directions. The piezo amplifier adds a constant voltage U o f f s e t to the control voltage U c o n t r o l to set a working point. displacement = 60 µm) is clamped on one side and may expand and contract freely, i.e. It comprises the elements given in Table 2. The following section presents such a model which is designed to model and compensate the hysteresis of a piezo actuator. They are shown to yield good results and are easy to calculate, which makes them favorable for high dynamic applications. Īnother type of hysteresis models use simple mathematical functions, e.g. Although the model is shown to yield highly accurate results, parameterization is challenging and it demands quite intensive processing. However, the model proved useful for hysteretic effects in general and was used in numerous applications. Ī prominent example is the Preisach model, originally developed to describe magnetization. While the first type allows further understanding of the underlying effects, the latter is generally preferred for real application because of lesser complexity. Hysteresis models can be classified into physical-based and phenomenological. This becomes important for dynamic applications like active vibration damping, since the sensitivity to the control signal is negatively affected. displacement) to lag behind the input (e.g. Hysteresis effects are a common nonlinearity present in various smart materials such as ferroelectrics, magnetic materials, shape memory alloys or piezo electrics and thus, utilizing them in actuators is often challenging, especially piezo actuators, where the effect is quite prominent.
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