The paper presents application of a modified, symmetrical Bouc-Wen model to simulate the mechanical behaviour of high-frequency piezoelectric actuators (PAs). In order to identify parameters of the model, a two-step algorithm was developed. In its first stage, the mechanical parameters were identified by taking into account their bilinear variability and using a square input voltage waveform. In the second step, the hysteresis parameters were determined based on a periodic excitation. Additionally, in order to reduce the influence of measurement errors in determination of selected derivatives the continuum wavelet transform (CWT) and translation-rotation transformation (TRT) methods were applied. The results proved that the modified symmetrical Bouc-Wen model is able to describe the mechanical behaviour of PAs across a wide frequency range.
Today, a cascaded system of position loop, velocity loop and current loop is standard in industrial motion controllers. The exact knowledge of significant parameters in the loops is the basis for the tuning of the servo controllers. A new method to support the commissioning has been developed. It enables the user to identify the moment of inertia as well as the time constant of the closed current loop simultaneously. The method is based on the auto relay feedback experiment by Aström and Hägglund. The model parameters are automatically adjusted according to the time behaviour of the controlled system. For this purpose, the auto relay feedback experiment is combined with the technique of gradual pole compensation. In comparison to other existing methods, this approach has the advantage that a parametric model for the open velocity loop is derived directly.
The paper presents an adapted least squares identification method for reduced-order parametric models. On the example of the open velocity loop, different model approaches were implemented in a motion control system. Furthermore, it is demonstrated how the accuracy of the method can be improved. Finally, experimental results are shown.
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