Abstract
The hysteresis nonlinearity greatly reduces the tracking precision of piezoceramic actuators for expected displacement in a high-accuracy positioning system. In order to effectively compensate the hysteresis for piezoelectric ceramics, a novel modeling method, namely, multislope PI (Prandtl–Ishlinskii) was proposed. In view of the minimum mean square error (MSE) criterion, the weights of an improved PI model were identified by the quadratic programming optimization algorithm. For verifying the accuracy of the proposed multislope PI hysteresis model, a feedforward compensation control for piezoceramic beam was achieved. The corresponding experimental system was established, and the displacement tracking experiments were carried out. The results indicated that the mean tracking error was 0.2828 μm and within 1% of full scale, as well as the MSE was 0.3100 μm. Compared with the conventional PI model, the proposed multislope PI model demonstrated a significant improvement in positioning performance for the piezoceramic beam.
Highlights
Mathematical Problems in Engineering envelope function was introduced into the play operator [16]. e hysteresis nonlinearity was described by a set of hysteresis operators, including gain coefficient and inputdependent hysteresis as well as parameter scheduling methods
Dong et al [19] proposed a three-stage PI model. e abovementioned phenomenological modeling methods started from the characteristics of piezoelectric hysteresis curves, established corresponding hysteresis models to fit the hysteresis curves, and reduced the drawbacks of hysteresis nonlinearity on piezoelectric positioning systems
Its voltage regulation range is 0∼1000 V and the current regulation range is 0∼0.1 A, with resolutions 10 mV and 1 mA. e model of displacement sensor is KEYENCE LK-H020, with a repeatability accuracy 0.02 μm and linearity ±0.02% F.S. e controller included three parts, a computer, displacement data acquisition, and feedforward compensation algorithm coded by LabVIEW. e displacement data of the piezoceramic beam was acquired by the LK-Navigator software for the KEYENCE laser sensor, and the feedforward compensation method was implemented in LabVIEW. e communication interface between LabVIEW and highvoltage power supply is RS485, with a baud rate of 19200 bps
Summary
It was necessary to perform driving experiments with voltage 0V–150 V on the PZT-5H piezoelectric ceramic beam to obtain and draw the hysteresis curve. When the threshold rk was greater than a certain value (rk >150 in this work, Figure 4(a)), the PI operator lost the stepdown process, which seriously affected the fitting precision of the PI model to the hysteresis curve. For the increase or decrease of the driving voltage, the operator difference between the two PI models was described as follows:. 0 ≤u (t) ≤150, the threshold value rk ≤ ≤0.5 rk + 75 ≤150, which implied that the intersection point would always exist with the interval of (rk, 150), and the operator shape can always show a concave characteristic during the driving voltage increasing phase.
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