Side view and top view of a piezoelectric tube scanner with quartered external electrodes and a continuous inner electrode.
Sensorless control of a piezoelectric tube scanner: (a) strain voltage induced in one electrode is used for feedback; (b) one of the electrodes is shunted to an impedance.
Frequency response of a piezoelectric tube scanner with quartered external electrodes and a single inner electrode. The arrangement is similar to Fig. 2(b). One of the electrodes is taken as the input. The lateral deflection of the tube was measured by a noncontact capacitive sensor with a bandwidth of . The apparent phase roll-off is due to the presence of a second order Butterworth low-pass filter in the capacitive sensor.
In order to force the scanner to trace a raster pattern (c) in the plane, a triangular signal (a) is applied to the fast axis and a psuedoramp signal (b) is applied to the slow axis.
Open-loop lateral movement of a piezoelectric tube scanner when driven by (a) , (b) , and (c) signals. The actuator was driven by a charge source, and thus no sign of hysteresis can be observed in these plots.
Hysteresis plots of a piezoelectric tube scanner driven by voltage and charge signals. The use of a charge source significantly diminishes the presence of nonlinearity.
Electrical circuit representing a piezoelectric tube scanner under (a) symmetrical and (b) asymmetrical actuations.
Frequency response of a piezoelectric tube scanner with quartered external electrodes and a single inner electrode. One of the electrodes is taken as the input. The voltage induced in the opposite electrode, due to the piezoelectric effect, is measured directly by a spectrum analyzer over a bandwidth of . Note that the first two poles of this transfer function are identical to the displacement frequency response of the tube in Fig. 3. However, the two transfer functions have different zeros. Moreover, the third mode that is missing from Fig. 3 is the piston mode of the tube.
The two frequency responses represent the lateral deflection of the free end of the tube measured by a capacitive sensor (–) and the piezoelectric voltage induced in the opposite electrode (--).
Schematics of a two-sensor-based tracking controller for a piezoelectric tube scanner. The capacitive sensor’s signal is low pass filtered to reduce its stochastic noise component, thus limiting its use to dc and low frequencies where the piezoelectric displacement signal is not reliable. The controller is designed to track a reference signal illustrated as a triangular waveform.
Closed-loop lateral movement of a piezoelectric tube scanner when driven by (a) , (b) , and (c) signals.
An alternative approach to the arrangement in Fig. 10. The two complementary sensor signals are “fused” together using a Kalman filter. The optimal estimate of the position is then used for feedback.
Electrical equivalent of a piezoelectric tube scanner. One side of the tube is driven by the tracking signal while the opposite side is shunted to an impedance. An impedance, when tuned to the tube’s first resonance frequency, is known to result in a better damped system.
Feedback structure of a shunted piezoelectric tube scanner. Note that the shunted tube is equivalent to a collocated tube under the feedback controller (8).
Both sides of a piezoelectric tube scanner can be used simultaneously for actuation and damping. The signal applied to the shunted electrode is inverted, using an inverting amplifier with a unity gain, and applied to the opposite electrode.
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