Piezo Act u ator Electrical F u n d a m entals

Dynamic Operation (Linear) Piezo actuators can provideaccelerations of thousands of g’s and are ideally suited fordynamic applications.Several parameters influencethe dynamics of a piezo posi-tioning system: current is calculated at 63 mA. For appropriate amplifiers, seethe “Piezo Drivers & Nano- positioning controllers” sec- tion, p. 6-8.The following equationsdescribe the relationship be-tween (reactive) drive power, actuator capacitance, operating frequency and drive voltage.The average power a piezodriver has to be able to providefor sinusoidal operation isgiven by:(Equation 19)Peak power for sinusoidaloperation is:(Equation 20) Where:i The slew rate [V/s] and themaximum current capacity of the amplifier limit the operating frequency of the piezo system. If sufficient electrical power is available from the amplifi- er, the maximum drive fre- quency may be limited by dynamic forces (see “Dyna- mic Operation”, p. 4-24). Where:P In closed-loop operation, the maximum operating fre-quency is also limited by thephase and amplitude response of the system. Rule of thumb: The higher the system resonant frequency, the better the phase and amplitude response, and thehigher the maximum usablefrequency. The sensor band- width and performance of the servo-controller (digital and analog filters, control algorithm, servo-bandwidth) determine the maximumoperating frequency of apiezoelectric system.
a * = average amplifiersource/sink current [A]i
max * = peak amplifiersource/sink current [A]f
max = maximum operatingfrequency [Hz]C** = piezo actuator capaci-tance [Farad (As/V)]U
a = average power [W]P
max = peak power [W]C** = piezo actuator capaci-tance [F]f = operating frequency[Hz]U
p-p = peak-to-peak drivevoltage [V]f =operating frequency[Hz]
p-p = peak-to-peak drivevoltage [V]U The average and maximumcurrent capacity for each PI piezo amplifier can be found in the product technical data tables. In continuous operation, heat generation can also Example Q: What peak current is required to obtain a sinewave displacement of 20 µm at 1000 Hz from a 40 nF HVPZT actua- tor with a nominal displace- ment of 40 µm at 1000V? A: The 20 µm displacementrequires a drive voltage of about 500 V peak-to-peak. With Equation 17 the required peak
max = nominal voltage ofthe amplifier [V] limit the operating frequency .The following equationsdescribe the relationship between amplifier output cur- rent, voltage and operating fre- quency. They help determine the minimum specifications of a piezo amplifier for dynamicoperation. (Equation 16)Long-term average currentrequired for sinusoidal opera- tion(Equation 17)Peak current required for sinu-soidal operation(Equation 18)Maximum operating frequencywith triangular waveform, as a function of the amplifier output current limit It is also essential that thepower supply be able to supply sufficient current.
* The power supply must be able to pro-vide enough current.** For large-signal conditions a margin of70% of the small-signal value should be added. © PI 1998-2005. Subject to change w/o notice. Cat 118 05/09.17 4-28