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Thomas Dehaeze
2020-10-15 21:36:53 +02:00
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content/book/fleming14_desig_model_contr_nanop_system.md
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@@ -9,7 +9,7 @@ Tags
Reference
: ([Fleming and Leang 2014](#orgb239e00))
: ([Fleming and Leang 2014](#orga9e1886))
Author(s)
: Fleming, A. J., & Leang, K. K.
@@ -821,15 +821,15 @@ Year
### Amplifier and Piezo electrical models {#amplifier-and-piezo-electrical-models}
<a id="orgea18894"></a>
<a id="orgddc1a2b"></a>
{{< figure src="/ox-hugo/fleming14_amplifier_model.png" caption="Figure 1: A voltage source \\(V\_s\\) driving a piezoelectric load. The actuator is modeled by a capacitance \\(C\_p\\) and strain-dependent voltage source \\(V\_p\\). The resistance \\(R\_s\\) is the output impedance and \\(L\\) the cable inductance." >}}
Consider the electrical circuit shown in Figure [1](#orgea18894) where a voltage source is connected to a piezoelectric actuator.
Consider the electrical circuit shown in Figure [1](#orgddc1a2b) where a voltage source is connected to a piezoelectric actuator.
The actuator is modeled as a capacitance \\(C\_p\\) in series with a strain-dependent voltage source \\(V\_p\\).
The resistance \\(R\_s\\) and inductance \\(L\\) are the source impedance and the cable inductance respectively.
<div class="examp">
<div class="bgreen">
<div></div>
Typical inductance of standard RG-58 coaxial cable is \\(250 nH/m\\).
@@ -902,7 +902,7 @@ For sinusoidal signals, the amplifiers slew rate must exceed:
\\[ SR\_{\text{sin}} > V\_{p-p} \pi f \\]
where \\(V\_{p-p}\\) is the peak to peak voltage and \\(f\\) is the frequency.
<div class="examp">
<div class="bgreen">
<div></div>
If a 300kHz sine wave is to be reproduced with an amplitude of 10V, the required slew rate is \\(\approx 20 V/\mu s\\).
@@ -948,4 +948,4 @@ The bandwidth limitations of standard piezoelectric drives were identified as:
## Bibliography {#bibliography}
<a id="orgb239e00"></a>Fleming, Andrew J., and Kam K. Leang. 2014. _Design, Modeling and Control of Nanopositioning Systems_. Advances in Industrial Control. Springer International Publishing. <https://doi.org/10.1007/978-3-319-06617-2>.
<a id="orga9e1886"></a>Fleming, Andrew J., and Kam K. Leang. 2014. _Design, Modeling and Control of Nanopositioning Systems_. Advances in Industrial Control. Springer International Publishing. <https://doi.org/10.1007/978-3-319-06617-2>.