Update content - 2026-10-14

content/book/du19_multi_actuat_system_contr.md

@@ -75,9 +75,9 @@ which includes the resonance model
 and the resonance \\(P\_{ri}(s)\\) can be represented as one of the following forms
 
 \begin{align\*}
- P\_{ri}(s) &= \frac{\omega\_i^2}{s^2 + 2 \xi\_i \omega\_i s + \omega\_i^2} \\\\
- P\_{ri}(s) &= \frac{b\_{1i} \omega\_i s + b\_{0i} \omega\_i^2}{s^2 + 2 \xi\_i \omega\_i s + \omega\_i^2} \\\\
- P\_{ri}(s) &= \frac{b\_{2i} s^2 + b\_{1i} \omega\_i s + b\_{0i} \omega\_i^2}{s^2 + 2 \xi\_i \omega\_i s + \omega\_i^2}
+ P\_{ri}(s) &= \frac{\omega\_i^2}{s^2 + 2 \zeta\_i \omega\_i s + \omega\_i^2} \\\\
+ P\_{ri}(s) &= \frac{b\_{1i} \omega\_i s + b\_{0i} \omega\_i^2}{s^2 + 2 \zeta\_i \omega\_i s + \omega\_i^2} \\\\
+ P\_{ri}(s) &= \frac{b\_{2i} s^2 + b\_{1i} \omega\_i s + b\_{0i} \omega\_i^2}{s^2 + 2 \zeta\_i \omega\_i s + \omega\_i^2}
 \end{align\*}
 
 
@@ -98,11 +98,11 @@ There characteristics are shown on [Table 1](#table--tab:microactuator).
   Performance comparison of microactuators
 </div>
 
-|              | Elect.                                        | PZT                                           | Thermal                    |
-|--------------|-----------------------------------------------|-----------------------------------------------|----------------------------|
-| TF           | \\(\frac{K}{s^2 + 2\xi\omega s + \omega^2}\\) | \\(\frac{K}{s^2 + 2\xi\omega s + \omega^2}\\) | \\(\frac{K}{\tau s + 1}\\) |
-| \\(\tau\\)   | \\(<\SI{0.1}{ms}\\)                           | \\(<\SI{0.05}{ms}\\)                          | \\(>\SI{0.1}{ms}\\)        |
-| \\(\omega\\) | \\(1-\SI{2}{kHz}\\)                           | \\(20-\SI{25}{kHz}\\)                         | \\(>\SI{15}{kHz}\\)        |
+|              | Elect.                                          | PZT                                             | Thermal                    |
+|--------------|-------------------------------------------------|-------------------------------------------------|----------------------------|
+| TF           | \\(\frac{K}{s^2 + 2\zeta\omega s + \omega^2}\\) | \\(\frac{K}{s^2 + 2\zeta\omega s + \omega^2}\\) | \\(\frac{K}{\tau s + 1}\\) |
+| \\(\tau\\)   | \\(<\SI{0.1}{ms}\\)                             | \\(<\SI{0.05}{ms}\\)                            | \\(>\SI{0.1}{ms}\\)        |
+| \\(\omega\\) | \\(1-\SI{2}{kHz}\\)                             | \\(20-\SI{25}{kHz}\\)                           | \\(>\SI{15}{kHz}\\)        |
 
 
 ### Single-Stage Actuation Systems {#single-stage-actuation-systems}
@@ -210,10 +210,10 @@ Equation means that \\(S(s)\\) can be shaped similarly to the inverse of the cho
 One form of \\(W(s)\\) is taken as
 
 \begin{equation}
-  W(s) = \frac{\frac{1}{M}s^2 + 2\xi\omega\frac{1}{\sqrt{M}}s + \omega^2}{s^2 + 2\omega\sqrt{\epsilon}s + \omega^2\epsilon}
+  W(s) = \frac{\frac{1}{M}s^2 + 2\zeta\omega\frac{1}{\sqrt{M}}s + \omega^2}{s^2 + 2\omega\sqrt{\epsilon}s + \omega^2\epsilon}
 \end{equation}
 
-where \\(\omega\\) is the desired bandwidth, \\(\epsilon\\) is used to determine the desired low frequency level of sensitivity magnitude and \\(\xi\\) is the damping ratio.
+where \\(\omega\\) is the desired bandwidth, \\(\epsilon\\) is used to determine the desired low frequency level of sensitivity magnitude and \\(\zeta\\) is the damping ratio.
 
 The controller can then be synthesis using the linear matrix inequality (LMI) approach.