Update Content - 2022-04-28

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title = "Feedback Control"
author = ["Dehaeze Thomas"]
draft = false
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## References
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title = "Feedforward Control"
author = ["Dehaeze Thomas"]
draft = false
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## References
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
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title = "Passive Damping"
author = ["Dehaeze Thomas"]
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## Bibliography {#bibliography}
## References
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The optimal parameters of the tuned mass damper can be roughly estimated as follows:
- Choose the maximum mass of the TMD \\(m\\) and note:
\\[ \mu = m/M \\]
where \\(M\\) is the mass of the system to damp
- Choose the maximum acceptable mass of the TMD \\(m\_2\\) and note:
\\[ \mu = m\_2/m\_1 \\]
where \\(m\_1\\) is the mass of the system to damp
- The resonance frequency of the tuned mass damper should be chosen to be
\\[ \nu = \frac{1}{1 + \mu} \approx 1 \\]
As usually we have \\(\mu \ll 1\\) (i.e. TMD mass small compared to the structure mass, for instance few percent)
- This allows to compute the stiffness of the TMD:
\\[ k = \nu^2 K \mu = K \frac{\mu}{(1 + \mu)^2} \\]
\\[ k\_2 = \nu^2 k\_1 \mu = k\_1 \frac{\mu}{(1 + \mu)^2} \\]
- Finally, the optimal damping of the TMD is:
\\[ \xi = \sqrt{\frac{3\mu}{8 (1 + \mu)}} \Longrightarrow c = 2 \xi \sqrt{k m} \\]
\\[ \xi\_2 = \sqrt{\frac{3 \mu}{8 (1 + \mu)}} \Longrightarrow c\_2 = 2 \xi\_2 \sqrt{k\_2 m\_2} \\]
## Simple TMD model {#simple-tmd-model}