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Update content - 2026-10-14
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tdehaeze committed 2026-10-14 16:07:55 +02:00
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content/phdthesis/jabben07_mechat.md
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@@ -195,8 +195,8 @@ If the PSD is given as a function \\(S\_x(j\omega)\\), the disturbance filter ca
> Given a positive even function \\(S\_x(f)\\) of finite area, find a minimum-phase stable function \\(L(s)\\), such that \\(|L(j2\pi f)|^2 = S(s)\\)
**Harmonic signals** can be approximately modeled by filtering white noise with a badly damped second order system, having a \\(+1\\) slope below the resonance frequency and a \\(-1\\) slope above the resonance frequency:
\\[ V\_h = \frac{s}{s^2 + 2 \xi \omega\_h + \omega\_h^2} \\]
with \\(\xi\\) the relative damping and \\(\omega\_h\\) the resonance frequency [rad/s].
\\[ V\_h = \frac{s}{s^2 + 2 \zeta \omega\_h + \omega\_h^2} \\]
with \\(\zeta\\) the relative damping and \\(\omega\_h\\) the resonance frequency [rad/s].
By making the \\(\mathcal{H}\_2\\) norm of \\(V\_h\\) equal to the RMS-value of the harmonic signal, the propagation of the disturbance to the performance channel can be well approximated.