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Appendix 4

# Bode Diagram

It is assumed that the transfer function in the s-domain for the solution of a linear differential equation can be written as follows:

$G\left(s\right)=\frac{K}{{s}^{n}}·\frac{{S}_{1}·{S}_{2}\cdots {S}_{k}·{Q}_{1}·{Q}_{2}\cdots {Q}_{l}}{{S}_{k+1}.{S}_{k+2}\dots {Q}_{l+1}·{Q}_{l+1}\dots }$ (A4.1) (A4.1)

for some n, l, k≥0, where Si and Qj are linear and quadratic expressions in s:

${S}_{i}=s·{\tau }_{i}+1$ (A4.2) (A4.2)

${Q}_{j}={\left(\frac{s}{{\omega }_{j}}\right)}^{2}+2·{\zeta }_{j}·\frac{s}{{\omega }_{j}}+1$ (A4.3) (A4.3)

The parameters τi, ωj, and ζj are all assumed positive. The functions (A4.2) and (A4.3) determine ...

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