Essentials of Vehicle Dynamics

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:

$G(s)=\frac{K}{s^n}·\frac{S_1·S_2\cdots S_k·Q_1·Q_2\cdots Q_l}{S_{k+1}.S_{k+2}\dots Q_{l+1}·Q_{l+1}\dots }$ (A4.1)

(A4.1)

for some n, l, k≥0, where S_i and Q_j 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 τ_i, ω_j, and ζ_j are all assumed positive. The functions (A4.2) and (A4.3) determine ...