Given the following transfer function:
$$H(s) = \frac{20ks + 1200k}{s^3 + 98s^2 + (20k - 191)s +900 + 1200k}$$
I'm asked to reduce this transfer function to a regular second order transfer function as \$k \to \infty\$:
$$H(s) = \frac{\omega_0^2}{s^2 + 2 \zeta \omega_0 s + \omega_0^2}$$
Here is the root locus of the original transfer function:
What do I have to take into account in generating the approximated transfer function?
Just use the dominant poles I've obtained from root-locus graph or is there more to it?
Another idea:
Neglect the term with \$s\$ in the denominator, omit \$s^3\$ in the denominator, leave \$s^2\$ as it is and ignore numbers in the lower degree monomial coefficients which are independent of \$k\$.
rlocus
command assumes that the varying gain is present only in the numerator as a multiplier to the whole numerator. The varying gaink
in your example is not in that format. \$\endgroup\$