Consider the two systems in Figure $4\mathrm{.}33.$

sensitiv

$T_1(s)=\frac{k_1{k}_2}{1+0\mathrm{.}009k_1{K}_2}$

$S_{K_1}^{{}_1}=\frac{del{T}_1}{del{K}_1}\frac{K_1}{T_1}=$

C$)$ Sensitive

$\frac{del{k}_2}{del{k}_1}\frac{k_1}{T_2}=$

$$

:

FIGURE $4\mathrm{.}33$ Two feedback systems with gains $K_1$ and $K_2.$

These systems have the same transfer function when $K_1=K_2=100.$ Which system is most sensitive to variations in the parameter $K_1?$ Compute the sensitivity using the nominal values $K_1=K_2=100.$

a$.$ System $($i$)$ is more sensitive and $S_{K_1}^T=0\mathrm{.}01$

b$.$ System $($ii$)$ is more sensitive and $S_{K_1}^T=0\mathrm{.}1$

c$.$ System $($ii$)$ is more sensitive and $S_{K_1}^T=0\mathrm{.}01$

d$.$ Both systems are equally sensitive to changes in $K_1.$