Question

\text { The polar plot of } G(s) H(s)=\frac{K}{s\left(s^{2}+4 s+5\right)} \text { is shown in Figure 5(b) for } K>0 \text {. } Is the system stable or unstable? Justify your answer, Find the range of Kvalues for the system to be stable. \text { Sketch the polar plot of } G(s) H(s)=\frac{K}{s\left(s^{2}+4 s+5\right)} \text { for } K<0 \text {, clearly labeled as in the } given Figure (arrows, o values, etc), and determine the stability of the system in this case. Justify your answer [4 points].

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6