Consider the second-order analog system described by Extra left or missing ight where T ( s

Consider the second-order analog system described by$$\text{Extra left or missing right}$$where $T\left(s\right)$ is the closed-loop transfer function and $G_p\left(s\right)$ is the plant transfer function. Show that the phase margin ${\varphi }_m$ and the damping ratio $\zeta$ are related by ${\varphi }_m\approx 100\zeta$ by sketching this relationship onto Fig. 8-2.

Figure 8-2

Transcribed Image Text:

Gp($) n T(s) 1 + Gp(s)' Gp(s) s(s + 2wn)