Old spec 5.3 numerical example, Bode diagram of a first order system (ENGR5001)

Old spec 5.3 numerical example, Bode diagram of a first order systemTutorialOld spec ENGR2022:210 min

ENGR202 (old spec) Control 5.3 Frequency Response Revisited, Bode diagram numerical example (slides 13-14)

For the first order system $G(s) = \dfrac{1}{1 + 3s}$ , find general expressions for the magnitude $M$ and phase $\phi$ of the frequency response, then complete a table of $M$ , $\log_{10}M$ and $\phi$ (radians and degrees) at $\omega = 0$ , $1/3$ , 1, 10 rad/s and $\omega \to \infty$ , and describe the Bode diagram.

Formulas you may need

$M = |G(j\omega)|$ , $\phi = \mathrm{Arg}\,G(j\omega)$ ; $|z_1/z_2| = |z_1|/|z_2|$ , $\mathrm{Arg}(z_1/z_2) = \mathrm{Arg}\,z_1 - \mathrm{Arg}\,z_2$ (learn this)
Corner frequency $\omega = 1/\tau$ , where $\log_{10}M = \log_{10}K - 0.15$ and $\phi = -45^\circ$ (learn this)

M at omega = 1/3 =

M at omega = 1 =

phase at omega = 1 =deg

M at omega = 10 =

phase at omega = 10 =deg