Question 13.8: Given the open-loop transfer function in Example 13.6, find ...

Dynamic Modeling and Control of Engineering Systems [EXP-11549]

Given the open-loop transfer function in Example 13.6, find the gain margin and phase margin of the system for the case in which K = 2.0.

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>> tf138=tf([2], [6 11 6 1])
Transfer function:
2
———————
6 s∧3 + 11 s∧2 + 6 s +1

Next, find the margins associated with this open-loop transfer function:

>> [gm pm wcg wcp]=margin(tf138)

which leads to the following results:

$k_{g} = 5.0 (14 dB)$ ,

$\gamma = 74.6^{◦}$ ,

$\omega_{cg} = 1.0$ ,

$\omega_{cp} = 0.373$ .

To better interpret these results, consider the Bode plot that is generated by the alternative call of margin, Fig. 13.12.

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