# Control Systems with Complex Poles

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Consider five different control systems, with descriptions below. Which system will have the slowest rise time? (see attached)

System 1: Two complex poles at -10 -j5, -10 +j5;

System 2: Two complex poles at -10 -j5, -10 +j5 and a zero at +2;

System 3: Two real poles at -10, -3;

System 4: Two complex poles at: -10 -j5, -10 +j5 and one real pole at -6;

System 5: Two real poles at -10, -3 and a zero at +2

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##### Solution Summary

The solution contains transfer functions and graphs for comparing each system.

##### Solution Preview

Please refer to the attached file. It has all necessary information.

Two complex poles at -10+j5, -10-j5

Transfer function:

1

----------------

s^2 + 20 s + 125

Two complex poles at -10+j5, ...

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