Question

For Each Pair of Second-order systems specifications that follow, find the locations of the second order poles:

a) Overshoot %= 12% , Ts= 0.6 seconds
b) Overshoot %= 10%, Tp= 5 seconds
c) Ts= 7 seconds, Tp= 3 seconds

Answer 1

To find the locations of the second order poles, you need to use the given specifications and formulas for damping ratio and natural frequency.

Step-by-step explanation:

To find the locations of the second order poles, you need to use the given specifications.

a) Overshoot %= 12%, Ts = 0.6 seconds: You can use the formula for damping ratio (ζ) to find the locations of the poles. Since the overshoot percentage is given, you can use the relationship between overshoot and damping ratio to solve for ζ. Once you have ζ, you can use the formula for natural frequency (ωn) to find the locations of the poles.

b) Overshoot %= 10%, Tp = 5 seconds: Similarly, you can use the relationship between overshoot and damping ratio to find ζ. Then, use the formula for natural frequency to find the locations of the poles.

c) Ts = 7 seconds, Tp = 3 seconds: In this case, you can use the relationship between settling time and damping ratio to find ζ. Then, use the formula for natural frequency to find the locations of the poles.