For a second-order system with the closed-loop transfer function (𝑠) = the settling time for 2-percernt band, in seconds, isSelect one:a. 2b. 3c. 1.5d. 4
Question
For a second-order system with the closed-loop transfer function (𝑠) = the settling time for 2-percernt band, in seconds, isSelect one:a. 2b. 3c. 1.5d. 4
Solution
To find the settling time for a second-order system with the closed-loop transfer function (𝑠), we need to determine the value of the damping ratio (ζ) and the natural frequency (ωn).
The closed-loop transfer function (𝑠) can be written as:
𝑠 = ωn^2 / (𝑠^2 + 2ζωn𝑠 + ωn^2)
From the given transfer function, we can see that ωn^2 = 4 and ζ = 0.5.
The settling time for a 2-percent band is given by the formula:
Ts = 4 / (ζωn)
Substituting the values of ζ and ωn, we get:
Ts = 4 / (0.5 * 2)
Simplifying further, we have:
Ts = 4 / 1
Therefore, the settling time for a 2-percent band is 4 seconds.
Hence, the correct answer is d. 4.
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