Question

31. For the unity feedback system shown in Figure 8.3, where \[ G(s)=\frac{K(s+6)}{\left(s^{2}+10 s+26\right)(s+1)^{2}(s+\alpha)} \] design \( K \) and \( \alpha \) so that the dominant complex poles of the closed-loop function have a damping ratio of 0.45 and a natural frequency of \( 9 / 8 \mathrm{rad} / \mathrm{s} \).

          31. For the unity feedback system shown in Figure 8.3, where
\[
G(s)=\frac{K(s+6)}{\left(s^{2}+10 s+26\right)(s+1)^{2}(s+\alpha)}
\]
design \( K \) and \( \alpha \) so that the dominant complex poles of the closed-loop function have a damping ratio of 0.45 and a natural frequency of \( 9 / 8 \mathrm{rad} / \mathrm{s} \).

31. For the unity feedback system shown in Figure 8.3, where

G(s)=(K(s+6))/((s^2+10 s+26)(s+1)^2(s+α))

design K and α so that the dominant complex poles of the closed-loop function have a damping ratio of 0.45 and a natural frequency of 9 / 8 rad / s.

Added by Elizabeth C.

Engineering Mechanics: Dynamics

J. L. Meriam, L. G. Kraige, J. N. Bolton 8th Edition

Chapter 8

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Solved by Expert Mahipal Kumawat

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We are given a transfer function \( G(s) \) for a unity feedback system and are asked to design values for \( K \) and \( \alpha \) such that the dominant complex poles of the closed-loop system have a damping ratio (\( \zeta \)) of 0.45 and a natural frequency Show more…

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31. For the unity feedback system shown in Figure 8.3, where \[ G(s)=\frac{K(s+6)}{\left(s^{2}+10 s+26\right)(s+1)^{2}(s+\alpha)} \] design \( K \) and \( \alpha \) so that the dominant complex poles of the closed-loop function have a damping ratio of 0.45 and a natural frequency of \( 9 / 8 \mathrm{rad} / \mathrm{s} \).