Question

Consider the open loop transfer function in the feedback loop as shown in Figure 1.\\ \\ $G(s) = \frac{1}{s(s^2 + s + 4)}$\\ \\ Y(s)\\ X(s)\\ K\\ G(s)\\ Figure 1. Block diagram of a closed loop system with feedback\\ Using Routh's stability criterion and, determine the range of K for stability. Using direct\\ substitution method, find the critical period. Assume step change in setpoint X(s).

          Consider the open loop transfer function in the feedback loop as shown in Figure 1.\\
\\
$G(s) = \frac{1}{s(s^2 + s + 4)}$\\
\\
Y(s)\\
X(s)\\
K\\
G(s)\\
Figure 1. Block diagram of a closed loop system with feedback\\
Using Routh's stability criterion and, determine the range of K for stability. Using direct\\
substitution method, find the critical period. Assume step change in setpoint X(s).

Consider the open loop transfer function in the feedback loop as shown in Figure 1.

G(s) = (1)/(s(s^2 + s + 4))

Y(s)

X(s)

K

G(s)

Figure 1. Block diagram of a closed loop system with feedback

Using Routh's stability criterion and, determine the range of K for stability. Using direct

substitution method, find the critical period. Assume step change in setpoint X(s).

Added by Alex W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Christopher Dzorkpata

Step 1

Step 1: Determine the open loop transfer function G(s) From the block diagram, we can see that the open loop transfer function is given by G(s) = 1/(s(s^2 + s + 4)) Show more…

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Consider the open loop transfer function in the feedback loop as shown in Figure 1. 1 G(s) s(s2 + s + 4) Y(s) X(s K G(s) Figure 1. Block diagram of a closed loop system with feedback Using Routh's stability criterion and, determine the range of K for stability. Using direct substitution method, find the critical period. Assume step change in setpoint X(s)