Consider an unstable plant

\[G(s)=\frac{s+2}{s^{3}+4 s^{2}-5 s}\]

with feedback control, as shown in Figure 10.15.

a. Using Routh's stability criterion, determine the range of the control gain \(K\) for which the closed-loop system is stable.

b. Use MATLAB commands to find the unit-step responses for open and closed-loop control. Assuming that the control gain is \(K=20\), compare the open- and closed-loop responses.

Transcribed Image Text:

FIGURE 10.15 Closed-loop control. E(s) U(s) Y(s) R(s) K G(s)