Question

The open-loop transfer function of a plant is given as $G\left(s\right)=\frac{1}{s^2-1}.$ If the plant is operated in a unity feedback configuration,then the lead compensator that can stabilize this control system is

• A. $\frac{10(s-1)}{s+2}$
• B. $\frac{10(s+4)}{s+2}$
• C. $\frac{10(s+2)}{s+10}$
• D. $\frac{2(s+2)}{s+10}$

Answer 1

The correct option is C $\frac{10(s+2)}{s+10}$

Lead compensator is required for stability.
Controllers given in option (a) and option (b) are not lead compensator. From option (c) and (d), with option (d) system becomes unstable hence option (c) is correct.