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# Lead – Lag compensator previous GATE questions

GATE EC-2012

The transfer function of  a compensator is given by  $G_c(s)$=$\frac{s+a}{s+b}$

1.  $G_c(s)$ is a lead compensator if

A) a=1, b=2     B) a=3,b=2       C) a=-3 b=-1        d) a=3, b=1

2. The phase of the above lead compensator is maximum at

a)  $\sqrt{3}$              b) $\sqrt{2}$          c) $\sqrt{6}$    d) $\sqrt{1/3}$

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

a) 10 $\frac{s-1}{s+2}$                                b) 10 $\frac{s-1}{s+2}$

c) 10 $\frac{s+2}{s+10}$                                       d) 2 $\frac{s+2}{s+10}$

4) The transfer function of a phase lead compensator is given by $G_c(s)$= $\frac{1+3Ts}{1+Ts}$ where T>0 . The maximum phase shift produced by such compensator is(in degrees)

a) 90             b) 30          c) 45            d) 60