Gain Calculation

Q.

A unity negative feedback system has the open-loop transfer function $G\left(s\right)=\frac{K}{s(s+1)(s+3)}$
The value of the gain $K(>0)$ at which the root locus crosses the imaginary axis is

1. 12

Q. A unity feedback control system has an open-loop transfer function $G\left(s\right)=\frac{K}{s(s^2+7s+12)}.$ The gain $K$ for which $s=-1+j1$ will lie on the root locus of the system is

1. $4$
2. $5.5$
3. $6.5$
4. $10$

Q.

The open-loop transfer function of a unity feedback configuration is given as $G\left(s\right)=\frac{K(s+4)}{(s+8)(s^2-9)}$
The value of a gain $K(>0)$ for which $-1+j2$ lies on the root locus is

1. 25.54

Q.

The loop transfer function of a negative feedback system is given by
$G\left(s\right)H\left(s\right)=\frac{K}{s(s+2)(s+6)},wherek>0.$ The value of K at the breakaway point of the root locus for the above system (rounded of to one decimal place) is

1. 5

Q. The root-locus diagram for a closed-loop feedback system is shown in the figure. The system is overdamped.

1. only if $0\le K\le 1$
2. only if $1<K<5$
3. only if $K>5$
4. if $0\le K<1$ or $K>5$

Q. A linear time invariant (LTI) system with the transfer function
$G\left(s\right)=\frac{K(s^2+2s+2)}{(s^2-3s+2)}$ is connected in unity feedback configuration as shown in the figure.

For the closed loop system shown, the root locus for $0<K<\infty$ intersects the imaginary axis for $K=1.5$ . the closed loop system is stable for

1. $K>1.5$
2. $1<K<1.5$
3. $0<K<1.5$
4. no positive value of $K$

Q. The gain at the breakaway point of the root locus of a unity feedback system with open loop transfer function $G\left(s\right)=\frac{Ks}{(s-1)(s-4)}$ is

1. 1
2. 2
3. 5
4. 9

Q. The open loop poles of a third order unity feedback system are at 0, -1, -2. Let the frequency corresponding to the point where the root locus of the system transits to unstable region be K. Now suppose we introduce a zero in the open loop transfer function at - 3, while keeping all the earlier open loop poles intact. Which one of the following is TRUE about the point where the root locus of the modified system transits to unstable region?

1. It corresponds to a frequency greater than K
2. It corresponds to a frequency less than K
3. It corresponding to a frequency K
4. Root locus of modified system never transits to unstable region

Q.

For the system shown in figure, $S=-2.75$ lies on the root locus if $K$ is

1. 0.3

Q. In a control system with unity gain feedback, the plant has the transfer fucntion $P\left(s\right)=\frac{3}{s}.$ Assuming that a controller of the form $C\left(s\right)=\frac{K}{(s+p)}$ is used, where K is positive constant, the value of p for which the root-locus of the closed-loop system passes through the points $-3\pm j3\sqrt{(}3)$ where $j=\sqrt{(}-1),is$

1. 3
2. $3\sqrt{3}$
3. 6
4. 9

Q. Complex conjugate roots of characteristic equation for lies on
$G\left(s\right)H\left(s\right)=\frac{1}{2s(s+\frac{1}{2})}$

1. straight line
2. parabola
3. circle
4. hyperbola