Electronics and Communication Engineering - Control System
Exam Duration: 45 Mins Total Questions : 30
The block diagram shown in Fig. (a) is to be represented as in Fig. (b) for what value of H(s)?
- (a)
4s+1
- (b)
\(\frac { s+4 }{ s } \)
- (c)
4(s+1)
- (d)
5(s+4)
Consider the SFG shown in figure below. The value of \(\triangle \) for this graph is
- (a)
1+G1H1-G2G3H3-G1G3H3-G1G3H3+G2G4H2H3
- (b)
1+G1H1+G2G3H3+G1G3H3+G1G3H3-G2G4H2H3
- (c)
1+G1H1+G1G2H2+G2G3H3-G4H3H1-G2G4H2H3
- (d)
1+G1H1+G2G3H3+G1G3H3+G1G3H3+G2G4H2H3
Consider the system shown in figure. If the forward path gain is reduced by 10% in each system, then the variation in C1 and C2 will be respectively
- (a)
10% and 1%
- (b)
2% and 10%
- (c)
10% and zero
- (d)
5% and 1%
Consider the block diagram :
In the above figure, \(\frac { { C }_{ 1 }(s) }{ { R }_{ 1 }(s) } \) is
- (a)
\(\frac { { G }_{ 1 } }{ 1+{ G }_{ 1 }{ G }_{ 2 }{ G }_{ 3 }{ G }_{ 4 } } \)
- (b)
\(\frac { { G }_{ 1 } }{ 1-{ G }_{ 1 }{ G }_{ 2 }{ G }_{ 3 }{ G }_{ 4 } } \)
- (c)
\(\frac { { G }_{ 2 } }{ 1-{ G }_{ 1 }{ G }_{ 2 }{ G }_{ 3 }{ G }_{ 4 } } \)
- (d)
\(\frac { { G }_{ 2 } }{ 1+{ G }_{ 1 }{ G }_{ 2 }{ G }_{ 3 }{ G }_{ 4 } } \)
The close-loop transfer function of a control system is given by \(\frac { C(s) }{ R(s) } =\frac { 1 }{ 1+s } \). For thd input r(t)=sint, the steady state value of c(t) is equal to
- (a)
\(\frac { 1 }{ \sqrt { 2 } } \cos { t } \)
- (b)
1
- (c)
\(\frac { 1 }{ \sqrt { 2 } } \sin { t+\frac { 1 }{ 2 } { e }^{ -t } } \)
- (d)
\(\frac { 1 }{ \sqrt { 2 } } \sin { \left( t-\frac { \pi }{ 4 } \right) +\frac { 1 }{ 2 } { e }^{ -t } } \)
The system with transfer function \(\frac { K }{ { s }^{ 2 }(1+sT) } \) is operated in closed-loop with unity feedback. The closed-loop system is
- (a)
stable
- (b)
unstable
- (c)
marginally stable
- (d)
conditionally stable
The number of roots of s3+2s2+7s+3=0 in the right half of s-plane is
- (a)
zero
- (b)
one
- (c)
two
- (d)
three
If the gain of the open-loop system is doubled, the gain margin
- (a)
is not affected
- (b)
gets double
- (c)
becomes half
- (d)
becomes one-fourth
Pole zero plot is shown in the figure for G(s)H(s).
The root locus is
- (a)
- (b)
- (c)
- (d)
The transfer function of a phase compensator is given by \(\frac { (1+aTs) }{ (1+Ts) } \) where a>1 and T>0. The type of compensator and maximum phase shift provided by such compensator is
- (a)
Phase lead, \(\sin ^{ -1 }{ \left( \frac { a-1 }{ a+1 } \right) } \)
- (b)
Phase lag, \(\sin ^{ -1 }{ \left( \frac { a-1 }{ a+1 } \right) } \)
- (c)
Phase lead, \(\cos ^{ -1 }{ \left( \frac { a-1 }{ a+1 } \right) } \)
- (d)
Phase lag, \(\cos ^{ -1 }{ \left( \frac { a-1 }{ a+1 } \right) } \)
State equation is represented by \(\overset { . }{ x } =\left[ \begin{matrix} 0 & 1 \\ -2 & -1 \end{matrix} \right] X+\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix} \right] u\) The Eigen values are
- (a)
-1, +1
- (b)
-0.5\(\pm \)j1.323
- (c)
-1, -1
- (d)
+1, +1
A system is described by the equation
\(\overset { . }{ x } =\left[ \begin{matrix} 0 & 1 \\ -3 & -2 \end{matrix} \right] x+\left[ \begin{matrix} 0 \\ 1 \end{matrix} \right] u\\ Y=\left[ \begin{matrix} 3 & 2 \end{matrix} \right] \left[ \begin{matrix} { x }_{ 1 } \\ { x }_{ 2 } \end{matrix} \right] \)
The poles of the system is
- (a)
-1. -3
- (b)
+1, -3
- (c)
-1\(\pm \)j\(\sqrt { 2 } \)
- (d)
1\(\pm \)j\(\sqrt { 2 } \)
Consider the system with
A=\(\left[ \begin{matrix} 0 & -2 \\ 0 & -3 \end{matrix} \right] \); B=\(\left[ \begin{matrix} 1 \\ 1 \end{matrix} \right] \) ; C=\(\left[ \begin{matrix} 1 & 0 \end{matrix} \right] \)
Then system is
- (a)
controllable and observable
- (b)
uncontrollable and unobservable
- (c)
controllable and unobservable
- (d)
observable and uncontrollable
The magnitude plot of a rational transfer function G(s) with real coefficients is shown below. When of the following compensators has such a magnitude plot?
- (a)
Lead compensator
- (b)
Lag compensator
- (c)
PID compensator
- (d)
Lead lag compensator
The transfer function of a control system is given by \(\frac { C(s) }{ R(s) } =\frac { 25 }{ { s }^{ 2 }+6s+25 } \). The first maximum value of the response occurs at a time tmax given by
- (a)
\(\frac { \pi }{ 8 } \)
- (b)
\(\frac { \pi }{ 4 } \)
- (c)
\(\frac { \pi }{ 2 } \)
- (d)
\(\pi \)
In the system shown below, x(t)=(sint)u(t). In steady-state, the response y(t) will be
- (a)
\(\frac { 1 }{ \sqrt { 2 } } \sin { \left( t-\frac { \pi }{ 4 } \right) } \)
- (b)
\(\frac { 1 }{ \sqrt { 2 } } \sin { \left( t-\frac { \pi }{ 4 } \right) } \)
- (c)
\(\frac { 1 }{ \sqrt { 2 } } { e }^{ -t }\sin { t } \)
- (d)
sint-cost
Which one of the following polar diagrams corresponds to a lag network?
- (a)
- (b)
- (c)
- (d)
The equivalent of the block diagram shown in figure is given in
- (a)
- (b)
- (c)
- (d)
If the characteristic equation of a closed-loop system is s2+2s+2=0, then the system is
- (a)
overdamped
- (b)
critically damped
- (c)
underdamped
- (d)
undamped
The system shown in figure has steady-state error 0.1 to unit step input. The value of K is
- (a)
0.1
- (b)
0.9
- (c)
1.0
- (d)
9.0
For the SFG shown in figure the transfer function \(\frac { C }{ R } \)
- (a)
\(\frac { { G }_{ 1 }+{ G }_{ 2 }+{ G }_{ 3 } }{ 1+{ G }_{ 1 }{ H }_{ 1 }+{ G }_{ 2 }{ H }_{ 2 }+{ G }_{ 3 }{ H }_{ 3 } } \)
- (b)
\(\frac { { G }_{ 1 }+{ G }_{ 2 }+{ G }_{ 3 } }{ 1+{ G }_{ 1 }{ H }_{ 1 }+{ G }_{ 2 }{ H }_{ 2 }+{ G }_{ 3 }{ H }_{ 3 }+{ G }_{ 1 }{ G }_{ 3 }{ H }_{ 1 }{ H }_{ 3 } } \)
- (c)
\(\frac { { G }_{ 1 }{ G }_{ 2 }{ G }_{ 3 } }{ 1+{ G }_{ 1 }{ H }_{ 1 }+{ G }_{ 2 }{ H }_{ 2 }+{ G }_{ 3 }{ H }_{ 3 } } \)
- (d)
\(\frac { { G }_{ 1 }{ G }_{ 2 }{ G }_{ 3 } }{ 1+{ G }_{ 1 }{ H }_{ 1 }+{ G }_{ 2 }{ H }_{ 2 }+{ G }_{ 3 }{ H }_{ 3 }+{ G }_{ 1 }{ G }_{ 3 }{ H }_{ 1 }{ H }_{ 3 } } \)
The transfer function of an open-loop system is
\(=G\left( s \right) =\frac { s+2 }{ \left( s+1 \right) s\left( s-1 \right) } \)
The Nyquist plot will be of the form
- (a)
- (b)
- (c)
- (d)
The open-loop transfer function of a ufb system is
\(G(s)=\frac { 1+s }{ s(1+0.5) } \)
The corner frequencies are
- (a)
0 and 2
- (b)
0 and 1
- (c)
0 and -1
- (d)
1 and 2
For ufb system shown in figure the transfer function
\(G(s)=\frac { 20(s+3)(s+4)(s+8) }{ { s }^{ 2 }(s+2)(s+15) } \)
If input is 30t 2 , then steady state error is
- (a)
0.9375
- (b)
zero
- (c)
infinite
- (d)
64
The transfer function of a phase-lead compensator is given by
\({ G }_{ c }(s)=\frac { 1+3Ts }{ 1+Ts } \) and where, T>0
The maximum phase shift provided by such a compensator is
- (a)
\(\frac { \pi }{ 2 } \)
- (b)
\(\frac { \pi }{ 3 } \)
- (c)
\(\frac { \pi }{ 4 } \)
- (d)
\(\frac { \pi }{ 6 } \)
A causal system having the transfer function \(H(s)=\frac { 1 }{ s+2 } \) is excited with 10u(t). The time at which the output reaches 99% of its steady state value is?
- (a)
2.7 s
- (b)
2.5 s
- (c)
2.4 s
- (d)
2.1 s
Represent the given system in state-space equation x=A.x=B.u. Choose the correction option for matrix A.
- (a)
\(\left[ \begin{matrix} 0 & 1 & -4 \\ 1 & 0 & 0 \\ -3 & 0 & 0 \end{matrix} \right] \)
- (b)
\(\left[ \begin{matrix} 0 & -1 & 4 \\ -1 & 0 & 0 \\ 3 & 0 & 0 \end{matrix} \right] \)
- (c)
\(\left[ \begin{matrix} -4 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & -3 \end{matrix} \right] \)
- (d)
\(\left[ \begin{matrix} 4 & -1 & 0 \\ 0 & 0 & -1 \\ 0 & 0 & 3 \end{matrix} \right] \)
Block diagram of a position control system is shown in figure.
If the damping ratio of the system is increased to 0.7 without affecting the steady state error, then the value of Ka and Kt are
- (a)
86, 12.8
- (b)
49,9.3
- (c)
24.5,3.9
- (d)
43,6.4
Consider the network shown in figure.
In state space representation matrix A is
- (a)
\(\left[ \begin{matrix} -\frac { 2 }{ 3 } & -\frac { 1 }{ 3 } & \frac { 1 }{ 3 } \\ -\frac { 1 }{ 3 } & -\frac { 2 }{ 3 } & \frac { 2 }{ 3 } \\ -\frac { 1 }{ 3 } & -\frac { 2 }{ 3 } & -\frac { 1 }{ 3 } \end{matrix} \right] \)
- (b)
\(\left[ \begin{matrix} \frac { 1 }{ 3 } & -\frac { 1 }{ 3 } & -\frac { 2 }{ 3 } \\ \frac { 2 }{ 3 } & -\frac { 2 }{ 3 } & -\frac { 1 }{ 3 } \\ -\frac { 1 }{ 3 } & -\frac { 2 }{ 3 } & -\frac { 1 }{ 3 } \end{matrix} \right] \)
- (c)
\(\left[ \begin{matrix} \frac { 2 }{ 3 } & -\frac { 1 }{ 3 } & -\frac { 1 }{ 3 } \\ \frac { 1 }{ 3 } & \frac { 2 }{ 3 } & \frac { 2 }{ 3 } \\ -\frac { 1 }{ 3 } & -\frac { 2 }{ 3 } & \frac { 1 }{ 3 } \end{matrix} \right] \)
- (d)
\(\left[ \begin{matrix} -\frac { 1 }{ 3 } & -\frac { 1 }{ 3 } & \frac { 2 }{ 3 } \\ -\frac { 2 }{ 3 } & -\frac { 2 }{ 3 } & \frac { 1 }{ 3 } \\ -\frac { 1 }{ 3 } & -\frac { 2 }{ 3 } & -\frac { 1 }{ 3 } \end{matrix} \right] \)
A system is described by the dynamic equations \(\overset { . }{ x } (t)=A.x(t)+B.u(t),\quad y(t)=C.x(t)\) where
\(A=\left[ \begin{matrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ -1 & -2 & -3 \end{matrix} \right] ,\quad B=\left[ \begin{matrix} 0 \\ 0 \\ 1 \end{matrix} \right] ,\quad C=[1\quad 0\quad 0]\)
The transfer-function relation between X(s) and U(s) is
- (a)
\(\frac { 1 }{ { s }^{ 3 }+3{ s }^{ 2 }+2s-1 } \left[ \begin{matrix} 1 \\ -s \\ { s }^{ 2 } \end{matrix} \right] \)
- (b)
\(\frac { 1 }{ { s }^{ 3 }+3{ s }^{ 2 }+2s+1 } \left[ \begin{matrix} 1 \\ s \\ { s }^{ 2 } \end{matrix} \right] \)
- (c)
\(\frac { 1 }{ { s }^{ 3 }+3{ s }^{ 2 }+2s+1 } \left[ \begin{matrix} 1 \\ -s \\ { s }^{ 2 } \end{matrix} \right] \)
- (d)
None of these