Control Systems - Online Test
Q1. Loop transfer function of a feedback system is 
Take the Nyquist contour in
the clockwise direction. Then, the Nyquist plot of G(s)H(s) encircles -1 + j0.
Take the Nyquist contour in
the clockwise direction. Then, the Nyquist plot of G(s)H(s) encircles -1 + j0.
Answer : Option A
Explaination / Solution:
Q2. Let x1(t) ↔ X1(ω) and x2(t) ↔ X2(ω) be two signals whose Fourier Transforms are as shown in the figure below. In the figure, h(t) = e-2|t| denotes the impulse response.
For the system shown above, the minimum sampling rate required to sample y(t), so that y(t) can be uniquely reconstructed from its samples, is
Answer : Option B
Explaination / Solution:
Q3. The open loop transfer function of a unity feedback control system is given by
The closed loop system will be stable if,
Answer : Option C
Explaination / Solution:
Q4. A second-order real system has the following properties:
a) the damping ratio ς = 0.5 and undamped natural frequency ωn =10 rad/s
b) the steady state value of the output, to a unit step input, is 1.02.
The transfer function of the system is
Answer : Option B
Explaination / Solution:
Q5. The gain at the breakaway point of the root locus of a unity feedback system with open loop
transfer function 
is
is
Answer : Option A
Explaination / Solution:
Q6. The transfer function of a system is given by, 
Let the output of the system be v0(t) = Vm sin(ωt + φ) for the input vi(t) = Vm sin(ωt). Then the minimum and maximum values of φ (in radians) are respectively
Let the output of the system be v0(t) = Vm sin(ωt + φ) for the input vi(t) = Vm sin(ωt). Then the minimum and maximum values of φ (in radians) are respectively
Answer : Option D
Explaination / Solution:
Q7. A closed loop system has the characteristic equation given by s3 + Ks2 +(K + 2)s + 3 = 0 For
this system to be stable, which one of the following conditions should be satisfied?
Answer : Option D
Explaination / Solution:
Q8. The transfer function of the system Y(s)/U(s) whose state-space equations are given below is:
Answer : Option D
Explaination / Solution:
Q9. In the system whose signal flow graph is shown in the figure, U1(s) and U2(s) are inputs. The
transfer function Y(s)/U1(s) is
Answer : Option A
Explaination / Solution:
Q10. 
As shown in the figure, a negative feedback system has an amplifier of gain 100 with ±10% tolerance in the forward path, and an attenuator of value 9/100 in the feedback path. The overall system gain is approximately:
Answer : Option A
Explaination / Solution:
No Explaination.
