Control Systems - Online Test
Q1. A speed signal, band limited to 4 kHz and peak voltage varying between +5 V and -5 V, is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits.
Assuming the signal to be uniformly distributed between its peak to peak value, the signal to noise ratio at the quantizer output is
Answer : Option C
Explaination / Solution:
Q2. A speed signal, band limited to 4 kHz and peak voltage varying between +5 V and -5 V, is sampled at the Nyquist rate. Each sample is quantized and represented by 8 bits.
The number of quantization levels required to reduce the quantization noise by a factor of 4 wo
Answer : Option B
Explaination / Solution:
No Explaination.
Q3. The impulse response h(t) of linear time - invariant continuous time system is given by h(t) = exp(- 2t)u(t), where u(t) denotes the unit step function.
The frequency response H(𝜔) of this system in terms of angular frequency 𝜔, is given by H(𝜔)
Answer : Option C
Explaination / Solution:
Q4. The transfer function Y(s)/R(s) of the system shown is
Answer : Option B
Explaination / Solution:
Q5. A system with transfer function 
has an output
for the input signal 
Then, the system parameter p is
has an output for the input signal Then, the system parameter p is
Answer : Option B
Explaination / Solution:
Transfer function is given as
Amplitude Response
Alternative :
Q6. 
For the asymptotic Bode magnitude plot shown below, the system transfer function can be
Answer : Option A
Explaination / Solution:
Initial slope is zero, so K = 1
At corner frequency 𝜔1 = 0.5 rad/ sec, slope increases by +20 dB/decade, so there is a zero in the transfer function at 𝜔1
At corner frequency 𝜔2 = 10 rad/ sec, slope decreases by -20 dB/decade and becomes zero, so there is a pole in transfer function at 𝜔2
Transfer function 
Q7. The residues of a complex function 
at its poles are
at its poles are
Answer : Option C
Explaination / Solution:
Q8. The transfer function of a discrete time LTI system is given by
Consider the following statements:
S1: The system is stable and causal for ROC: |z| > 1/2
S2: The system is stable but not causal for ROC: |z| < 1/4
S3: The system is neither stable nor causal for ROC: 1/4 < |z| < 1/2
Which one of the following statements is valid ?
Answer : Option C
Explaination / Solution:
By partial fraction H(z) can be written as
For ROC : |z| > 1/2
Thus system is causal. Since ROC of H(z) includes unit circle, so it is stable also. Hence S1 is True
For ROC : |z| < 1/4
System is not causal. ROC of H(z) does not include unity circle, so it is not stable and S3 is True
Q9.
A unity negative feedback closed loop system has a plant with the transfer function 
and a controller GC (s) in the
and a controller GC (s) in thefeed forward path. For a unit set input, the transfer function of the controller that gives minimum steady state error is
Answer : Option D
Explaination / Solution:
Steady state error is given as
ess will be minimum if 
is maximum In option (D)
is maximum In option (D)
Q10. The signal flow graph of a system is shown below:
The state variable representation of the system can be
Answer : Option D
Explaination / Solution:
