# Control Systems Gate Questions | Control Systems

## Control Systems Subject Wise

 Question 1
Let Y(s) be the unit-step response of a causal system having a transfer function

that is,  The forced response of the system is

 A U(t) – 2e-tu(t) + e-3tu(t) B U(t) C 2u(t) – 2e-tu(t) + e-3tu(t) D 2u(t)
Question 1 Explanation:
 Question 2
For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles Np and the number of system zeros Nz in the frequency range 1 Hz ≤ f ≤ 107 Hz is
 A Np = 6, Nz = 3 B Np = 5, Nz = 2 C Np = 4, Nz = 2 D Np = 7, Nz = 4
Question 2 Explanation:
From the given Bode plot and it’s slopes
Number of poles = 6
Number of zeros = 3
at F = 10 Hz we have one pole
At F = 102
Hz we can see two more poles are added as slope is decreased by 40 dB/decade
At F = 103 Hz we have 1 zero
At F = 104 Hz we have two zero’s
At F = 105 Hz we have two pole’s
At F = 106 we have one pole
Total poles NP = 6
And total zeros NZ = 3
Note:
 Question 3
Consider a unity feedback system as in the figure shown with an integral compensator k/s and open-loop transfer function as
,where K > 0,
find the positive value of K for which there are exactly two poles of the unity feedback system on the jω axis is equal to ___________ (rounded off to two decimal places).

 A Fill in the Blank Type Question
Question 3 Explanation:
 Question 4
The block diagram of a system is illustrated in the figure shown, where X(s) is the input and Y(s) is the output. The transfer function  is

 A B C D
Question 4 Explanation:
 Question 5
Consider a causal second-order system with the transfer function  with a unit-step  as an input. Let C(s) be the corresponding output. The time taken by the system output c(t) to reach 94% of its steady-state value  rounded off to two decimal places, is
 A 4.5 B 2.81 C 5.25 D 3.89
Question 5 Explanation:
 Question 6
Let the state-space representation of an LTI system be  y(t) = C x(t) + d u(t) where A, B, C are matrics, d is a scalar, u(t) is the input to the system, and y(t) is its output. Let B = [0 0 1]T and d = 0. Which one of the following options for A and C will ensure that the transfer function of this LTI system is

 A and C = [1 0 0] B and C = [0 0 1] C and C = [0 0 1] D and C = [1 0 0]
Question 6 Explanation:

 Question 7
Consider the following statements for continuous-time linear time invariant (LTI) systems.
I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane.
II. There is non causal and BIBO stable system with a pole in the right half of the complex plane.
Which one among the following is correct?
 A Both I and II are true B Both I and II are false C Only I is true D Only II is true
Question 7 Explanation:
If a system is non-causal then a pole on right half of the s-plane can give BIBO stable system. But for a causal system to be BIBO all poles must lie on left half of the complex plane.
 Question 8
Consider the D-Latch shown in the figure, which is transparent when its clock input CK is high and has zero propagation delay. In the figure, the clock signal CLK1 has a 50% duty cycle and CLK2 is a one-fifth period delayed version of CLK1. The duty cycle at the output latch in percentage is ____.
 A Fill in the Blank Type Question
Question 8 Explanation:
 Question 9
 A __________________________________
Question 9 Explanation:
To get steady state error zero for unit step input and 6 for unit ramp input, the type of the system is one.
 Question 10
Which of the following can be pole-zero configuration of a phase-lag controller (lag compensator)?
 A B C D
Question 10 Explanation:
In phase lag compensator pole is near to jω- axis,
 Question 11
A DC series motor is driven by a chopper circuit. The supply voltage is 220 V and the duty cycle is 25%. Determine the DC voltage applied to the motor
 A 165 V B 55 V C 220 V D 110 V
Question 11 Explanation:
Here we have to find out the value of DC voltage that is being applied to the motor.
Given
=> Vin=220V, Duty cycle=25%

Now, for a chopper circuit, we have:
Average output voltage=Duty cycle x Supply voltage
=> (25/100) x (220)=>55.
So, correct option is B
 Question 12
A single-phase full-wave AC phase controller feeds power to a resistive load of 100 from a 220 V, 50 Hz supply. What will be the R.M.S. output voltage at delay angles a1= a2 = a = /2 of both transistors?
 A V B V C x 220 V D x 220 V
Question 12 Explanation:
Here we have to find the RMS output voltage at delay angles a1=a2=a=/2
Now, we have a single phase full wave AC phase controller. We know the formula for Vout(Mean square value) for a AC phase controller . It is given as:
Vout(mean square)= Vm/[(α)+sin2α/2](1/2)
Here, it is already given in question that
Vm=220V=> 220
, and α=/2

So, putting all these values in Vout formula, we will get answer as option (a)
 Question 13
Consider the feedback system

The value of gain for which system is marginally stable is
 A K = 4 B K = 6 C K = 10 D K = 2
Question 13 Explanation:
Given: G(s)= k(s+4)/s(s+1) and H(s)=1/s+2
We have to determine the range of K for which the system is marginally stable.
Now, for stability=> Routh array should be constructed, and marginally stable means some roots on the imaginary axis, and some roots on the left side of the s plane.
Closed loop transfer function is given as:
C(s)/R(s)= G(s)/1+G(s)H(s)
So, putting the values as given in the question, we get:
k(s+4)/s(s+1) / 1+(k(s+4)/s(s+1))(1/s+2)
So, from we can write the characteristic equation as: s3+3s2+s(k+2)+4k=0
Now from this we can construct the routh array as follows:
s3 1 (k+2)
s2 3 4k
s1 (6-k)/3 0
s0 4k
Now, for a marginally stable system, elements the first column should be examined and proper element should be equated to 0.
Here to find K, let us equate s1 element:
(6-k)/3=0=> k= 6
 Question 14
Consider the Bode plots (magnitude and phase) of two different open loop transfer functions of two unity feedback systems. The open loop transfer functions have poles in right half plane. The closed loop system formed from these open loop systems. Which of the following holds true?
 A Closed loop system with I is stable and with II is unstable B Closed loop systems using I and II both are unstable C Closed loop system with I is unable and II is stable D Closed loop system with I and II are stable
Question 14 Explanation:
->Both gain and phase margin positive is Stable system,
->Both gain and phase margin negative is Unstable system.

From diagram (i)
Gain margin=0-(-4)=4dB
And, phase margin= -160-(-180)=20⁰
So, both positive values is Stable system.
From diagram (II)
Gain margin= 4-(-0)=4dB
Phase margin= -180-(-200)=-20⁰
Negative value is Unstable system.
So, (i) is stable and (ii) in unstable system.
 Question 15
A linear time invariant (LTI) system with the transfer function G(s) = is connected in unity feedback configuration as shown in the figure.

For the closed loop system shown, the root locus for 0 < K < ∞ intersects the imaginary axis for K = 1.5. The closed loop system is stable for
 A K >1.5 B 1 < K <1.5 C 0 < K <1 D no positive value of K
Question 15 Explanation:
 Question 16
Which one of the following options correctly describes the locations of the roots of the equation s 4+s 2+1 =0 on the complex plane?
 A Four left half plane (LHP) roots B One right half plane (RHP) root, one LHP root and two roots on the imaginary axis C Two RHP roots and two LHP roots D All four roots are on the imaginary axis
Question 16 Explanation:
 Question 17
The Nyquist plot of the transfer function G(s) = does not encircle the point (1+j0) for K=10 but does encircle the point (-1+j0) for K=100. The the closed loop system (having unity gain feedback) is
 A stable for K = 10 and stable for K = 100 B stable for K = 10 and unstable for K = 100 C unstable for K = 10 and stable for K =100 D unstable for K = 10 and unstable for K = 100
Question 17 Explanation:
Given
G(s) =
C.E =
If system to stable
24>k+4K+4>0
k>-4k<20
(i) Stable condition -4
Means If k =10 system stable
k =100 system unstable
Or G(jω)=
If ω G(jω)=
ω G(jω)=

So If k =10 touching point= 0.5
If k =100 touching point =5
N= P-Z, Here P=0
N=-Z
If closed loop system to be stable, then z=0,N=0,
So, k=0 is stable system
 Question 18
The Nyquist stability criterion and the Routh criterion both are powerful analysis tools for determining the stability of feedback controllers. Identify which of the following statements is FALSE.
 A Both the criteria provide information relative to the stable gain range of the system. B The general shape of the Nyquist plot is readily obtained from the Bode magnitude plot for all minimum-phase systems. C The Routh criterion is not applicable in the condition of transport lag, which can be readily handled by the Nyquist criterion. D The closed-loop frequency response for a unity feedback system cannot be obtained from the Nyquist plot.
Question 18 Explanation:
(A)Both the criteria provides information about the stability of system
so Option (A) is true

(B)is true as in a minimum-phase system, Bode magnitude plot is enough to obtain a general approximation of its Nyquist plot
so Option (B) is true

(C) Routh criterion can be applied to any system to check the stability of a system but a transport lag controller can only by explained using Nyquist Criterion.
so Option (C) is true

(D) We can obtain closed-loop frequency response for Unity Feedback system easily by substituting s = jω, and draw the plot for different values of ω. Usually this is not done as it is not necessary as OLTF is enough to comment on the stability.

Thus, (D) is false.
 Question 19
Consider with all real coefficients. It is known that its derivative has no real roots. The number of real roots of is
 A 0 B 1 C 2 D 3
Question 19 Explanation:
By Rolle’s theorem
“Between any two real roots of f(n) there exist at least one real root of f'(n) ” But in this question if you observe it is given that there exist no real root of P'(s) and p(s) has 3 roots whereas p’(s) has 2 roots and none of which are real. Thus, p(s) has to have 1 real and 2 complex roots.
 Question 20
For a unity feedback control system with the forward path transfer function The peak resonant magnitude of the closed-loop frequency response is 2.The corresponding value of the gain (correct to two decimal places) is ____________.
 A Fill in the Blank Type Question
Question 20 Explanation:
 Question 21
The figure below shows the Bode magnitude and phase plots of a stable function Consider the negative unity feedback configuration with gain in the feed forward path. The closed loop is stable for The maximum value of is ____________.
 A Fill in the Blank Type Question
Question 21 Explanation:
 Question 22
The state equation and the output equation of a control system are given below:

The transfer function representation of the system is
 A B C D
Question 22 Explanation:
In terms of State Space form, the Transfer function is given as,

 Question 23
For the system shown in the figure, Y (s) / X (s) = _____
 A Fill in the Blank Type Question
Question 23 Explanation:
 Question 24
Which of the following statements is incorrect?
 A Lead compensator is used to reduce the settling time. B Lag compensator is used to reduce the steady state error. C Lead compensator improves transient responce of a system. D Lag compensator always stabilizes an unstable system.
Question 24 Explanation:
The phase-lead controller adds zero and a pole, with the zero to the right of the pole, to the forward-path transfer function. The general effect is to add more damping to the closed-loop system. The rise time and settling time are reduced in general.
Reduces the speed of response (i.e. decreases)
Increases the gain of original network without affecting stability
Permits the increases of gain if phase margin is acceptable
System becomes lesser stable
Reduces the effect of noise
Decrease the bandwidth
 Question 25
A unity feedback control system is characterized by the open-loop transfer function The value of k for which the system oscillates at 2 rad/s is_____
 A Fill in the Blank Type Question
Question 25 Explanation:
 Question 26
A second – order LTI system is described by the following state equations

Where x1(t) and x2(t) are the two state variables and r(t) denotes the input. The output c(t) = x1(t). The system is
 A Undamped B Under damped C Critically damped D Over damped
Question 26 Explanation:
 Question 27
A unity feedback control system is characterized by the open-loop transfer function G(s)= The Nyquist path and the corresponding Nyquist plot of G(s) are shown in the figures below. If 0 < K < 1, then the number of poles of the closed-loop transfer function that lie in the right – half of the s-plane is
 A 0 B 1 C 2 D 3
Question 27 Explanation:
Given
 Question 28
Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh's Table of the system characteristic equation.
X: The system is stable
Y: The system is unstable
Z: The test breaks down

P: when all elements are positive
Q: when any one element is zero
R: when there is a change in sign of coefficients
 A . B C D
Question 28 Explanation:
 Question 29
A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer function
 A Encircles the s-plane point (-1 + j0) in the counterclockwise direction as many times as the number of right-half s-plane poles. B encircles the s-plane point (0–j1) in the clockwise direction as many times as the number of right-half s-plane poles. C Encircles the s-plane point (-1 + j0) in the counterclockwise direction as many times as the number of left-half s-plane poles. D Encircles the s-plane point (-1 + j0) in the counterclockwise direction as many times as the number of right-half s-plane zeros.
Question 29 Explanation:
 Question 30

The open-loop transfer function of a unity-feedback control system is

The positive value of K at the breakaway point of the feedback control system's root-locus plot is

 A Fill in the Blank Type Question
Question 30 Explanation:
 Question 31
The open-loop transfer function of a unity-feedback control system is given by . For the peak overshoot of the closed-loop system to a unit step input to be 10%, the value of K is ____.
 A Fill in the Blank Type Question
Question 31 Explanation:
K = 2.86
Peak over shoot 10%

The characteristic equation of above transfer function is
Comparing with standard equation
 Question 32
The transfer function of a linear time invariant system is given by
The number of zeros in the right half of the s-plane is _____.
 A Fill in the Blank Type Question
Question 32 Explanation:
 Question 33
An analog pulse s(t) is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is r(t) = s(t) + n(t), where n(t) is additive white Gaussian noise with power spectral Density . The received signal is passed through a filter with impulse response h(t). Let Es 2 and Eh denote the energies of the pulse s(t) and the filter h(t), respectively. When the signal-to-noise ratio (SNR) is maximized at the output of the filter (), which of the following holds?
 A B C D
Question 33 Explanation:
 Question 34
Negative feedback in a closed-loop control system DOES NOT
 A reduce the overall gain B reduce bandwidth C improve disturbance rejection D reduce sensitivity to parameter variation
Question 34 Explanation:
Negative Feedback reduces gain but Bandwidth is increased because gain bandwidth product remains same. So, Negative feedback in a closed-loop control system DOES NOT reduce bandwidth.
Negative feedback in a closed loop
(i) Increases bandwidth
(ii) Reduces gain
(iii) Improve disturbance rejection
(iv) Reduce sensitivity to parameter variation.
Hence, the correct option is B.
 Question 35
A unity negative feedback system has the open-loop transfer function . The value of the gain K(>0) at which the root locus crosses the imaginary axis is
 A Fill in the Blank Type Question
Question 35 Explanation:

Now, we obtain the Routh array as

Row of s1 to be zero for oscillatory response or for poles to be on imaginary axis.

Method 2
For third order system to be marginally stable, IP = EP
1 * K = 4 * 3
K = 12

Hence, The correct Answer is 12
 Question 36
The polar plot of the transfer function for will be in the
Question 36 Explanation:
 Question 37
In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value of (in Volts) at t = 1 sec is ____________.
 A Fill in the Blank Type Question
Question 37 Explanation:
 Question 38
The open-loop transfer function of a plant in a unity feedback configuration is given as . The value of the gain K( > 0) for which –1 + j2 lies on the root locus is __________.
 A Fill in the Blank Type Question
Question 38 Explanation:
 Question 39
A lead compensator network includes a parallel combination of R and C in the feed-forward path. If the transfer function of the compensator is , the value of RC is _________.
 A Fill in the Blank Type Question
Question 39 Explanation:
 Question 40
A plant transfer function is given as . When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is
 A B C D
Question 40 Explanation:

The closed loop transfer function for unity feedback

Using Routh's tabular form:

For system to be stable, the first row should not have any sign change.
To get this, there are two conditions:

And Or
Or
 Question 41
The response of the system to the unit step input the value of at t=0is
 A Fill in the Blank Type Question
Question 41 Explanation:

Since system transfer function to a unit step input G(s) .

T(s) = Y(s)/X(s) = (s-2)/(s+1)(s+3)

where X(s) = 1/s because x(t) = u(t)

Y(s) can be written as in the form of partial fraction

on Solving above equation with residue method to obtain the value for A, B & C

Taking Inverse Laplace of Y(s) -

y(t) = -(2/3) U(t) + (3/2)e-t -(5/6) e-3t

Considering its first derivative

y'(t) = -(2/3) δ(t) - (3/2)e-t + (5/2) e-3t

Since in the question the value of y'(t) is asked at t = 0+. We have already know that the impulse function  [δ(t)=1] exist only at t = 0, otherwise its value will be zero.

so  y'(t) = -(3/2)e-t + (5/2) e-3t

y'(t) at t = 0+; y'(0+) = -3/2 + 5/2 = 1

 Question 42
The number and direction of encirclements around the point –1 + j0 in the complex plane by the Nyquist plot of is
 A Zero B one, anti- clockwise C One, clockwise D two, clockwise
Question 42 Explanation:
 Question 43
In the feedback system shown below

The positive value of k for which the gain margin of the loop is exactly 0 dB and the phase margin of the loop is exactly zero degree is _______
 A Fill in the Blank Type Question
Question 43 Explanation:
The given condition implied marginal stability. One alternative way without going for gain margin, phase margin concepts is find k value for marginal stability using reflection.

For marginal stability odd order row of S should be zero. i.e.,

K = 60 For Marginal Stable
 Question 44
The asymptotic Bode phase plot of with k and p1 both positive, is shown below. The value of p1 is______
 A Fill in the Blank Type Question
Question 44 Explanation:
Since it is the phase plot given we can't use the slope concept as these are nonlinear curves. So we can take any phase angle of a given frequency as reference and can obtain P1
Phase of transfer function

From the plot at ω=1, Φ=-135°

Solving for p1, we get p1 = 1.
 Question 45
An ideal band-pass channel 500 Hz - 2000 Hz is deployed for communication. A modem is designed to transmit bits at the rate of 4800 bits/s using 16-QAM. The roll-off factor of a pulse with a raised cosine spectrum that utilizes the entire frequency band is
 A Fill in the Blank Type Question
Question 45 Explanation:
 Question 46
For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as

The steady state error essdue to a unit step input is
 A 0 B 0.5 C 1 D 10
Question 46 Explanation:
 Question 47
The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as

The range of K for which the system is stable is
 A −2.0 < K < 0.5 B 0< K < 0.5 C D
Question 47 Explanation:

So, the conditions are and k>-2
and combining k > 0.5
 Question 48
The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as
and H(s)=1
Respectively, If the variable parameter K is real positive, then the location of the breakaway point on the root locus diagram of the system is_____.
 A Fill in the Blank Type Question
Question 48 Explanation:
To find break point, from characteristic equation we need to arrange k as function of s, then the root of gives break point
Characteristic equation is given by

To find the valid break point we need to find that lies on root locus
3.414 lies on root locus
So break point – 3.414.
 Question 49
The transfer function of a first-order controller is given as

Where K, a and b are positive real numbers. The condition for this controller to act as a phase lead compensator is
 A a < b B a > b C K < ab D K > ab
Question 49 Explanation:
 Question 50
Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued.

The value of fH – fL (in H’z) is____________.
 A Fill in the Blank Type Question
Question 50 Explanation:
 Question 51
Consider a continuous-time signal defined as

Where ‘*’ denotes the convolution operation and t is in seconds. The Nyquist sampling rate In samples/sec) for x (t) is_________.
 A Fill in the Blank Type Question
Question 51 Explanation:

Time domain convolution = frequency domain multiplication so, we obtain

Thus, the multiplication will result in maximum frequency of 0.2. Hence,
Nyquist rate = 2 fm = 2(0.2) = 0.4 sample/sec
 Question 52
For the system shown in the figure, s = –2.75 lies on the root locus if K is _______.
 A Fill in the Blank Type Question
Question 52 Explanation:
 Question 53
A unity negative feedback system has an open-loop transfer function . The gain K for the system to have a damping ratio of 0.25 is ______.
 A 300 B 250 C 400 D 200
Question 53 Explanation:
 Question 54
By performing cascading and/or summing/differencing operations using transfer function blocks G1(s) and G2(s), one CANNOT realize a transfer function of the form.
 A G ­1(s) G2 (s) B C D
Question 54 Explanation:
 Question 55
A sinusoidal signal of amplitude A is quantized by a uniform quantizer Assume that the signal utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8 dB the number of levels in the quantizer is _________-
 A 32 B 65 C 80 D 33
Question 55 Explanation:
Given : SQNR =31.8dB
For sinusoidal signal,
signal to quantization noise ratio is given by,
SNRq = (1.76 + 6n) dB
where n = number of bits
Given SNR = 31.8 dB
So, 1.76 + 6n = 31.8 dB
or 6n + 30
or n = 5
Hence, Levels = 2n = 25 = 32
= 32 levels
 Question 56
The state variable representation of a system is given as

The response y(t) is
 A Sin(t) B 1 - et C 1 – cos(t) D 0
Question 56 Explanation:

Since,
where, is state transition matrix given by

Hence,
 Question 57
The forward path transfer function of a unity negative feedback system is given by

The value of K which will place both the poles of the closed-loop system at the same location, is ______.
 A 2.25 B 2.5 C 2.75 D 3.15
Question 57 Explanation:
 Question 58
Consider the feedback system shown in the figure. The Nyquist plot of G(s) is also shown.
Which one of the following conclusions is correct?
 A G(s) is an all-pass filter B G(s) is a strictly proper transfer function C G(s) is a stable and minimum-phase transfer function D The closed-loop system is unstable for sufficiently large and positive k
Question 58 Explanation:
For larger values of K, the radius of circle increases and it will encircle the critical point (-1+j0), which makes closed-loop system unstable.
 Question 59
Consider the state space model of a system, as given below

The system is
 A controllable and observable B uncontrollable and observable C uncontrollable and unobservable D controllable and unobservable
Question 59 Explanation:
From the given state model,

The system is uncontrollable and observable
 Question 60
The phase margin in degrees of calculated using the asymptotic Bode plot is_______.
 A 55 B 40 C 50 D 45
Question 60 Explanation:
 Question 61
Consider the periodic square wave in the figure shown.

The ratio of the power in the 7th harmonic to the power in the 5th harmonic for this waveform is closest in value to _______.
 A 0.5 B 1 C 1.5 D 2
Question 61 Explanation:
For a periodic sequence wave, nth harmonic component is
power in nth harmonic component is
Ratio of the power in 7th harmonic to power in 5th harmonic for given waveform is
 Question 62
The natural frequency of an undamped second-order system is 40 rad/s. If the system is damped with a damping ratio 0.3, the damped natural frequency in rad/s is ________.
Question 62 Explanation:
Given the natural frequency of an undamped second order system

 Question 63
The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by bits per second (bps), where W is the channel bandwidth, P is the average power received and is the one-sided power spectral density of the AWGN. For a fixed the channel capacity (in kbps) with infinite bandwidth is
approximately
 A 1.44 B 1.08 C 0.72 D 0.36
Question 63 Explanation:
 Question 64
The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure.

If the system is connected in a unity negative feedback configuration, the steady state error of the closed loop system, to a unit ramp input, is_________.
 A 0 B 0.5 C 0.8 D 1
Question 64 Explanation:

Due to initial slope, it is a type-1 system, and it has non zero velocity error coefficient

The magnitude plot is giving 0dB at 2r/sec.
Which gives

given unit ramp input; A 1

 Question 65
Consider the state space system expressed by the signal flow diagram shown in the figure.

The corresponding system is
 A always controllable B always observable C always stable D always unstable
Question 65 Explanation:
From the given signal flow graph, the state model is

it is always controllable
 Question 66
Consider the following block diagram in the figure.

The transfer function
 A B C D
Question 66 Explanation:
 Question 67
The input -3e2tu(t), where u(t) is the unit step function, is applied to a system with transfer function. If the initial value of the output is -2, then the value of the output at steady state is __________________.
 A 0 B 1 C 2 D 3
Question 67 Explanation:
 Question 68
Let h(t) denote the impulse response of a causal system with transfer function Consider the following three statements.
S1: The system is stable.
S2: is independent of t for t=0.
S3: A non-causal system with the same transfer function is stable.
For the above system,
 A Only S1 and S2 are true B only S2 and S3 are true C Only S1 and S3 are true D S1, S2 and S3 are true
Question 68 Explanation:

S1: System is stable (TRUE)
Because h(t) absolutely integrable
is independent of time (TRUE)
(independent of time)
S3: A non-causal system with same transfer function is stable
(a non-causal system) but this is not absolutely integrable thus unstable.
Only S1 and S2 are TRUE
 Question 69
The steady state error of the system shown in the figure for a unit step input is _______.
 A 0.5 B 0.7 C 0.8 D 0.9
Question 69 Explanation:
 Question 70
The state equation of a second-order linear system is given by
 A B C D
Question 70 Explanation:
 Question 71
In the root locus plot shown in the figure, the pole/zero marks and the arrows have been removed. Which one of the following transfer functions has this root locus?
 A B C D
Question 71 Explanation:
For transfer function

There are three poles and one zero. Since only two root loci branches tend to infinity. Option (d) is eliminated.

→ First two dots going to left from origin are poles since they collide and go to infinity. There are poles at s = – 1 and s = – 2. Option (a) is eliminated.

→ Centroid of option (c) is (-3,0)

Not the case hence option (c) is also eliminated.

 Question 72
In a Bode magnitude plot, which one of the following slopes would be exhibited at high frequencies by a 4th order all-pole system?
Question 72 Explanation:
 Question 73
For the second order closed-loop system shown in the figure, the natural frequency (in rad/s) is
 A 16 B 4 C 2 D 1
Question 73 Explanation:
 Question 74
The state transition matrix of a system
 A B C D
Question 74 Explanation:
 Question 75
Consider a closed loop transfer function with p a positive real parameter. The maximum value of p until which remains stable is ________.
 A 2 B 4 C 6 D 8
Question 75 Explanation:

For stability, first column elements must be positive and non-zero

The maximum value of p until whichremains stable is 2.
 Question 76
The characteristic equation of a unity negative feedback system 1 + KG(s) = 0. The open loop transfer function G(s) has one pole at 0 and two poles at -1. The root locus of the system for varying K is shown in the figure.

The constant damping ratio line, for intersects the root locus at point A. The distance from the origin to point A is given as 0.5. The value of K at point A is ________ .
 A 0.275 B 0.345 C 0.375 D 0.425
Question 76 Explanation:
We know that the co-ordinate of point A of the given root locus i.e., magnitude condition

Here, the damping factor and the length of OA = 5

Then in the right angle triangle

So, the co-ordinate of point A is
Substituting the above value of A in the transfer function and equating to 1 i.e. by magnitude condition,

Alternative Explanation
 Question 77
Consider a communication scheme where the binary valued signal X satisfies P{X = +1} = 0.75 and P{X = -1} = 0.25. The received signal Y = X + Z, where Z is a Gaussian random variable with zero mean and variance The received signal Y is fed to the threshold detector. The output of the threshold detector

To achieve a minimum probability of error the threshold should be
 A Strictly positive B Zero C Strictly negative D Strictly positive, zero, or strictly negative depending on the nonzero value of
Question 77 Explanation:
 Question 78

The Bode plot of a transfer function G(s) is shown in the figure below.

The gain (20 log|G(s)| ) is 32 dB and –8 dB at 1 rad/s and 10 rads/s respectively. The phase is negative for all ω. Then G(s) is

 A B C D
Question 78 Explanation:
 Question 79
Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
 A All the poles of the system must lie on the left side of the jω axis. B Zeros of the system can lie anywhere in the s- Plane C All the poles must lie within |s| = 1 D All the roots of the characteristic equation must be located on the left side of the jω axis.
Question 79 Explanation:
For a system to be casual, the R.O.C. of the transfer function of the H (s) system which is rational must be in the right half-plane and to the right of the rightmost pole. For the stability of the LTI system. All the poles of the system must be in the left half of the S-plane and no repeated pole must be on the imaginary axis. Consequently, options A, B and D satisfy both the stability of the LTI system and the causality. However, option C is not true for the stable system because, | S | = 1 also has a pole(1 pole) in the right hand plane.
 Question 80
Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is
 A u(t) B tu(t) C D
Question 80 Explanation:
 Question 81
The signal flow graph for a system is given below. The transfer function for this system is
 A B C D
Question 81 Explanation:
From Signal Flow Graph, we have two forward paths
Pk1 =(1)(s-1)(s-1)(1)=(s-2)
Pk2 =(1)(s-1)(1)(1)=(s-1)

Since, all the loops are touching to the paths Pk1 and Pk2 so,
Now, we have
(sum of individual loops)
+ (sum of product of nontouching loops)
Here, the loops are

As all the loop L1, L2, L3 and L4 are touching to each other so,

By using Mason’s Gain Formula
 Question 82
The state diagram of a system is shown below. A system is described by the state-variable equations

The state variable equations of the system in the figure above are:
 A B C D
Question 82 Explanation:
 Question 83
The state transition matrix of the system shown in the figure above is
 A B C D
Question 83 Explanation:
 Question 84
In a baseband communications link, frequencies upto 3500 Hz are used for signalling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible signalling rate in symbols per second is
 A 1750 B 2625 C 4000 D 5250
Question 84 Explanation:
With a raised cosine pulse shape, the bandwidth is larger than the minimum required pulse shape and is related as

The term α is called the excess bandwidth factor which is given here 0.75

W=3500 Hz, the goal is to find the maximum possible symbol rate 1/T

Refer : http://www.dsplog.com/2012/11/01/gate-2012-ece-q3-communication/
 Question 85
In the following figure, C1 and C2 are ideal capacitors. C1 has been charged to 12 V before the ideal switch S is closed at t = 0. The current i(t) for all t is
 A zero B a step function C an exponentially decaying function D an impulse function
Question 85 Explanation:
 Question 86
A system with transfer function is excited by sin(ωt). The steady-state output of the system is zero at
Question 86 Explanation:
Transfer function is

Input

So output

Now

this will be zero if s2 + ω2 will cancel (s2 + 9) term as only then final value theorem will be applicable.
So at ω2 = 9 => ω = 3 rad/sec, steady state output will be zero.
 Question 87
A BPSK scheme operating over an AWGN channel with noise power spectral density of N0/2, uses equi-probable signal
over the symbol interval (0, T). If the local oscillator in a coherent receiver is ahead in phase by 45 ° with respect to the received signal, the probability of error in the resulting system is
 A B C D
Question 87 Explanation:
Probability of error in coherent BPSK is given by

If  the local oscillator in a coherent receiver is ahead in phase by  with respect to the received signal then Probability of error in coherent BPSK is given by

 Question 88

The feedback system shown below oscillates at 2 rad/s when

 A K = 2 and a = 0.75 B K = 3 and a = 0.75 C K = 4 and a = 0.5 D K= 2 and a = 0.5
Question 88 Explanation:
Characteristic equation is
1+G(s)H(s)=0

S3 + as2 + (2+K)s + 1(1+K) = 0

For oscillation

Now
as2 + (1+K) = 0
- aω2 +(1+K) = 0
-4a+(1+K) = 0

-4(1+K)+(2+K)(1+K) = 0
(1+K)[(2+K)-4] = 0
K=-1,2
but K = -1 is not possible as system will not oscillate for this as a = 0
So, K = 2
 Question 89
The state variable description of an LTI system is given by

Where y is the output and u is the input. The system is controllable for
 A a1 ≠ 0, a2 = 0, a3 ≠ 0 B a1 = 0, a2 ≠ 0, a3 ≠ 0 C a1 = 0, a2 ≠ 0, a3 = 0 D a1 ≠ 0, a2 ≠ 0, a3 = 0
Question 89 Explanation:

for system to be controllable
|Qc| ≠ 0
(0 = a1a22) 0
a1 0
a2 ≠ 0
 Question 90
The transfer function of a compensator is given as
Gc(s) is a lead compensator if
 A a = 1, b = 2 B a = 3, b = 2 C a = –5, b = –1 D a = 3, b = 1
Question 90 Explanation:

Phase
for lead comparators phase must be +ve.
For this
So, a = 1, b = 2
 Question 91
Consider the feedback system

The value of gain for which system is marginally stable is
 A K = 4 B K = 6 C K = 10 D K = 2
Question 91 Explanation:
The Correct Answer Among All the Options is B
Given: G(s)= k(s+4)/s(s+1) and H(s)=1/s+2
We have to determine the range of K for which the system is marginally stable.
Now, for stability=> Routh array should be constructed, and marginally stable means some roots on the imaginary axis, and some roots on the left side of the s plane.
Closed loop transfer function is given as:
C(s)/R(s)= G(s)/1+G(s)H(s)
So, putting the values as given in the question, we get:
k(s+4)/s(s+1) / 1+(k(s+4)/s(s+1))(1/s+2)
So, from we can write the characteristic equation as: s3+3s2+s(k+2)+4k=0
Now from this we can construct the routh array as follows:
s3 1 (k+2)
s2 3 4k
s1 (6-k)/3 0
s0 4k
Now, for a marginally stable system, elements the first column should be examined and proper element should be equated to 0.
Here to find K, let us equate s1 element:
(6-k)/3=0=> k= 6
Refer the Topic Wise Question for Routh-Hurwitz Control Systems
 Question 92
Consider the Bode plots (magnitude and phase) of two different open loop transfer functions of two unity feedback systems. The open loop transfer functions have poles in right half plane. The closed loop system formed from these open loop systems. Which of the following holds true?
 A Closed loop system with I is stable and with II is unstable B Closed loop systems using I and II both are unstable C Closed loop system with I is unable and II is stable D Closed loop system with I and II are stable
Question 92 Explanation:
The Correct Answer Among All the Options is A
Here, the bode plot is given and we have to determine which system is stable and which one is not.
Important concept: Both gain and phase margin positive=> Stable system, and both gain and phase margin negative=>Unstable system.
Now, looking at diagram (i) given in the question, we can say
Gain margin=0-(-4)=4dB
And, phase margin= -160-(-180)=20⁰
So, both positive values=> Stable system.
Again for diagram (ii):
Gain margin= 4-(-0)=4dB
Phase margin= -180-(-200)=-20⁰
Negative value=> Unstable system.
So, (i) is stable and (ii) in unstable system.
Refer the Topic Wise Question for Routh-Hurwitz Control Systems
 Question 93
For the given transfer function

The response y(t) for a step input r(t) = 5u(t) will be Where u(t) is a unit step input.
 A B C D
Question 93 Explanation:
Given
r(t) = 5u(t)
R(s) =
Now

 Question 94
The price for improvement in sensitivity by the use of feedback is paid in terms of
 A loss of system gain B rise of system gain C improvement in transient response, delayed response D poor transient response
Question 94 Explanation:
• Negative feedback reduces the system gain which is one of the disadvantages of feedback
• With feedback, sensitivity improved by factor of (1/1+GH) Hence gain reduces by factor (1/1+GH)
 Question 95
Consider a feedback system with the characteristic equation

The asymptotes of the three branches of root locus plot of this system will form the following angles with the real axis
 A 60o, 120o and 300o B 60o, 120o and 180o C 60o, 180o and 300o D 40o, 120o and 200o
Question 95 Explanation:
 Question 96
If the characteristic equation of a feedback control system is given by.
s4 + 20s3 + 15s2 + 2s + K = 0
then the range of values of K for the system to be stable will be
 A 1 < K < 2.49 B 0 < K < 1.49 C 1 < K < 4.49 D 0 < K < 3.49
Question 96 Explanation:
 Question 97
For a Type-2 system, the steady-state errors for unit step and unit ramp input are
 A 0 and ∞ B ∞ and 0 C 0 and 0 D ∞ and ∞
Question 97 Explanation:

For type – 2 system steady state error for unit step and unit ramp input will be zero
 Question 98
Consider the following open-loop transfer function:

The characteristic equation of the unity negative feedback will be
 A (s + 1) (s + 4) + K(s + 2) = 0 B (s + 2) (s + 1) + K(s + 4) = 0 C (s + 1) (s – 2) + K(s + 4) = 0 D (s + 2) (s + 4) + K(s + 1) = 0
Question 98 Explanation:
Given open loop transfer function
G(S) =
and unity feedback H (S) = 1
For a unity negative feedback system, the characteristic equation is given by
q (S) = 1 + G(s) H (S) = 0

Option A
 Question 99
The magnitude and phase relationship between the sinusoidal input and the steady-state output of a system is called as
 A magnitude response B transient response C steady-state response D frequency response
Question 99 Explanation:
• Frequency response of a system defines the magnitude response and phase response at steady state for a sinusoidal input.
• Here we are talking about relationship between amplitude of input & output are well as relationship between phase of input & output which means frequency of the input signal is varied which Is known as frequency response of an LTI system
 Question 100
A transfer function having all its poles and zeros only in the left-half of the s-plane is called
 A a minimum-phase function B a complex transfer function C an all-pass transfer function D a maximum-phase transfer function
Question 100 Explanation:
• If all the poles & zeros of a transfer function lie in the left half of the S–plane the transfer function is called minimum phase transfer function except poles and zeros at origin & infinity.
• A maximum phase transfer function has poles & zeros on right half of s-plane.
• An all pass transfer function has poles & zeros symmetrically located w.r.t. jω axis.
• A complex transfer function has complex poles & zeros, not necessarily on a particular half.
 Question 101
The frequency where magnitude M has a peak value in frequency response is known as
 A normalized frequency B resonant frequency C peak frequency D tuned frequency
Question 101 Explanation:
At resonant frequency where magnitude m has a peak value in frequency response in known as resonant frequency.
 Question 102
For a lead compensator having transfer function

1)
2)
3) τ > 0
4) τ < 0
Which of the above are correct?
 A 1 and 4 B 1 and 3 C 2 and 4 D 2 and 3
Question 102 Explanation:
GC (S) =
For lead compensator zero is dominant over pole

|Zc| < |Pc|

α < 1
α =
& is the time constant it can’t be negative
> 1
 Question 103
The attenuation (magnitude) produced by a lead compensator at the frequency of maximum phase lead is
 A B C D
Question 103 Explanation:
 Question 104
Signal flow diagram of following analog computer circuit is
 A B C D
Question 104 Explanation:
The Correct Answer Among All the Options is A

Converting this into SFG, we get

Refer the Topic Wise Question for Basics of Control System Control Systems
 Question 105
Which of the following Oscillation types this waveform represents when the difference between input frequency and natural frequency is small? Assume the generating system to be a lossless mechanical system.
 A Damped Forced Oscillation B Undamped Forced Vibration C Damped Vibration D None of the above
Question 105 Explanation:
The Correct Answer Among All the Options is B
Damped means gradually reduces to oscillation , but here the oscillations are sustained.
Refer the Topic Wise Question for Basics of Control System Control Systems
 Question 106
For a feedback system shown below, If Kt = 0 and Ka = 5, then steady state error for unit ramp input is 0.2. What will be the new value of Kt and Ka if damping ratio is increased to 0.5 without affecting steady state error.
 A Kt = 1.5, Ka = 1.25 B Kt = 1.5, Ka = 12.5 C Kt = 15, Ka = 12.5 D Kt = 15, Ka = 1.25
Question 106 Explanation:
The Correct Answer Among All the Options is B

G(s) =
G(s)= & H(s)=1
Therefore, =
=
On comparing it with standard 2nd order equation which is
We get ,

Also , given,
………………………………….(1)
As, R(t)=tu(t)R(s)=
Therefore,
=
Given ,

…………………………………………………..(2)
On solving (1) and (2), we get

Refer the Topic Wise Question for Time Domain Analysis Control Systems
 Question 107
For a negative unity feedback system, Gain is given by
G(s) = 0.25/((s2+1)(8s+3))
Transfer function of a lead compensator aimed at achieving gain crossover frequency of 0.5rad/sec and phase margin of 30 deg is
 A B C D
Question 107 Explanation:
The Correct Answer Among All the Options is C
Putting ω=0.5rad/sec in all the options, only option (C) gives |G(jω)|=1
G(jω)=
|G(jω)|= 1
Refer the Topic Wise Question for Compensators and Controllers Control Systems
 Question 108
A sensitivity of transfer function T=(A1+kA2)/ (A3+kA4) with respect to parameter k is given by
 A k(A2A3 – A1A4)/ ((A3 + kA4) (A1 + kA2)) B (A2A3 – A1A4)/ ((A3 + kA4)2) C k(A2A3 – A1A4)/ ((A3 + kA4)2) D (A2A3 – A1A4)/ ((A3 + kA4) (A1 + kA2))
Question 108 Explanation:
The Correct Answer Among All the Options is A
T=(A1+kA2)/ (A3+kA4)
Sensitivity , =
=
=
On putting given values,

=
Refer the Topic Wise Question for Feedback Principle and Frequency Response Control Systems
 Question 109
A binary communication system receives equally likely symbole x1 (t) and x2 (t) plus Additive White Gaussian Noise at the input of matched detector. If the noise power spectral density (N0) is 10-11 W/Hz, compute Eb/N0 (in dB). Assume system characteristics impedance as 1 .
 A 3 dB B 4 dB C 7 dB D 10 dB
Question 109 Explanation:
The Correct Answer Among All the Options is C
As the signal and noise are in additive form, we can do the separate analysis of signal and noise.
Binary ‘1’ ,
Binary ‘0’ ,
Energy per bit , for binary 1; =
=
=
= 5

Given,

= 10 log 5
=7dB
Refer the Topic Wise Question for SNR, BER and Bandwidth Control Systems
There are 109 questions to complete.