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Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE) PDF Download

Q1: Consider the stable closed-loop system shown in the figure. The magnitude and phase values of the frequency response of G(s) are given in the table. The value of the gain K1(>0) for a 50° phase margin is (rounded off to 2 decimal places).  (2024)
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(a) 1.12
(b) 2.25
(c) 1.68
(d) 2.92
Ans:
(a)
Sol: Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q2: Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of G(s) has a constant slope of −20 dB/ decade at least till 100rad/sec with the gain crossover frequency being 10rad/sec. Hie asymptotic Bode phase plot remains constant at  −90° at least till ω = 10rad/sec. The steady-state error of the closed-loop system for a unit ramp input is _____ (rounded off to 2 decimal places).  (2024)
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(a) 0.25
(b) 0.1
(c) 0.36
(d) 0.42
Ans:
(b)
Sol: Initial slppe = −20 dB/sec
Open loop transfer function  = k/s
20 log10k = 20
k = 10
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)ess for type -1 system for ramp input
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q3: Consider a lead compensator of the form
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)The frequency at which this compensator produces maximum phase lead is 4rad/s. At this frequency, the gain amplification provided by the controller, assuming asymptotic Bodemagnitude plot of K( s), is  6 dB. The values of α, β, respectively, are  (2023)
(a) 1, 16
(b) 2, 4
(c) 3, 5
(d) 2.66, 2.25
Ans:
(b)
Sol: K(s) Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Max. phase lead occur at, Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Given : ωm = 4rad/sec
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE) Now,
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Put, s = jω
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Given :  M = 6  
20 log(4/a) = 6
⇒ a = 2
From eqn. (1), we get
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q4: In the Nyquist plot of the open-loop transfer function
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in s-plane is mapped into a point at  (2023)
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(a) G(s)H(s)=G(s)H(s) = ∞
(b) G(s)H(s)=0G(s)H(s) = 0
(c) G(s)H(s)=3G(s)H(s) = 3
(d) G(s)H(s)=5G(s)H(s) = −5
Ans:
(c)
Sol: Nyquist Contour :
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Given:
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q5: The open loop transfer function of a unity gain negative feedback system is given as
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)The Nyquist contour in the s-plane encloses the entire right half plane and a small neighbourhood around the origin in the left half plane, as shown in the figure below. The number of encirclements of the point (−1 + j0) by the Nyquist plot of G(s), corresponding to the Nyquist contour, is denoted as N. Then N equals to  (2022)
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(a) 0
(b) 1
(c) 2
(d) 3
Ans: 
(b)
Sol: Given: P = 1 (Because, Nyquist contour encircle one pole i.e s = 0)
We have, N = P - Z
N = 1 - Z
Characteristic equation
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)R-H criteria:
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Hence, z = 0 (because no sign change in first column of R-H criteria)
(where, z = closed loop pole on RHS side of s-plane)
Therefore, N = 1.

Q6: An LTI system is shown in the figure where
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE) The steady state output of the system, to the input r(t), is given as y(t) = a + b sin(10t + θ). The values of a and b will be  (2022)
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(a) a = 1, b = 10
(b) a = 10, b = 1
(c) a = 1, b = 100
(d) a = 100, b = 1
Ans: 
(a)
Sol: Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q7: The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is −180°. This system has  (2022)
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(a) one LHP pole and one RHP zero at the same frequency
(b) one LHP pole and one LHP zero at the same frequency
(c) two LHP poles and one RHP zero
(d) two RHP poles and one LHP zero.
Ans: 
(a)
Sol: The given system is non-minimum phase system Therefore, transfer function, Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Hence, one LHP pole and one RHP zero at the same frequency.

Q8: The Bode magnitude plot for the transfer function Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE) of the circuit is as shown. The value of R is _____________ Ω. (Round off to 2 decimal places.)  (2021)
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(a) 0.1
(b) 0.2
(c) 0.25
(d) 0.05
Ans:
(a)
Sol: From response plot
Mr = 26 dB = 20
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
From electrical network
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)∴ R = 0.10Ω

Q9: A stable real linear time-invariant system with single pole at p, has a transfer function Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE) with a dc gain of 5. The smallest positive frequency, in rad/s at unity gain is closed to:  (2020)
(a) 8.84
(b) 11.08
(c) 78.13
(d) 122.87
Ans: 
(a)
Sol: Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q10: Consider a negative unity feedback system with forward path transfer function Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE) where K, a, b, c are positive real numbers. For a Nyquist path enclosing the entire imaginary axis and right half of the s-plane in the clockwise direction, the Nyquist plot of (1 + G(s)), encircles the origin of (1 + G(s))-plane once in the clockwise direction and never passes through this origin for a certain value of K. Then, the number of poles of  Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE) lying in the open right half of the s-plane is _________ .  (2020)
(a) 1
(b) 2
(c) 3
(d) 4
Ans:
(b)
Sol: Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q11: The asymptotic Bode magnitude plot of a minimum phase transfer function G(s) is shown below.
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Consider the following two statements.
Statement I: Transfer function G(s) has three poles and one zero.
Statement II: At very high frequency (ω → ∞), the phase angle ∠G(jω) = −(3π/2).
Which one of the following options is correct?  (2019)
(a) Statement I is true and statement II is false.
(b) Statement I is false and statement II is true.
(c) Both the statements are true
(d) Both the statements are false
Ans:
(b)
Sol: Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Transfer function shows 2 poles and no zeros. So statement I is false.
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)So statement II is true.

Q12: The open loop transfer function of a unity feedback system is given by
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)In G(s) plane, the Nyquist plot of G(s) passes through the negative real axis at the point  (2019)
(a) (-0.5, j0)
(b) (-0.75, j0)
(c) (-1.25,  j0)
(d)     (-1.5, j0)
Ans:
(a)
Sol: Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q13: Consider the unity feedback control system shown. The value of K that results in a phase margin of the system to be 30° is _______.  (SET-1(2017))
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(a) 0.5
(b) 1.04
(c) 2.09
(d) 4.029
Ans:
(b)
Sol: Forward path transfer function, Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Given,
Phase margin = 30°
Phase margin = 180° + ϕ
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)[where ωgc is gain crossover frequency]
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q14:  The transfer function of a system is given by Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Let the output of the system be
v
o(t)=Vmsin(ωt+φ)
vo(t) = Vmsin(ωt + φ) for the input vi(t) = Vmsin(ωt).
Then the minimum and maximum values of φ (in radians) are respectively  (SET-1  (2017))
(a) Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)

(b) Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
(c) 0 and π/2
(d) −π and 0
Ans:
(d)
Sol: Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)For the minimum and maximum values of ′ϕ′
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q15: Loop transfer function of a feedback system is G(s)H(s) = ((s+3)/(s2(s−3))). Take the Nyquist contour in the clockwise direction. Then, the Nyquist plot of G(s)H(s) encircles -1 + j0  (SET-1 (2016))
(a) once in clockwise direction
(b) twice in clockwise direction
(c) once in anticlockwise direction
(d) twice in anticlockwise direction
Ans:
(a)
Sol: Nyquist plot of  G(s)H(s) = Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE) is as shown below
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)From the Nyquist plot G(s)H(s) encircle -1 + j0 once in clockwise direction.
Alternate Solution:
Characteristic equation,

Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)using Routh's array
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)There are two sign changes, hence two poles in right side of s-plane exist.
 Z = 2, P = 1
 N = P − Z = −1
One encirclement in clockwise direction.

Q16: Consider the following asymptotic Bode magnitude plot (ω is in rad/s).
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Which one of the following transfer functions is best represented by the above Bode magnitude plot?  (SET-1(2016))
(a) Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)

(b) Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
(c) Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
(d) Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Ans: (a)
Sol: From the given Bode plot, it is evident that there are 3(three) poles in the transfer function, out of which there are double poles at corner frequency near but less than ω = 8 rad/sec and one pole is near but greater than ω = 0.5 rad/sec. The initial slope is +20 dB/dec. Therefore one zero exist at s = 0. So from all the given options, option (A) satisfies all the conditions. Therefore Option (A) is correct.

Q17: The phase cross-over frequency of the transfer function G(s) = 100/(s+3)3 in rad/s is  (SET-1(2016))
(a) √3
(b) 1/√3
(c) 3
(d) 3√3
Ans: 
(a)
Sol: Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)For phase corssover frequency ωphImg[G(jω)] = 0;
Hence, ω(3 − ω2) = 0
ω = 0; ± √3
Therefore, ωph = √3 rad/sec  

Q18: Nyquist plots of two functions G1(s) and G2(s) are shown in figure.
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Nyquist plot of the product of G1(s) and G2(s) is  (SET-2(2015))
(a) Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(b) Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(c) Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(d) Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Ans:
(b)
Sol: Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q19: A Bode magnitude plot for the transfer function G(s) of a plant is shown in the figure. Which one of the following transfer functions best describes the plant?  (SET-1(2015))
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(a) Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)

(b) Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
(c) Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
(d) Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Ans: (d)
Sol: From initial line equation,
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)now, from the given plot we know type of system is one.
Hence, Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q20: The magnitude Bode plot of a network is shown in the figure
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)The maximum phase angle ϕm and the corresponding gain Gm respectively, are  (SET-3(2014))
(a) −30° and 1.73 dB
(b) −30° and 4.77 dB
(c) +30° and 4.77 dB
(d) +30° and 1.73 dB  
Ans:
(c)
Sol: From the given Bode plot, it is clear that corner frequencies,
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)∴ Transfer function of given system is given by
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)As α < 1, therefore the transfer function T(s) represents a lead compensator having α = 1/3
∴ Maximum phase shift,
Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Previous Year Questions- Frequency Response Analysis - 1 | Control Systems - Electrical Engineering (EE)

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FAQs on Previous Year Questions- Frequency Response Analysis - 1 - Control Systems - Electrical Engineering (EE)

1. What is frequency response analysis in control systems?
Ans.Frequency response analysis is a method used in control systems to evaluate how a system responds to different frequencies of input signals. It typically involves measuring the output of a system in response to sinusoidal inputs at various frequencies, allowing engineers to understand system stability, resonance, and bandwidth.
2. How do you determine the frequency response of a system?
Ans.To determine the frequency response of a system, one can use methods such as Bode plots, Nyquist plots, or frequency response functions. These methods involve applying sinusoidal inputs of varying frequencies to the system and measuring the corresponding output, which is then analyzed to visualize the gain and phase shift over the frequency range.
3. What is the significance of Bode plots in frequency response analysis?
Ans.Bode plots are significant in frequency response analysis as they provide a graphical representation of a system's gain and phase shift across a range of frequencies. They help engineers quickly assess stability margins, gain crossover frequency, and phase crossover frequency, which are crucial for designing and tuning control systems.
4. What are the common types of systems analyzed using frequency response?
Ans.Common types of systems analyzed using frequency response include linear time-invariant (LTI) systems, electrical circuits, mechanical systems, and digital control systems. These systems can be modeled and analyzed to determine their dynamic behavior and performance under various input conditions.
5. How does frequency response analysis aid in system design and stability?
Ans.Frequency response analysis aids in system design and stability by allowing engineers to identify potential stability issues and design compensators to improve performance. By understanding how a system reacts to different frequencies, engineers can make informed decisions on controller design, bandwidth limitations, and enhance the overall robustness of the system.
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