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

Q1: Consider the standard second-order system of the form Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE) with the poles p and p having negative real parts. The pole locations are also shown in the figure. Now consider two such second-order systems as defined below :
System 1 : ω= 3rad/sec and θ = 60°
System 2 : ω= 1rad/sec and θ = 70°
Which one of the following statements is correct?  (2024)
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(a) Settling time of System 1 is more than that of System 2.
(b) Settling time of System 2 is more than that of System 1.
(c) Settling times of both the systems are the same.
(d) Settling time cannot be computed from the given information.
Ans:
(b)
Sol: Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)In system -1
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)In system -2
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q2: The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as ζ and  ωn, respectively. The values of ζ and ωn are  (2022)
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(a) ζ=0.5 and ωn=10rad/sζ = 0.5 and ωn = 10rad/s
(b) ζ = 0.1 and ωn = 10rad/s
(c) ζ = 0.707 and ωn = 10rad/s
(d) ζ = 0.707 and ωn = 100rad/s
Ans: 
(a)
Sol: Reduced the block diagram:
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Transfer function,
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Standard form,
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q3: In the given figure, plant Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE) and compensator Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)The external disturbance input is D(s). It is desired that when the disturbance is a unit step, the steady-state error should not exceed 0.1 unit. The minimum value of K is ______.
(Round off to 2 decimal places.)  (2021)
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE) (a) 12.25
(b) 14.12
(c) 9.54
(d) 6.22
Ans: 
(c)
Sol: Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
∴ Kmin = 9.54

Q4: Consider a closed-loop system as shown. Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE) is the plant transfer function and Gc(S) = 1 is the compensator. For a unit-step input, the output response has damped oscillations. The damped natural frequency is _____ rad/srad/s. (Round off to 2 decimal places.)  (2021)
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(a) 10.9
(b) 4.62
(c) 12.02
(d) 8.05
Ans:
(a)
Sol: Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q5: Consider a negative unity feedback system with the forward path transfer function Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE) where K is a positive real number. The value of K for which the system will have some of its poles on the imaginary axis is ________ .      (2020)
(a) 9
(b) 8
(c) 7
(d) 6
Ans:
(b)
Sol: CE is
1 + G(s)H(s) = 0
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)⇒ s3+3s2+3s+(1+K) = 0  
R.H. criteria:
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)9 − (1 + K) = 0
⇒ K = 8

Q6: Which of the following option is correct for the system shown below?  (2020)
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(a) 4th order and stable
(b) 3rd3rd order and stable
(c) 4th4th order and unstable
(d) 3rd order and unstable
Ans:
(c)
Sol: Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Given system is fourth order system and unstable.
Stablity Status: Since it has one missing term of 's' thus undoubtedly given transfer function is unstable.

Q7: Consider a linear time-invariant system whose input r(t) and output y(t) are related by the following differential equation.
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE) 

The poles of this system are at   (2020)
(a) +2j, -2j
(b) +2, -2
(c) +4, -4
(d) +4j, -4j
Ans:
(a)
Sol: Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Poles: s2 + 4 = 0
s = ±j2

Q8: The unit step response y(t) of a unity feedback system with open loop transfer function
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
 is shown in the figure. The value of K is _______ (up to 2 decimal places).   (2018)
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(a) 4
(b) 8
(c) 10
(d) 12
Ans:
(b)
Sol: Closed loop transfer function,
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Given R(s) = 1/s
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE) ⇒ K = 8  

Q9: Consider a unity feedback system with forward transfer function given by Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE) The steady-state error in the output of the system for a unit-step input is _________(up to 2 decimal places).   (2018)
(a) 0.25
(b) 0.45
(c) 0.66
(d) 0.85
Ans: 
(c)
Sol: Steady state error for type-0 and step input, 
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)0.66 uinits 

Q10: Match the transfer functions of the second-order systems with the nature of the systems given below.  (2018)
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(a) P-I, Q-II, R-III
(b) P-II, Q-I, R-III
(c) P-III, Q-II, R-I
(d) P-III, Q-I, R-II
Ans: 
(c)
Sol: Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)ωn = √15 = 3.872 rad/sec
2ξ × 3.872 = 5
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)ωn = √25 = 5 rad/sec  
2ξ × 5 = 10
ξ = 1(Critically damped)
Observing all the options, option (C) is correct.

Q11: Which of the following systems has maximum peak overshoot due to a unit step input?  (SET-2 (2017))
(a) Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)

(b) Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
(c) Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
(d) Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Ans: (c)
Sol: For maximum peak over shoot MP ∝ (1/ξ)
ξ = 0.25 for option (C) which is least among all options. Therefore correct option is C.

Q12: When a unit ramp input is applied to the unity feedback system having closed loop transfer function Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE) the steady state error will be  (SET-2(2017))
(a) 0
(b) a/b
(c) (a+K)/b
(d) (a-K)/b
Ans: 
(d)
Sol: Closed loop transfer function Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Open loop transfer function Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Steady state error for ramp input given to type-1 system = 1/KV 
where, velocity error coefficient,
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE) Steady state error,
ess = (a-K)/b

Q13: A second-order real system has the following properties:
a) the damping ratio ξ = 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  (SET-2  (2016))
(a) Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)

(b) Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
(c) Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
(d) Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Ans: (b)
Sol: Damping ratio ξ = 0.5
Undamped natural frequency ωn = 10  rad/sec
Steady state output toa unit step input Css = 1.02
Hence steady state error ess = 1.02 − 1.00 = 0.02
∵ Characteristic equation is,
s+ 2ξωns + ω2n = 0
s+ 2 × 0.5 × 10s + 100 = 0
s+ 10s + 100 = 0
From options, if we take option (B) then
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Css = 1.02
Hence, Option (B) is correct answer.

Q14: The unit step response of a system with the transfer function Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE) is given by which one of the following waveforms?  (SET-2 (2015))
(a) Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(b) Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(c) Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)(d) Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Ans: 
(a)
Sol: Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)For A,
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)For B,
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)
Q15:  An open loop control system results in a response of e−2(sin5t + cos5t) for a unit impulse input. The DC gain of the control system is ______.  (SET-2 (2015))
(a) 0.82
(b) 0.24
(c) 0.55
(d) 1.47
Ans: 
(b)
Sol: Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)Putting s = 0,
Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE)

The document Previous Year Questions- Time Response Analysis - 1 | Control Systems - Electrical Engineering (EE) is a part of the Electrical Engineering (EE) Course Control Systems.
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FAQs on Previous Year Questions- Time Response Analysis - 1 - Control Systems - Electrical Engineering (EE)

1. What is Time Response Analysis in the context of engineering?
Ans. Time Response Analysis refers to the study of how a system responds over time to external inputs or disturbances. It is crucial in engineering to understand system behavior, stability, and performance, particularly in control systems.
2. Why is Time Response Analysis important for control systems?
Ans. Time Response Analysis is essential for control systems as it helps engineers evaluate how quickly and accurately a system can respond to changes. This analysis aids in designing systems that meet performance specifications and ensures stability and reliability.
3. What are the key parameters evaluated in Time Response Analysis?
Ans. The key parameters evaluated in Time Response Analysis include rise time, settling time, overshoot, and steady-state error. These parameters provide insights into the speed and accuracy of the system's response.
4. How can Time Response Analysis be applied in real-world scenarios?
Ans. Time Response Analysis can be applied in various real-world scenarios, such as in automotive control systems (like ABS), aerospace (flight control systems), and manufacturing processes. It helps in optimizing performance and ensuring safety and efficiency.
5. What tools or methods are commonly used for Time Response Analysis?
Ans. Common tools and methods for Time Response Analysis include simulation software (like MATLAB/Simulink), mathematical modeling, and graphical analysis techniques such as Bode plots or step response tests to visualize system behavior over time.
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