Direction: Question consists of two statements, one labelled as the 'Assertion (A)' and the other as 'Reason (R)'.Examine these two statements carefully and select the answer to this question using the codes given below:Assertion (A): A linear system gives a bounded output if the input is bounded.Reason (R): The roots of the characteristic equation have all negative real parts and the response due to initial conditions decay to zero as time t tends to infinity.

Both A and R are individually true and R is the correct explanation of A

Both A and R are individually true but R is not the correct explanation of A

For a critically damped system, the closed-loop poles are

complex conjugate with negative real part

Directions: The item consists of two statements, one labeled as the ‘Assertion (A)’ and the other as ‘Reason (R)’.You are to examine these two statements carefully and select the answers to the item using the codes given below:Assertion (A): Steady-state error can be reduced by increasing integral gain.Reason (R): Overshoot can be reduced by increasing derivative gain.

Both A and R individually true and R is the correct explanation of A

Both A and R are individually true but R is not the correct explanation of A

Of following transfer function of second order linear time-invariant systems, the under damped system is represented by?

\(H\left( s \right) = \frac{1}{{{s^2} + 4s + 4}}\)

\(H\left( s \right) = \frac{1}{{{s^2} + 5s + 4}}\)

\(H\left( s \right) = \frac{1}{{{s^2} + 4.5s + 4}}\)

\(H\left( s \right) = \frac{1}{{{s^2} + 3s + 4}}\)

A second order system has poles at -1 ± j2 and zero at 1. What is the transfer function of the system if the steady state output to an input of unit step is c(t) = 3?

\(\frac{\left( s-1 \right)}{{{s}^{2}}+2s+4}\)

\(\frac{\left( s-1 \right)}{{{s}^{2}}+2s+5}\)

\(\frac{-15\left( s-1 \right)}{{{s}^{2}}+2s+5}\)

\(\frac{\left( s-1 \right)}{{{s}^{2}}+2s+4}\)

\(\frac{5\left( s-1 \right)}{{{s}^{2}}+2s+5}\)

For the following system \(G\left( s \right) = \frac{1}{{\left( {s + 1} \right)\left( {s + 2} \right)}}\)The 2% settling time of the step response is required to be less than 2 sec.Which one the following compensator C(s) can achieve this

\(5\left( {\frac{{0.03}}{s} + 1} \right)\)

Match the unit-step responses (1), (2) and (3) with the transfer functions P(s), Q(s) and R(s), given below.\(P\left( s \right) = \frac{{ - 1}}{{\left( {s + 1} \right)}}\)\(Q\left( s \right) = \frac{{2\left( {s - 1} \right)}}{{\left( {s + 10} \right)\left( {s + 2} \right)}}\)\(R\left( s \right) = \frac{1}{{{{\left( {s + 1} \right)}^2}}}\)

P(s) – (2), Q(s) – (1), R(s) – (3)

P(s) – (3), Q(s) – (2), R(s) – (1)

P(s) – (1), Q(s) – (2), R(s) – (3)

P(s) – (2), Q(s) – (1), R(s) – (3)

P(s) – (1), Q(s) – (3), R(s) – (2)

Direction: It consists of two statements, one labeled as Statement (I) and the other as Statement (II). Examine these two statements carefully and select the answers to these items using the codes given below:Statement (I): If a ramp input is applied to a second-order system, the steady-state error of the response can be reduced by reducing damping and increasing the natural frequency of oscillationStatement (II): In the frequency response of a second-order system, the change in slope at one of the corner frequencies is of ±40 dB/decade

Statement (I) is true but Statement (II) is false

Both statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)

Both statement (I) and Statement (II) are individually true and Statement (II) is not the correct explanation of Statement (I)

Statement (I) is true but Statement (II) is false

Statement (I) is false but Statement (II) is true

If the response of LTI continuous time system to unit step input is \(\left( {\frac{1}{2} - \frac{1}{2}{e^{ - 2t}}} \right)\), then impulse response of the system is

\(\left( {1 - {e^{ - 2t}}} \right)\)

\(\left( {\frac{1}{2} - \frac{1}{2}{e^{ - 2t}}} \right)\)

\(\left( {{e^{ - 2t}}} \right)\)

\(\left( {1 - {e^{ - 2t}}} \right)\)

59 + Mcqs in Time Response Analysis in Control Systems Page 1 McqOptions

1.	Given the differential equation model of a physical system, determine the time constant of the system:\(40 \frac{dx}{dt}+2x=f(t)\)
A.	10
B.	20
C.	1.1
D.	4
Answer» C. 1.1

Discussion

2.	For the following First Order System. The value of steady state error is given by
A.	0 (zero)
B.	∞ (infinite)
C.	(1 - e-t / T)
D.	(1 + e-t / T)
Answer» B. ∞ (infinite)

Discussion

3.	Direction: Question consists of two statements, one labelled as the 'Assertion (A)' and the other as 'Reason (R)'.Examine these two statements carefully and select the answer to this question using the codes given below:Assertion (A): A linear system gives a bounded output if the input is bounded.Reason (R): The roots of the characteristic equation have all negative real parts and the response due to initial conditions decay to zero as time t tends to infinity.
A.	Both A and R are individually true and R is the correct explanation of A
B.	Both A and R are individually true but R is not the correct explanation of A
C.	A is true but R is false
D.	A is false but R is true
Answer» E.

Discussion

4.	A system has a transfer function \(\frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{4}{{{s^2} + 1.6s + 4}}\)For a unit-step response and 2% tolerance band, the settling time will be
A.	5 seconds
B.	4 seconds
C.	3 seconds
D.	2 seconds
Answer» B. 4 seconds

Discussion

5.	A second order control system has a damping ratio as 0.6 and natural frequency of oscillations as 11 rad/sec. What will be the Damped frequency of oscillation?
A.	2.6 rad/sec
B.	8.8 rad/sec
C.	6.9 rad/sec
D.	5.6 rad/sec
Answer» C. 6.9 rad/sec

Discussion

6.	In a feedback control system, if \(G(s)=\frac{4}{s(s+3) }\)and \(H(s)=\frac{1}{s}\), then the closed-loop system will be of type
A.	3
B.	2
C.	1
D.	0
Answer» C. 1

Discussion

7.	For a critically damped system, the closed-loop poles are
A.	purely imaginary
B.	real, equal and negative
C.	complex conjugate with negative real part
D.	real, unequal and negative
Answer» C. complex conjugate with negative real part

Discussion

8.	Consider a second-order all-pole transfer function model, if the desired settling time (5%) is 0.60 sec and the desired damping ratio 0.707, where should the poles be located in the s-plane?
A.	5 ± j4√2
B.	5 ± j5
C.	4± j5√2
D.	- 4 ± j7
Answer» C. 4± j5√2

Discussion

9.	If the output of the system at steady state does not agree with the input, then the system is said to have _________ which determines the _________ of the system.
A.	Steady state error, accuracy
B.	Residual error, overshoot
C.	Steady state error, tolerance
D.	Residual error, tolerance
Answer» B. Residual error, overshoot

Discussion

10.	Directions: The item consists of two statements, one labeled as the ‘Assertion (A)’ and the other as ‘Reason (R)’.You are to examine these two statements carefully and select the answers to the item using the codes given below:Assertion (A): Steady-state error can be reduced by increasing integral gain.Reason (R): Overshoot can be reduced by increasing derivative gain.
A.	Both A and R individually true and R is the correct explanation of A
B.	Both A and R are individually true but R is not the correct explanation of A
C.	A is true but R is false
D.	A is false but R is true
Answer» C. A is true but R is false

Discussion

11.	For type 2 system with input as unit ramp, velocity error constant and steady state error are respectively
A.	0, ∞
B.	∞, 0
C.	∞, ∞
D.	0, 0
Answer» C. ∞, ∞

Discussion

12.	A system is having \(TF = \frac{{25s}}{{{s^2} + 8s + 25}}\) What is the time taken to reach maximum peak overshoot for a step input?
A.	π/5
B.	π/3
C.	π/25
D.	None of the above
Answer» C. π/25

Discussion

13.	Consider the following statements regarding the steady-state error of type ‘0’ system.(a) with unit step input \({e_{ss}} = \frac{1}{{1 + k}}\) where k is a constant (b) With unit ramp input \({e_{ss}} = \frac{1}{k}\)where k is a constant (c) With unit parabolic input \({e_{ss}} = \frac{1}{k}\;\)where k is a constant (d) with unit parabolic input ess = ∞Which of the above statements are correct?
A.	(a) and (b)
B.	(a) and (c)
C.	(b) and (c)
D.	(a) and (d)
Answer» E.

Discussion

14.	For a unity feedback control system, the forward path transfer function is given by \(G\left( s \right) = \frac{{40}}{{s\left( {s + 2} \right)\left( {{s^2} + 2s + 30} \right)}}\)The steady-state error of the system for the input \(\frac{{5{t^2}}}{2}\) is
A.	0
B.	∞
C.	20t2
D.	30t2
Answer» C. 20t2

Discussion

15.	A unity feedback control system has forward path transfer function \(G\left( s \right) = \frac{K}{{s\left( {s + 2} \right)}}.\) If the design specification is that the steady state error due to unit ramp input is 0.05. The value of gain K will be.
A.	10
B.	20
C.	40
D.	80
Answer» D. 80

Discussion

16.	For a critically damped second order system, if gain constant (K) is increased, the system behaviour
A.	becomes oscillatory
B.	becomes under damped
C.	becomes over damped
D.	shows no change
Answer» C. becomes over damped

Discussion

17.	If the overshoot of the unit-step response of a second order system is 30%, then the time at which peak overshoot occurs (assuming ωn = 10 rad / sec)
A.	0.36 sec
B.	0.363 sec
C.	0.336 sec
D.	0.633 sec
Answer» D. 0.633 sec

Discussion

18.	For a feedback control system of type-2, the steady-state error for a ramp input is
A.	infinity
B.	constant
C.	zero
D.	indeterminate
Answer» D. indeterminate

Discussion

19.	Of following transfer function of second order linear time-invariant systems, the under damped system is represented by?
A.	\(H\left( s \right) = \frac{1}{{{s^2} + 4s + 4}}\)
B.	\(H\left( s \right) = \frac{1}{{{s^2} + 5s + 4}}\)
C.	\(H\left( s \right) = \frac{1}{{{s^2} + 4.5s + 4}}\)
D.	\(H\left( s \right) = \frac{1}{{{s^2} + 3s + 4}}\)
Answer» E.

Discussion

20.	For the characteristic equation, s2 + 4.8s + 72 = 0, the damping ratio and natural frequency are
A.	0.212, 8.1 rad/sec
B.	0.283, 8.48 rad/sec
C.	0.299, 8.66 rad/sec
D.	None of the above
Answer» C. 0.299, 8.66 rad/sec

Discussion

21.	A control system is defined by the following mathematical relationship \(\frac{d^2 x}{dt^2 }+6 \frac{dx}{dt} ~5x(t)=10 (1-e^{-5t})\). The response of the system as t → ∞ is
A.	x = 2
B.	x = 6
C.	x = 5
D.	x = -2
Answer» B. x = 6

Discussion

22.	A sensor requires 30 s to indicate 90% of the response to a step input. If the sensor is a first-order system, the time constant is [given, loge (0.1) = -2.3]
A.	15 s
B.	13 s
C.	21 s
D.	28 s
Answer» C. 21 s

Discussion

23.	A second order system has poles at -1 ± j2 and zero at 1. What is the transfer function of the system if the steady state output to an input of unit step is c(t) = 3?
A.	\(\frac{\left( s-1 \right)}{{{s}^{2}}+2s+5}\)
B.	\(\frac{-15\left( s-1 \right)}{{{s}^{2}}+2s+5}\)
C.	\(\frac{\left( s-1 \right)}{{{s}^{2}}+2s+4}\)
D.	\(\frac{5\left( s-1 \right)}{{{s}^{2}}+2s+5}\)
Answer» C. \(\frac{\left( s-1 \right)}{{{s}^{2}}+2s+4}\)

Discussion

24.	For the following system \(G\left( s \right) = \frac{1}{{\left( {s + 1} \right)\left( {s + 2} \right)}}\)The 2% settling time of the step response is required to be less than 2 sec.Which one the following compensator C(s) can achieve this
A.	\(\frac{3}{{s + 5}}\)
B.	\(5\left( {\frac{{0.03}}{s} + 1} \right)\)
C.	2(s + 4)
D.	\(4(\frac{s+8}{s+3}) \)
Answer» D. \(4(\frac{s+8}{s+3}) \)

Discussion

25.	Match List 1 with List 2For time response of a second order systemList 1List 2 (a) Slower time constant (i) \(\frac{1}{{\left( {\xi + \sqrt {{\xi ^2} + 1} } \right){\omega _n}}}\) (b) Rise time (ii) \(\frac{1}{{4\xi {\omega _n}}}\) (c) Setting time (iii) \(\frac{{\pi - \phi }}{{{\omega _n} - \sqrt {1 - {\xi ^2}} }}\) (d) Faster time constant (iv) \(\frac{1}{{\left( {\xi - \sqrt {{\xi ^2} - 1} } \right){\omega _n}}}\)Choose the correct answer from the options given below:(1) (a) - (i), (b) -(iii), (c) - (iv), (d) -(ii)(2) (a) - (ii), (b) -(iii), (c) - (iv), (d) -(i)(3) (a) - (iv), (b) -(iii), (c) - (ii), (d) -(i)(4) (a) - (iii), (b) -(iv), (c) - (i), (d) -(ii)
A.	1
B.	2
C.	3
D.	4
Answer» D. 4

Discussion

26.	Let Y(s) be the unit-step response of a causal system having a transfer function\(G\left( s \right) = \frac{{3 - s}}{{\left( {s + 1} \right)\left( {s + 3} \right)}}\)that is, \(Y\left( s \right) = \frac{{G\left( s \right)}}{S}\). The forced response of the system is
A.	u(t) – 2e -t + e-3t u(t)
B.	2 u(t) – 2e -t + e-3t u(t)
C.	2u(t)
D.	u(t)
Answer» E.

Discussion

27.	Consider the following statements:For a type-1 and a unity feedback system, having unity gain in the forward path1. positional error constant Kp is equal to zero2. acceleration error constant Ka is equal to zero3. steady-state error ess per unit-step displacement input is equal to 0Which of the above statements are correct?
A.	1, 2 and 3
B.	1 and 2 only
C.	2 and 3 only
D.	1 and 3 only
Answer» D. 1 and 3 only

Discussion

28.	In control systems, the type of system depends on the number of:
A.	Zero at infinity
B.	poles on S plane
C.	Poles at infinity
D.	Poles at origin of S plane
Answer» E.

Discussion

29.	Acceleration error constant is a measure of the steady state error of the system when the input is _______
A.	unit step function
B.	ramp function
C.	impulse function
D.	parabolic function
Answer» E.

Discussion

30.	For a unity feedback control system the open-loop transfer function G(s) = 10 (s + 2)/s2(s + 1) find acceleration error constant
A.	10
B.	20
C.	∞
D.	0
Answer» C. ∞

Discussion

31.	Match the unit-step responses (1), (2) and (3) with the transfer functions P(s), Q(s) and R(s), given below.\(P\left( s \right) = \frac{{ - 1}}{{\left( {s + 1} \right)}}\)\(Q\left( s \right) = \frac{{2\left( {s - 1} \right)}}{{\left( {s + 10} \right)\left( {s + 2} \right)}}\)\(R\left( s \right) = \frac{1}{{{{\left( {s + 1} \right)}^2}}}\)
A.	P(s) – (3), Q(s) – (2), R(s) – (1)
B.	P(s) – (1), Q(s) – (2), R(s) – (3)
C.	P(s) – (2), Q(s) – (1), R(s) – (3)
D.	P(s) – (1), Q(s) – (3), R(s) – (2)
Answer» C. P(s) – (2), Q(s) – (1), R(s) – (3)

Discussion

32.	Consider a permanent magnet dc (PMDC) motor which is initially at rest. At t = 0, a dc voltage of 5 V is applied to the motor. Its speed monotonically increases from 0 rad/s to 6.32 rad/s in 0.5 s and finally settles to 10 rad/s. Assuming that the armature inductance of the motor is negligible, the transfer function for the motor is
A.	\(\frac{{10}}{{0.5s + 1}}\)
B.	\(\frac{2}{{0.5s + 1}}\)
C.	\(\frac{2}{{s + 0.5}}\)
D.	\(\frac{{10}}{{s + 0.5}}\)
Answer» C. \(\frac{2}{{s + 0.5}}\)

Discussion

33.	Direction: It consists of two statements, one labeled as Statement (I) and the other as Statement (II). Examine these two statements carefully and select the answers to these items using the codes given below:Statement (I): If a ramp input is applied to a second-order system, the steady-state error of the response can be reduced by reducing damping and increasing the natural frequency of oscillationStatement (II): In the frequency response of a second-order system, the change in slope at one of the corner frequencies is of ±40 dB/decade
A.	Both statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
B.	Both statement (I) and Statement (II) are individually true and Statement (II) is not the correct explanation of Statement (I)
C.	Statement (I) is true but Statement (II) is false
D.	Statement (I) is false but Statement (II) is true
Answer» C. Statement (I) is true but Statement (II) is false

Discussion

34.	If a zero is added in a forward path of a second-order system:
A.	rise time will decrease
B.	rise time will increase
C.	bandwidth will decrease
D.	system will be less stable
Answer» B. rise time will increase

Discussion

35.	A unity feedback system has \(G\left( s \right) = \frac{{K\left( {s + 12} \right)}}{{\left( {s + 14} \right)\left( {s + 18} \right)}}\)What is the value of K to yield 10% error in steady state for unit step input
A.	672
B.	189
C.	100
D.	21
Answer» C. 100

Discussion

36.	Given a unity feedback system with \(G(s)=\dfrac{K}{s(s+6)}\), the value of K for damping ratio of 0.75 is
A.	1
B.	4
C.	16
D.	64
Answer» D. 64

Discussion

37.	For the second order closed loop system shown below, the natural freq (ωn) in rad/sec is
A.	16
B.	4
C.	2
D.	1
Answer» D. 1

Discussion

38.	In a control system, the response is critically damped if:
A.	Damping factor is 1
B.	Damping factor is > 1
C.	Damping factor is < 1
D.	Damping factor is 0
Answer» B. Damping factor is > 1

Discussion

39.	Consider a unity feedback control system with open loop transfer function G(s) = K/s(s+1). The steady state error for unit step input is
A.	0
B.	K
C.	1/K
D.	infinity
Answer» B. K

Discussion

40.	For an overdamped system consisting of poles at -4 and -6a/4 the poles can lie at (-3 + j4) if the damping ratio is
A.	increased
B.	decreased
C.	held constant
D.	none of the above
Answer» C. held constant

Discussion

41.	A unity feedback system has an open-loop transfer function \(G\left( s \right) = \frac{K}{{s\left( {s + 10} \right)}}\) If the damping ratio is 0-5, then what is the value of K?A unity feedback system has an open-loop transfer function If the damping ratio is 0-5, then what is the value of K?
A.	150
B.	100
C.	50
D.	10
Answer» C. 50

Discussion

42.	Consider the following input and system types:Input typeSystem typeUnit stepType ‘0’Unit rampType ‘1’Unit parabolicType ‘2’ Which of the following statements are correct?1. Unit step input is acceptable to all the three types of system.2. Type ‘0’ system cannot accept unit parabolic input.3. Unit ramp input is acceptable to Type ‘2’ system only
A.	1 and 2 only
B.	1 and 3 only
C.	2 and 3 only
D.	1, 2 and 3
Answer» B. 1 and 3 only

Discussion

43.	A second order control system exhibits 100% overshoot. Its damping ratio is:
A.	Less than 1
B.	Equal to 1
C.	Greater than 1
D.	Equal to zero
Answer» E.

Discussion

44.	A ramp input applied to a unity feedback system results in 5% steady state error. The type number and zero frequency gain of the system are
A.	1 and 20
B.	0 and 20
C.	0 and 1/20
D.	1 and 1/20
Answer» B. 0 and 20

Discussion

45.	A unity feedback system as shown has damping ratio of 0.8 using derivative controlFollowing parameter are obtained(A) Characteristic equation is s2 + 1.6s + 16 = 0(B) ξ = 0.2 (without derivative control)(C) ξ = 0.8 (without derivative control)(D) ωn = 4 rad/secChoose the most appropriate answer from the options given below:(1) (A), (C) and (D) only(2) (B), (D) only(3) (A), (B), (D) only(4) (C), (D)
A.	1
B.	2
C.	3
D.	4
Answer» D. 4

Discussion

46.	In the control system shown in the figure below, a reference signal 2 r(t) = t2 is applied at time t = 0. The control system employs a PID controller C(s) = KP + KI/ s + KDs and the plant has a transfer function P(s) = 3/s. If KP = 10, KI = 1 and KD = 2, the steady state value of e is
A.	0
B.	2/3
C.	1
D.	∞
Answer» C. 1

Discussion

47.	Consider the open-loop transfer function:\(G\left( s \right)H\left( s \right) = \frac{{5\left( {s + 1} \right)}}{{{s^2}\left( {s + 5} \right)\left( {s + 12} \right)}}\)The steady-state error due to a ramp input is
A.	0
B.	5
C.	12
D.	∞
Answer» B. 5

Discussion

48.	From the point of view of stability and response speed of a closed loop system, the appropriate range for the value of damping ratio lies between:
A.	0 to 0.2
B.	0.4 to 0.7
C.	0.8 to 1.0
D.	1.1 to 1.5
Answer» C. 0.8 to 1.0

Discussion

49.	A first-order low-pass filter of time constant T is excited with different input signals (with zero initial conditions up to t = 0). Match the excitation signals X, Y, Z with the corresponding time responses for t ≥ 0:X: Impulse P: 1 −
A.	X→R, Y→Q, Z→P
B.	X→Q, Y→P, Z→R
C.	X→R, Y→P, Z→Q
D.	X→P, Y→R, Z→Q
Answer» D. X→P, Y→R, Z→Q

Discussion

50.	If the response of LTI continuous time system to unit step input is \(\left( {\frac{1}{2} - \frac{1}{2}{e^{ - 2t}}} \right)\), then impulse response of the system is
A.	\(\left( {\frac{1}{2} - \frac{1}{2}{e^{ - 2t}}} \right)\)
B.	\(\left( {{e^{ - 2t}}} \right)\)
C.	\(\left( {1 - {e^{ - 2t}}} \right)\)
D.	Constant
Answer» C. \(\left( {1 - {e^{ - 2t}}} \right)\)

Discussion

Explore topic-wise MCQs in Control Systems.

Given the differential equation model of a physical system, determine the time constant of the system:\(40 \frac{dx}{dt}+2x=f(t)\)

For the following First Order System. The value of steady state error is given by

A system has a transfer function \(\frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{4}{{{s^2} + 1.6s + 4}}\)For a unit-step response and 2% tolerance band, the settling time will be

A second order control system has a damping ratio as 0.6 and natural frequency of oscillations as 11 rad/sec. What will be the Damped frequency of oscillation?

In a feedback control system, if \(G(s)=\frac{4}{s(s+3) }\)and \(H(s)=\frac{1}{s}\), then the closed-loop system will be of type

For a critically damped system, the closed-loop poles are

Consider a second-order all-pole transfer function model, if the desired settling time (5%) is 0.60 sec and the desired damping ratio 0.707, where should the poles be located in the s-plane?

If the output of the system at steady state does not agree with the input, then the system is said to have _________ which determines the _________ of the system.

For type 2 system with input as unit ramp, velocity error constant and steady state error are respectively

A system is having \(TF = \frac{{25s}}{{{s^2} + 8s + 25}}\) What is the time taken to reach maximum peak overshoot for a step input?

For a unity feedback control system, the forward path transfer function is given by \(G\left( s \right) = \frac{{40}}{{s\left( {s + 2} \right)\left( {{s^2} + 2s + 30} \right)}}\)The steady-state error of the system for the input \(\frac{{5{t^2}}}{2}\) is

A unity feedback control system has forward path transfer function \(G\left( s \right) = \frac{K}{{s\left( {s + 2} \right)}}.\) If the design specification is that the steady state error due to unit ramp input is 0.05. The value of gain K will be.

For a critically damped second order system, if gain constant (K) is increased, the system behaviour

If the overshoot of the unit-step response of a second order system is 30%, then the time at which peak overshoot occurs (assuming ωn = 10 rad / sec)

For a feedback control system of type-2, the steady-state error for a ramp input is

Of following transfer function of second order linear time-invariant systems, the under damped system is represented by?

For the characteristic equation, s2 + 4.8s + 72 = 0, the damping ratio and natural frequency are

A control system is defined by the following mathematical relationship \(\frac{d^2 x}{dt^2 }+6 \frac{dx}{dt} ~5x(t)=10 (1-e^{-5t})\). The response of the system as t → ∞ is

A sensor requires 30 s to indicate 90% of the response to a step input. If the sensor is a first-order system, the time constant is [given, loge (0.1) = -2.3]

A second order system has poles at -1 ± j2 and zero at 1. What is the transfer function of the system if the steady state output to an input of unit step is c(t) = 3?

For the following system \(G\left( s \right) = \frac{1}{{\left( {s + 1} \right)\left( {s + 2} \right)}}\)The 2% settling time of the step response is required to be less than 2 sec.Which one the following compensator C(s) can achieve this

Let Y(s) be the unit-step response of a causal system having a transfer function\(G\left( s \right) = \frac{{3 - s}}{{\left( {s + 1} \right)\left( {s + 3} \right)}}\)that is, \(Y\left( s \right) = \frac{{G\left( s \right)}}{S}\). The forced response of the system is

In control systems, the type of system depends on the number of:

Acceleration error constant is a measure of the steady state error of the system when the input is _______

For a unity feedback control system the open-loop transfer function G(s) = 10 (s + 2)/s2(s + 1) find acceleration error constant

If a zero is added in a forward path of a second-order system:

A unity feedback system has \(G\left( s \right) = \frac{{K\left( {s + 12} \right)}}{{\left( {s + 14} \right)\left( {s + 18} \right)}}\)What is the value of K to yield 10% error in steady state for unit step input

Given a unity feedback system with \(G(s)=\dfrac{K}{s(s+6)}\), the value of K for damping ratio of 0.75 is

For the second order closed loop system shown below, the natural freq (ωn) in rad/sec is

In a control system, the response is critically damped if:

Consider a unity feedback control system with open loop transfer function G(s) = K/s(s+1). The steady state error for unit step input is

For an overdamped system consisting of poles at -4 and -6a/4 the poles can lie at (-3 + j4) if the damping ratio is

A unity feedback system has an open-loop transfer function \(G\left( s \right) = \frac{K}{{s\left( {s + 10} \right)}}\) If the damping ratio is 0-5, then what is the value of K?A unity feedback system has an open-loop transfer function If the damping ratio is 0-5, then what is the value of K?

A second order control system exhibits 100% overshoot. Its damping ratio is:

A ramp input applied to a unity feedback system results in 5% steady state error. The type number and zero frequency gain of the system are

In the control system shown in the figure below, a reference signal 2 r(t) = t2 is applied at time t = 0. The control system employs a PID controller C(s) = KP + KI/ s + KDs and the plant has a transfer function P(s) = 3/s. If KP = 10, KI = 1 and KD = 2, the steady state value of e is

Consider the open-loop transfer function:\(G\left( s \right)H\left( s \right) = \frac{{5\left( {s + 1} \right)}}{{{s^2}\left( {s + 5} \right)\left( {s + 12} \right)}}\)The steady-state error due to a ramp input is

From the point of view of stability and response speed of a closed loop system, the appropriate range for the value of damping ratio lies between:

A first-order low-pass filter of time constant T is excited with different input signals (with zero initial conditions up to t = 0). Match the excitation signals X, Y, Z with the corresponding time responses for t ≥ 0:X: Impulse P: 1 −

If the response of LTI continuous time system to unit step input is \(\left( {\frac{1}{2} - \frac{1}{2}{e^{ - 2t}}} \right)\), then impulse response of the system is

If the output of the system at steady state does not agree with the input, then the system is said to have _ which determines the _ of the system.