Control System Engineering Set 3

Electrical Engineering

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This set of Control System Engineering (CSE) Multiple Choice Questions & Answers (MCQs) focuses on Control System Engineering Set 3

Q1 | Delay time is the time required by a system to reach a quarter of its steady state value.
  • true
  • false
Answer: false
Explaination:
the delay time is defined as the time required by the system to reach half of
Q2 | For non-unity feedback system, the error is calculated with respect to the reference signal.
  • true
  • false
Answer: false
Explaination:
the error will be calculated with respect to the actuating signal i.e the feedback signal is either added or subtracted from the reference signal and the error is calculated with respect to the resultant signal. hence, the above statement is false.
Q3 | Which of the following command will reveal the damping ratio of the system?
  • damp()
  • damp[]
  • damping{}
  • dr()
Answer: damp()
Explaination:
damp() is the correct command to find the damping ration of the system. we need to represent the system by it’s transfer function and give it as an input to the damp()
Q4 | If the damping factor is zero, the unit-step response is
  • purely sinusoidal
  • ramp function
  • pulse function
  • impulse function
Answer: purely sinusoidal
Explaination:
the generalized time response of a second order control system reduces to a
Q5 | If the damping ratio is equal to 1, a second-order system is                    
  • having maginary roots of the characteristic equation
  • underdamped
  • critically damped with unequal roots
  • critically damped with equal roots
Answer: critically damped with equal roots
Explaination:
the time response of a system with a damping ratio of 1 is critically damped. but the roots of the characteristic equation will be equal and equal to negative of the natural undamped frequency of the system.
Q6 | From the following graphs of the generalized transfer function 1/s+a, which plot shows a transfer function with a bigger value of a?
  • blue plot
  • red plot
  • yellow plot
  • purple plot
Answer: purple plot
Explaination:
as the value of a increases, the inverse laplace transform of the given transfer function suggests that the e-at value is reducing. hence for a higher a, the graph reaches a 0 earlier. from the given figure, the purple plot reaches the steady state faster so purple plot is correct only.
Q7 | From the following graphs of the generalized transfer function 1/as2, which plot shows the transfer function for a higher a?
  • blue
  • red
  • yellow
  • purple
Answer: purple
Explaination:
the impulse response of the given transfer function is a ramp function of slope 1/a. if a increases, the slope decreases. hence, from the above figure, purple is the correct one.
Q8 | If the damping factor is less than the damping factor at critical damping, the time response of the system is                        
  • underdamped
  • overdamped
  • marginally damped
  • unstable
Answer: underdamped
Explaination:
if the damping factor is less than the damping factor at critical damping
Q9 | This makes the system underdamped since the response of the system becomes a decaying sinusoid in nature.
  • 9/(s2+2s+9)
  • 16/(s2+2s+16)
  • 25/(s2+2s+25)
  • 36/(s2+2s+36)
Answer: 36/(s2+2s+36)
Explaination:
comparing the characteristic equation with the standard equation the value of the damping factor is calculated and the value for the option d is minimum hence the system will have the maximum overshoot .
Q10 | The system in originally critically damped if the gain is doubled the system will be :
  • remains same
  • overdamped
  • under damped
  • undamped
Answer: under damped
Explaination:
hence due to this g lies between 0 and 1.
Q11 | Let c(t) be the unit step response of a system with transfer function K(s+a)/(s+K). If c(0+) = 2 and c(∞) = 10, then the values of a and K are respectively.
  • 2 and 10
  • -2 and 10
  • 10 and 2
  • 2 and -10
Answer: 10 and 2
Explaination:
applying initial value theorem which state that the initial value of the system is at time t =0 and this is used to find the value of k and final value theorem to find the value of a.
Q12 | The damping ratio and peak overshoot are measures of:
  • relative stability
  • speed of response
  • steady state error
  • absolute stability
Answer: speed of response
Explaination:
speed of response is the speed at which the response takes the final value and this is determined by damping factor which reduces the oscillations and peak overshoot as the peak is less then the speed of response will be more.
Q13 | A system has a complex conjugate root pair of multiplicity two or more in its characteristic equation. The impulse response of the system will be:
  • a sinusoidal oscillation which decays exponentially; the system is therefore stable
  • a sinusoidal oscillation with a time multiplier ; the system is therefore unstable
  • a sinusoidal oscillation which rises exponentially ; the system is therefore unstable
  • a dc term harmonic oscillation the system therefore becomes limiting stable
Answer: a sinusoidal oscillation which rises exponentially ; the system is therefore unstable
Explaination:
poles are the roots of the denominator of the transfer function and on imaginary axis makes the system stable but multiple poles makes the system unstable.
Q14 | The step response of the system is c(t) = 10+8e-t-4/8e-2t . The gain in time constant form of transfer function will be:
  • -7
  • 7
  • 7.5
  • -7.5
Answer: -7.5
Explaination:
differentiating the equation and getting the impulse response and then taking the inverse laplace transform and converting the form into time constant form we get k =
Q15 | The steady state error for a unity feedback system for the input r(t) = Rt^2/2 to the system G(s) = K(s+2)/s(s3+7s2+12s) is
  • 0
  • 6r/k
  • ∞
  • 3r/k
Answer: 6r/k
Explaination:
ka = 2k/12 = k/6
Q16 | Find the velocity error constant of the system given below :
  • 0
  • 2
  • 4
  • ∞
Answer: 4
Explaination:
comparing with the characteristic equation the values of g and w are calculated as g = 1 and w = 4 and hence the system is critically damped.
Q17 | Consider the unity feedback system with open loop transfer function the minimum value of the steady state error to a ramp input r(t) = 6tu(t) is OLTF = K/s(s+1)(s+2)
  • 1
  • 2
  • 3
  • 4
Answer: 2
Explaination:
routh-hurwitz criterion is used to calculate the stability of the system by checking the sign changes of the first row and
Q18 | 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 respectively
  • 1 and 20
  • 0 and 20
  • 0 and 1/20
  • 1 and 1/20
Answer: 1 and 20
Explaination:
steady state error is the error calculated between the final output and desired output and for the good control system the error must be less and this steady state error is inversely proportional to gain.
Q19 | A particular control system yielded a steady state error of 0.20 for unit step input. A unit integrator is cascaded to this system and unit ramp input is applied to this modified system. What is the value of steady- state error for this modified system?
  • 0.10
  • 0.15
  • 0.20
  • 0.25
Answer: 0.25
Explaination:
the integrator is similar to the phase lag systems and it is used to reduce or eleminate the steady state error and when it is cascaded with the ramp input hence the acceleration error constant is calculated which is equal to 0.25.
Q20 | The error constants described are the ability to reduce the steady state errors.
  • true
  • false
Answer: true
Explaination:
as the type of the system becomes higher more steady state errors are eliminated.
Q21 | Systems of type higher than 2 are not employed in practice.
  • true
  • false
Answer: true
Explaination:
these are more difficult to stabilize and dynamic errors are much larger.
Q22 | Steady state refers to
  • error at the steady state
  • error at the transient state
  • error at both state
  • precision
Answer: error at the steady state
Explaination:
steady state errors are the change in the output at the steady state with respect to the change in the input.
Q23 | The disadvantages of the error constants are:
  • they do not give the information of the steady state error when the inputs are other than the three basic types
  • error constant fail to indicate the exact manner in which the error function change with time.
  • they do not give information of the steady state error and fail to indicate the exact manner in which the error function change with time
  • they give information of the steady state error
Answer: they do not give information of the steady state error and fail to indicate the exact manner in which the error function change with time
Explaination:
the disadvantages of the error constants are as they do not give the information of the steady state error when the inputs are other than the three basic types and error constant fail to indicate the exact manner in which the error function change with time.
Q24 | The input of a controller is
  • sensed signal
  • error signal
  • desired variable value
  • signal of fixed amplitude not dependent on desired variable value
Answer: error signal
Explaination:
controller is the block in the control system that control the input and provides the output and this is the first block of the system having the input as the error signal.
Q25 | Phase lag controller:
  • improvement in transient response
  • reduction in steady state error
  • reduction is settling time
  • increase in damping constant
Answer: reduction in steady state error
Explaination:
phase lag controller is the integral controller that creates the phase lag and does not affect the value of the damping factor and that tries to reduce the steady state error.
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