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# Multiple choice question for engineering

## Set 1

1. Which among the following is a unique model of a system?
a) Transfer function
b) State variable
c) Block diagram
d) Signal flow graphs

Answer: a [Reason:] Transfer Function is defined as the ratio of the Laplace output to the Laplace input with the zero initial conditions and is a unique model of the system.

2. Which among the following is a disadvantage of modern control theory?
a) Implementation of optimal design
b) Transfer function can also be defined for different initial conditions
c) Analysis of all systems take place
d) Necessity of computational work

Answer: d [Reason:] Modern control theory is also not best suited in every respect it has also some disadvantages and the major disadvantage is that it requires computational work.

3. According to the property of state transition method, e0 is equal to _____
a) I
b) A
c) e-At
d) -eAt

Answer: c [Reason:] By definition state transition matrix is defined as e-At and this is the matrix that comes into the picture when the total response is considered that is with the free response and forced response.

4. Which mechanism in control engineering implies an ability to measure the state by taking measurements at output?
a) Controllability
b) Observability
c) Differentiability

Answer: b [Reason:] Observability and controllability are the two methods to check the output response characteristics and observability in control engineering implies an ability to measure the state by taking measurements at output.

5. State model representation is possible using _________
a) Physical variables
b) Phase variables
c) Canonical state variables
d) All of the mentioned

Answer: d [Reason:] State model representation is the representation of the control system is the form of the state variables and state vectors and is possible using physical variables, phase variables and canonical state variables.

6. Which among the following constitute the state model of a system in addition to state equations?
a) Input equations
b) Output equations
c) State trajectory
d) State vector

Answer: b [Reason:] Output Equations constitute the state model of a system in addition to state equations and for the complete state model mainly input model, output model and state models are required.

7. Which among the following plays a crucial role in determining the state of dynamic system?
a) State variables
b) State vector
c) State space
d) State scalar

Answer: a [Reason:] State Variables are the integral part of the state variable analysis and plays a crucial role in determining the state of dynamic system.

8. Which among the following are the interconnected units of state diagram representation?
a) Scalars
c) Integrator
d) All of the mentioned

Answer: d [Reason:] Scalars, adders and integrator are the interconnected units of state diagram representation and this representation helps in determination of the state of the control system.

9. State space analysis is applicable even if the initial conditions are _____
a) Zero
b) Non-zero
c) Equal
d) Not equal

Answer: b [Reason:] State space analysis is the analysis different from the transfer function approach as it has state variables and state vectors used for the analysis and can be used even if initial conditions are non-zero.

10. Conventional control theory is applicable to ______ systems
a) SISO
b) MIMO
c) Time varying
d) Non-linear

Answer: a [Reason:] The major advantage of state space analysis is that it can be applied to MIMO systems also while the conventional control theory that is transfer function approach is applicable to the SISO systems only.

## Set 2

1. 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
a) 0
b) 6R/K
c) ∞
d) 3R/K

Answer: b [Reason:] Ka = 2K/12 = K/6 Ess = 6R/K.

2. A control system is operated with a parabolic input as shown below If Ka is static error constant of the system, then its dynamic error constant K2 is
a) 0.01
b) 0.02
c) 0.03
d) 0.04

Answer: b [Reason:] Ka = 100/(s+2) K2 = 1/50 = 0.02.

3. Find the velocity error constant of the system given below : a) 0
b) 2
c) 4
d) ∞

Answer: c [Reason:] 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.

4. 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)
a) 1
b) 2
c) 3
d) 4

Answer: b [Reason:] Routh-Hurwitz criterion is used to calculate the stability of the system by checking the sign changes of the first row and from Routh-Hurwitz criterion maximum value of K = 6 ess = A/Kv for type-1 system and A = 6then for Kv = K/2, ess = 2.

5. 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
a) 1 and 20
b) 0 and 20
c) 0 and 1/20
d) 1 and 1/20

Answer: a [Reason:] 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.

6. 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?
a) 0.10
b) 0.15
c) 0.20
d) 0.25

Answer: d [Reason:] 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.

7. The error constants described are the ability to reduce the steady state errors.
a) True
b) False

Answer: a [Reason:] As the type of the system becomes higher more steady state errors are eliminated.

8. Systems of type higher than 2 are not employed in practice.
a) True
b) False

Answer: a [Reason:] These are more difficult to stabilize and dynamic errors are much larger.

9. Steady state refers to
a) Error at the steady state
b) Error at the transient state
c) Error at both state
d) Precision

Answer: a [Reason:] Steady state errors are the change in the output at the steady state with respect to the change in the input.

10. The disadvantages of the error constants are:
a) They do not give the information of the steady state error when the inputs are other than the three basic types
b) Error constant fail to indicate the exact manner in which the error function change with time.
c) 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
d) They give information of the steady state error

Answer: c [Reason:] 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.

## Set 3

1. A variable reluctance stepper motor is constructed of ______________ material with salient poles.
a) Paramagnetic
b) Ferromagnetic
c) Diamagnetic
d) Non-magnetic

Answer: b [Reason:] A variable reluctance stepper motor is the motor that has motion in steps with respect to increase in time and constructed of ferromagnetic material with salient poles.

2. In a three-stack 12/8-pole VR motor, the rotor pole pitch is
a) 15º
b) 30º
c) 45º
d) 60º

Answer: c [Reason:] Pole pitch is defined as the number of armature slots to the pole pitch and here this has been converted into degrees.

3. A stepper motor having a resolution of 300 steps/rev and running at 2400 rpm has a pulse rate of- pps.
a) 4000
b) 8000
c) 6000
d) 10,000

Answer: c [Reason:] Pulse per second is mathematically given as PPS = (Rpm/60)*(number of steps per minute).

4. If a hybrid stepper motor has a rotor pitch of 36º and a step angle of 9º, the number of its phases must be
a) 4
b) 2
c) 3
d) 6

Answer: a [Reason:] Step angle is defined as =(Ns-Nr)/(Ns+Nr)*360.

5. The rotor of a stepper motor has no
a) Windings
b) Commutator
c) Brushes
d) All of the mentioned

Answer: d [Reason:] The rotor is the rotatory part of the motor of a stepper motor and has no windings, commutator and brushes.

6. A stepping motor is a ____________ device.
a) Mechanical
b) Electrical
c) Analogue
d) Incremental

Answer: d [Reason:] A stepping motor is a motor in which the motion in the form of steps and is a incremental device i which as the time increases the steps are increased.

7. The rotational speed of a given stepper motor is determined solely by the
b) Step pulse frequency
c) Polarity of stator current
d) Magnitude of stator current.

Answer: b [Reason:] The stator part of a motor is the stationary part of the motor and rotational speed of a given stepper motor is given by the step pulse frequency.

8. Which of the following phase switching sequence represents half-step operation of a VR stepper motor ?
a) A, B, C,A……..
b) A, C, B,A…….
c) AB, BC, CA, AB……..
d) A, AB, B, BC……..

Answer: d [Reason:] In the half step operation of a Variable reluctance motor physical step resolution is multiplied by 2 and control signals appear to be digital rather than analog.

9. A stepper motor may be considered as a ____________ converter.
a) Dc to dc
b) Ac to ac
c) Dc to ac
d) Digital-to-analogue

Answer: d [Reason:] A stepper motor is a motor in which the motion is in steps and it is an increemental device and may be considered as a digital to analog converter.

10. What is the step angle of a permanent-magnet stepper motor having 8 stator poles and 4 rotor poles?
a) 60º
b) 45º
c) 30º
d) 15º

Answer: b [Reason:] Step angle is defined as =(Ns-Nr)/(Ns+Nr)*360 where Ns is the number of stator poles and Nr is the number of rotor poles.

## Set 4

1. The system with the open loop transfer function 1/s(1+s) is:
a) Type 2 and order 1
b) Type 1 and order 1
c) Type 0 and order 0
d) Type 1 and order 2

Answer: d [Reason:] Type is defined as the number of poles at origin and order is defined as the total number of poles and this is calculated with the help of the transfer function from the above transfer function the type is 1 and order is 2.

2. The identical first order system have been cascaded non-interactively. The unit step response of the systems will be:
a) Overdamped
b) Underdamped
c) Undamped
d) Critically damped

Answer: d [Reason:] Since both the systems that is the first order systems are cascaded non-interactively, the overall unit step response will be critically damped.

3. A third order system is approximated to an equivalent second order system. The rise time of this approximated lower order system will be:
a) Same as the original system for any input
b) Smaller than the original system for any input
c) Larger than the original system for any input
d) Larger or smaller depending on the input

Answer: b [Reason:] As order of the system increases the system approaches more towards the ideal characteristics and if the third order system is approximated to an equivalent second order system then the rise time of this will be smaller than the original system for any input.

4. A system has a single pole at origin. Its impulse response will be:
a) Constant
b) Ramp
c) Decaying exponential
d) Oscillatory

Answer: a [Reason:] For a single pole at origin the system is of type 1 and impulse response of the system with single pole at the origin will be constant.

5. When the period of the observation is large, the type of the error will be:
a) Transient error
b) Steady state error
c) Half-power error
d) Position error constant

Answer: b [Reason:] The error will be the steady state error if the period of observation is large as the time if large then the final value theorem can be directly applied.

6. When the unit step response of a unity feedback control system having forward path transfer function G (s) =80/s(s+18)?
a) Overdamped
b) Critically damped
c) Under damped
d) Un Damped oscillatory

Answer: a [Reason:] The open loop transfer function is first converted into the closed loop as unity feedback is used and then value of damping factor is calculated.

7. With negative feedback in a closed loop control system, the system sensitivity to parameter variation:
a) Increases
b) Decreases
c) Becomes zero
d) Becomes infinite

Answer: b [Reason:] Sensitivity is defined as the change in the output with respect to the change in the input and due to negative feedback reduces by a factor of 1/ (1+GH).

8. An underdamped second order system with negative damping will have the roots :
a) On the negative real axis as roots
b) On the left hand side of complex plane as complex roots
c) On the right hand side of complex plane as complex conjugates
d) On the positive real axis as real roots

Answer: c [Reason:] An underdamped second order system is the system which has damping factor less than unity and with negative damping will have the roots on the right hand side of complex plane as complex conjugates.

9. Given a unity feedback system with G (s) =K/ s (s+4). What is the value of K for a damping ratio of 0.5?
a) 1
b) 16
c) 4
d) 2

Answer: b [Reason:] Comparing the equation with the standard characteristic equation gives the value of damping factor, natural frequency and value of gain K.

10. How can the steady state error can be reduced?
a) By decreasing the type of the system
b) By increasing system gain
c) By decreasing the static error constant
d) By increasing the input

Answer: d [Reason:] Steady state error is the error as it is the difference between the final output and the desired output and by increasing the input the steady state error reduces as it depends upon both the states and input.

## Set 5

1. First order system is defined as :
a) Number of poles at origin
b) Order of the differential equation
c) Total number of poles of equation
d) Total number of poles and order of equation

Answer: d [Reason:] First order system is defined by total number of poles and also which is same as the order of differential equation.

2. A unit step is applied at t=0 to a first order system without time delay. The response has the value of 1.264 units at t=10 mins, and 2 units at steady state. The transfer function of the system is_____________
a) 3/(1+600s)
b) 2/(1+500s)
c) 5/(1+220s)
d) 2/(1+600s)

Answer: d [Reason:] a(t)= k[1-e^-t/T] K=2 0.632= 1-e^-10/T T=600 sec G(s)=2/(1+600s).

3. The transfer function of the system is G(s) =100/(s+1) (s+100). For a unit step input to the system the approximate settling time for 2% criterion is:
a) 100 sec
b) 4 sec
c) 1 sec
d) 0.01 sec

Answer: b [Reason:] G(s) =100/(s+1) (s+100) Taking the dominant pole consideration, S=-100 pole is not taken. G(s)= 100/s+1 Now it is first order system, ts=4T=4 sec.

4. If a first order system and its time response to a unit step are as shown below, the gain K is :  a) 0.25
b) 0.8
c) 1
d) 4

Answer: d [Reason:] Y(s)/R(s)=K/1+sT+K By, use of partial fraction, K/T/s+(K+1/T) Taking inverse Laplace transform on both the sides Y(t)=K/K+1[1-e^(K+1/T)t] K=4

5. The unit impulse response of a system having transfer function K/(s+a) is shown below. The value of a is : a) t1
b) t2
c) 1/t1
d) 1/t2

Answer: d [Reason:] G(s) = K/s+a C(s) =K/(s+a) Since R(s) =1 C(t) =Ke^-at T=1/a C(t) =0.37K T= t2=1/a.

6. A system with transfer function 1/Ts+1, subjected to a step input takes to seconds to reach 50% of step height. The value of t is :
a) 6.9s
b) 10s
c) 14.4s
d) 20s

Answer: c [Reason:] The response of a first order system is: A(t)=a[1-e^-t/T] ½= 1-e^-10/t T= 14.43 sec.

7.A first order system and its response to a unit step input are shown in figure below. The system parameters are____________
a) a=5 and k=12
b) a=10 and k=5
c) a=5 and k=10
d) a=8 and k=9

Answer: c [Reason:] time constant=0.2 sec. 1/a=0.2 a=5 final value=lims→0 sC(s) =K/a K/a=2 K=10.

8. Assertion (A): It is observed that step function is first derivative of a ramp function and impulse function is first derivative of a step function.
Reason (R): From the derived time response expression it is concluded that the output time response also follows the same sequence as that of input functions.
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true but R is not correct explanation of A
c) Both A is True but R is false
d) Both A is False but R is true

Answer: b [Reason:] If response due to one standard signal is known then response due to other signals can also be derived.

9. Laplace transform of unit impulse signal is :
a) A/s
b) A
c) 1
d) 1/s