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# Multiple choice question for engineering

## Set 1

1. State models presented employed:
a) Physical variables
b) Phase variables
c) Canonical variables
d) All of the mentioned

Answer: d [Reason:] State models are used in the state model analysis and is employed in all the variables as physical, phase and canonical phase analysis.

2. State model is generally not suitable for measuring:
a) Investigation of system properties
b) Evaluation of time response
c) Real variables
d) Both a and b

Answer: d [Reason:] State models are used in the state model analysis and is employed in all the variables as physical, phase and canonical phase analysis and is generally not suitable for investigation of system properties and evaluation of time response.

3. ______________ are the techniques for converting general state models into canonical one.
a) Observable
b) Controllable
c) Diagoanlization
d) Cannonical

Answer: c [Reason:] Diagonalization is the form in which the roots are in the daigonal of the matrix and are the techniques for converting general state models into canonical one.

4. The values of the characteristic equation is given by:
a) Eigen values
b) State matrix
c) Eigen vector
d) None of the mentioned

Answer: a [Reason:] Eigen values are the values that are obtained by solving the characteristic equation these are the roots of the characteristic equation.

5. The matrix constructed by placing the Eigen vectors together is diagonalizing matrix.
a) True
b) False

Answer: a [Reason:] Eigen values are the values that are obtained by solving the characteristic equation these are the roots of the characteristic equation and the matrix constructed by placing the Eigen vectors together is diagonalizing matrix.

6. The diagonalizing matrix is also known as:
a) Eigen matrix
b) Modal matrix
c) Constant matrix
d) State matrix

Answer: b [Reason:] The modal matrix is the matrix formed formed by placing the eigen values that is the roots of the characteristic equation and this is also known as the diagonalizing matrix.

7. In an open loop control system
a) Output is independent of control input
b) Output is dependent on control input
c) Only system parameters have effect on the control output
d) None of the mentioned

Answer: a [Reason:] In an open loop control system the system in which there is no feedback present and in which the output is independent of control input.

8. Which of the following is exhibited by Root locus diagrams?
a) The poles of the transfer function for a set of parameter values
b) The bandwidth of the system
c) The response of a system to a step input
d) The frequency response of a system

Answer: a [Reason:] Root locus diagram is the diagram that is constructed in which the locus is traced with the gain with increasing frequency has the poles of the transfer function for a set of parameter values.

9. The first order control system, which is well designed, has a
a) Small bandwidth
b) Negative time constant
c) Large negative transfer function pole
d) None of the mentioned

Answer: c [Reason:] The first order control system is the control system which has atleast the one pole at the origin or at max one pole, which is well designed has a large negative transfer function pole.

10. A.C. servomotor is basically a
a) Universal motor
b) Single phase induction motor
c) Two phase induction motor
d) Three phase induction motor

Answer: c [Reason:] A.C. servomotor is a rotary actuator or linear actuator that allows for precise control of angular or linear position, velocity and acceleration is basically a two phase induction motor.

## Set 2

1. Difference equation model results in:
a) Sampled-data systems
b) Numerical analysis of continuous time systems
c) Continuous time feedback systems
d) Both a and b

Answer: d [Reason:] Equation in discrete time systems can be difference equation which are similar to the differentiation in the continuous time systems and difference equation results in sampled data system and numerical analysis of continuous system.

2. Difference equation is used in :
a) Discrete time analysis
b) Continuous time analysis
c) Digital analysis
d) None of the mentioned

Answer: a [Reason:] Difference equation are similar to the differentiation in the continuous systems and they have same function in discrete time systems and is used in discrete time analysis.

3. Difference equation in discrete systems is similar to the _____________ in continuous systems.
a) Difference equation
b) Differential equation
d) None of the mentioned

Answer: b [Reason:] Difference equation are the equations used in discrete time systems and difference equations are similar to the differential equation in continuous systems.

4. Difference equation solution yields at the sampling instants only:
a) True
b) False

Answer: a [Reason:] Difference equation are the equations used in discrete time systems and difference equations are similar to the differential equation in continuous systems solution yields at the sampling instants only.

5. Difference equation technique for higher order systems is used in:
a) Laplace transform
b) Fourier transform
c) Z-transform
d) None of the mentioned

Answer: c [Reason:] For higher order systems Z- transform which is transforming discrete time domain into z domain and is technique is convenient for analysis and design of linear sampled data systems.

6. Assertion (A): An LTI discrete system represented by the difference equation. y (n+2)-5y(n+1)+6y(n) =x(n) is unstable.
Reason (R): A system is unstable if the roots of the characteristic equation lie outside the unit circle.
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 the correct explanation of A
c) A is true but R is false
d) A is false but R is false

Answer: a [Reason:] Difference equation is y (n+2)-5 y (n+1) + 6 y (n) =x (n). Taking z-transform, H (z) =1/ (z-2) (z-3). The characteristic equation has roots z =2, 3. Since, the characteristic equation has roots outside the unit circle, hence the system is unstable.

7. The poles of a digital filter with linear phase response can lie
a) Only at z =0
b) Only on the unit circle
c) Only inside the unit circle but not at z =0
d) On the left side of Real (z) =0 line

Answer: b [Reason:] For stable systems the poles in z plane must lie inside or on the unit circle and Minimum number of delay elements = (Maximum power of z)-(minimum power of z).

8. If X(z) =(z+z-3)/(z+z-1), then x(n) series has:
a) Alternate 0s
b) Alternate 1s
c) Alternate 2s
d) Alternate -1s

Answer: a [Reason:] Using the long division method divide from denominator. So, x(n) series has alternate zeros n =1,3,5……

9. Assertion (A): The stability of the system is assured if the ROC includes the unit circle in z-plane.
Reason (R): For a causal stable system all the poles should be outside the unit circle in the z-plane.
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true bit 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 [Reason:] A causal system LTI system is stable if and only if all of poles of H(z) lie inside the unit circle.

10. Assertion (A): For the rational transfer function H(z) to be causal, stable and causally invertible, both the zeroes and the poles should lie within the unit circle in the z-plane.
Reason (R): For a rational system, ROC is bounded by poles
a) Both A and R are true and R is the correct explanation of A
b) Both A and R are true bit 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: b [Reason:] For the rational transfer function H (z) to be causal, stable and causally invertible, both the zeroes and the poles should lie within the unit circle in the z-plane. For a rational system, ROC is bounded by poles.

## Set 3

1. If the Liapunov’s function cannot be found then the system is:
a) Stable
b) Unstable
c) Conditionally stable
d) Marginally stable

Answer: b [Reason:] It is very difficult to find the Liapunov’s function and several techniques are devised for the same and if the Liapunov’s function is not available then the system is unstable.

2. Liapunov’s stability analysis is for the :
a) LTI system
b) Time variant system
c) Non-linear system
d) Linear system

Answer: c [Reason:] Liapunov’s stability criterion is for the non-linear system.

3. The system is unstable for:
a) W (x)>0; x not equal to zero
b) W (0) =0
c) W (x) has continuous partial derivative with respect to all components of x
d) All of the mentioned

Answer: d [Reason:] It requires much ingenuity of devise a suitable W function to devise a Liapunov function V. In stability analysis of nonlinear systems, it is valuable to establish conditions for which the system is unstable.

4. Liapunov’s stability for non-linear system is same as the Routh Hurwitz criteria for the linear system.
a) True
b) False

Answer: a [Reason:] Liapunov stability is similar in function as the Routh Hurwitz criteria and Silvester’s theorem can be used to prove it.

5. Conditions of ___________ are necessary and sufficient condition for the asymptotic stability of the system.
a) Linear system
b) Krasovskii’s method
c) positive definiteness

Answer: c [Reason:] For the system to be asymptotic stable which is desired for the Liapunov stability positive definiteness of the system must be fulfilled.

6. It is difficult to form Liapunov’s function for:
a) Linear system
b) Non-linear
c) Time variant systems
d) Time –invariant systems

Answer: b [Reason:] For non-linear system it is difficult to form the Liapunov’s function And we use various method to do this.

7. If the V is positive definite, for the system to be asymptotically stable, Q should be negative definite.
a) Krasovskii’s method
c) Constant method

Answer: a [Reason:] If the V is positive definite, for the system to be asymptotically stable, Q should be negative definite. For Krasovskii’s method and in addition V should tend to infinity and the system is asymptotically stable in-the large.

8. The method which provides considerable flexibility in finding the Liapunov’s function is:
a) Krasovskii’s method
c) Constant method

Answer: b [Reason:] Variable gradient method provides considerable flexibility in finding the Liapunov’s function as the quadratic form approach is too restrictive.

9. Liapunov stability analysis is different from the classical theories approach of stability.
a) True
b) False

Answer: a [Reason:] Liapunov’s stability theorem is applied for the non-linear systems but other stability theorems are applied for the linear systems.

10. For non-linear systems the equation for damping factor as in linear system is called__________
a) Krasovskii’s equation
b) Vander Pol’s equation
c) Constant method

Answer: b [Reason:] For non-linear systems the equation for damping factor as in linear system is called Vander pol’s equation which depends upon x and damping factor has large positive values for this.

## Set 4

1. Which of the following are the not characteristics of the closed loop systems?
a) It does not compensate for disturbance
b) It reduces the sensitivity of plant-parameter variations
c) It does not involve output measurements
d) It does not has the ability to control the system transient response

Answer: d [Reason:] Feedback refers to the comparison of the final output to the desired output at respective input so as to get accurate and error free result and in the system improves the transient response of the system.

2. Which one of the following effect in the system is not caused by negative feedback?
a) Reduction in gain
b) Increased in bandwidth
c) Increase in distortion
d) Reduction in output impedance

Answer: c [Reason:] Distortion refers to the error in the open loop system and it has many oscillations in the output and is reduced in case of negative feedback.

3. Which of the statement is correct with regard to the bandwidth of the control loop system:
a) In systems where the low frequency magnitude in 0 dB on the bode diagram, the bandwidth is measured at the -3 dB frequency
b) The bandwidth is the measurement of the accuracy of the closed loop system
c) The stability is proportional to the bandwidth
d) The system with larger bandwidth provides slower step response and lower fidelity ramp response

Answer: a [Reason:] Bandwidth is the frequency measured at the gain of 3dB and for the good control system the value of the bandwidth must be large but the large value of the bandwidth increses the noise in the system.

4. Which of the statements are the advantages of closed loop systems over the open loop system:
a) The overall reliability of the open loop system is more than the closed loop system is more than closed loop system.
b) The transient response in closed loop system decays more quickly than in open loop system.
c) In open loop system closing the loop increases the gain of the system
d) In open loop system the effect of parameter variation is reduced

Answer: b [Reason:] Speed of response refers to the time taken to give the final output and it depends upon the rise and settling time of the transient response and speed of response of closed loop system is more than that of open loop system.

5. In control system excessive bandwidth is not employed because
a) Noise is proportional to bandwidth
b) It leads to low relative stability
c) It leads to slower time response
d) Noise is proportional to the square of the bandwidth

Answer: a [Reason:] In closed loop system the bandwidth of the system is more as compared to the open loop system and this is so required as higher the bandwidth means lower the selectivity and hence higher the noise.

6. Feedback control system is basically
a) High pass filter
b) Low pass filter
c) Band pass filter
d) Band stop filter

Answer: b [Reason:] Low pass filter is mainly as integral controller and it is used as the controller in the system so as to increase the accuracy by reducing or proper eliminating the steady state error of the control system.

7. Which of the following will not decrease as a result of introduction of negative feedback?
a) Instability
b) Bandwidth
c) Overall gain
d) Distortion

Answer: b [Reason:] Bandwidth always increases due to negative feedback as the speed of response is directly proportional to the bandwidth.

8. As compared to the closed loop system, an open loop system is
a) More stable but less accurate
b) Less stable as well as less accurate
c) More stable as well as more accurate
d) Less stable but more accurate

Answer: a [Reason:] Open loop system always follows the input but closed loop system always reduces the error irrespective of the input applied.

9. Insertion of negative feedback in control system affects:
a) The transient response to vanish uniformly
b) The transient response to decay very fast
c) No change in transient response
d) The transient response decays at slow rate

Answer: b [Reason:] Feedback can be positive or negative but practically positive feedback is not used as it causes oscillations in the system with more gain and hence negative feedback is use which causes speed of response to increase.

10. Open loop system is ___________ stable than closed loop system
a) More
b) Less
c) Inclined
d) Exponential

Answer: a [Reason:] Open loop system always follows the input but closed loop system always reduces the error irrespective of the input applied.

11. For the gain feedback system, does not affect the system output if KG is :

a) Small
b) Negative
c) One
d) Very large

Answer: d [Reason:] T(s)=KG/(1+KGH) If KG>>1: then C(s)=R(s)/H.

12. Determine the sensitivity of the overall transfer function for the system shown in the figure below, at w=1 rad/sec with respect to the feedback path transfer function.

a) 1.11
b) -1.11
c) 2.22
d) -2.22

13. Primary purpose of using Feedback is :
a) To reduce the sensitivity of the system to parameter variations.
b) To increase the bandwidth of the system
c) To reduce the noise and distortion of the system
d) To increase stability of the system

Answer: a [Reason:] The major requirement of the feedback is to reduce of the system with parameter variations that may vary with age, with changing environment.

## Set 5

1. The mechanism of control of body temperature is non feedback system?
a) True
b) False

Answer: b [Reason:] It is feedback system as the temperature of our body is regulated periodically and being warm blooded we regulate our body temperature w.r.t. to the climate.

2. Benefits of feedback:
a) Performance of system is greater.
b) Need for system much larger path gain and system instability.
c) Controlled variable accurately follows the desired value
d) Affected by parameter variations

Answer: d [Reason:] Closed loop system is the system with the feedback and this can be positive or negative feedback and having feedback have less dependence on parameter variation.

3. Feedback always increases the gain?
a) True
b) False

Answer: b [Reason:] It cannot always increase gain it can also reduce the gain as gain of Open loop control system is more as compared to it.

4. Effect of feedback on sensitivity is minimum in:
a) Open loop control system
b) Closed loop control system
c) None of the mentioned
d) Both of the mentioned

Answer: b [Reason:] Sensitivity is defined as the change in output with respect to change in parameter or input and for a good control system the sensitivity must be less and in closed loop control system it gets reduced by the factor of 1/(1+GH).

5. Feedback control systems are:
a) Insensitive to both forward and feedback path parameter changes
b) Less sensitive to feedback path parameter changes than to forward path parameter changes
c) Less sensitive to forward path parameter changes that to feedback path parameter changes
d) Equally sensitive to forward feedback path parameter changes

Answer: c [Reason:] Feedback control system can be positive and negative but positive feedback systems less widely used as the positive feedback systems are more sensitive to parameter variations but negative feedback are less sensitive to change in G than change in H.

6. Consider the following statements with respect to the feedback of the control systems:
1. Feedback can improve stability or be harmful to stability if it is not properly applied.
2. Feedback can always improve stability
3. In many situations the feedback can reduce the effect of noise and disturbance on system performance.
4. In general the sensitivity of the system gain of a feedback system of a parameter variation depends on where the parameter is located.
a) 1,2 and 3 only
b) 1,3 and 4 only
c) 1,2 and 4 only
d) 1,2,3 and 4 only

Answer: b [Reason:] Negative feedback increases stability but not positive positive feedback reduces the stability and for this reason negative feedback systems are used .

7. The closed system has higher ________ than open loop control system, this implies increased speed of response.
a) Gain
b) Bandwidth
c) Frequency
d) Speed

Answer: b [Reason:] As transient response of the system is improved by the use of feedback and it causes the settling time to reduce and closed loop system has higher bandwidth than open loop systems and this implies increase in speed of response.

8. Feedback can always reduce the effects of noise and disturbance on system performance?
a) True
b) False

Answer: a [Reason:] Feedback has many advantages as it can reduces the effects of noise and disturbance on system performance by increasing speed of response.

9. Multiple signals as input can be used in which systems:
a) Feedback systems
b) Non feedback systems
c) Feedforward systems
d) None of the mentioned