**Most Latest **Stability in Frequency Domain **MCQs ( Control Systems ) MCQs – ****Control Systems ****MCQs**

**Latest Control Systems MCQs**

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#### Control Systems MCQs – Stability in Frequency Domain MCQs ( Control Systems ) MCQs

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# Mathematical Preliminaries

**1. Which of the following devices is used for conversion of co-ordinates?**

a) Microsyn

b) Selsyn**c) Synchro-resolver**

d) Synchro-transformer**Answer: c****Explanation: Synchro-Resolver is rotary transformer used for measuring degree of rotation and used for the conversion of the co-ordinates.****2. The effect of error damping is to**

a) Provide larger settling lime

b) Delay the response**c) Reduce steady state error**

d) All of the mentioned**Answer: c****Explanation: Error damping is to reduce steady state error as it is used to enhance the steady state response of the system and this can be done by increasing the damping of the system.****3. ______________technique gives quick transient and stability response****a) Root locus**

b) Bode

c) Nyquist

d) Nichols**Answer: a****Explanation: Root locus is the right technique for the quick transient and stability response and gives the final response and quickly.****4. A phase lag lead network introduces in the output**

a) Lag at all frequencies

b) Lag at high frequencies and lead at low frequencies**c) Lag at low frequencies and lead at high frequencies**

d) None of the above mentioned**Answer: c****Explanation: A phase lag lead network is the combination of the lead and lag network and also it lags at low frequencies and lead at high frequencies.****5. Which of the following is the non-linearity caused by servomotor?**

a) Static friction

b) Backlash**c) Saturation**

d) None of the mentioned**Answer: c****Explanation: Linearity in the servo-motor is due to the saturation present and which is the important consideration for any type of the practical device.****6. ____________can be extended to systems which are time-varying?**

a) Bode-Nyquist stability methods

b) Transfer functions

c) Root locus design**d) State model representatives****Answer: d****Explanation: State model representation is the best advantage for the systems over transfer function approach as it can be applied for the non-linear systems.****7. Laplace transform is used for the systems with:**

a) Initial conditions infinite**b) Initial conditions zero**

c) Initial conditions finite

d) Initial conditions equal to the initial input**Answer: b****Explanation: By definition of the transfer function by Laplace transform the initial conditions of the systems are considered to be zero.****8. Which of the following is an electromechanical device?**

a) Induction relay

b) Thermocouple**c) LVDT**

d) All of the mentioned**Answer: c****Explanation: LVDT is the electromechanical device which converts the displacement of the core to the electrical energy by the action of the transformer.****9. A differentiator is usually not a part of a control system because it**

a) Reduces damping

b) Reduces the gain margin**c) Increases input noise**

d) Increases error**Answer: c****Explanation: A differentiator is generally not the part of the control system as it increases the input noise due to reduced gain and increased bandwidth.****10. If the gain of the critical damped system is increased it will behave as****a) Oscillatory**

b) Critically damped

c) Overdamped

d) Underdamped**Answer: a****Explanation: On increasing the gain damping will automatically get reduced and hence the oscillations in the system increases.**

**Nyquist Stability Criterion**

**1. Which principle specifies the relationship between enclosure of poles & zeros by s-plane contour and the encirclement of origin by q(s) plane contour?****a) Argument**

b) Agreement

c) Assessment

d) Assortment**Answer: a****Explanation: Argument principle specifies the relationship between enclosure of poles & zeros by s-plane contour and the encirclement of origin by q(s) plane contour.****2. If a Nyquist plot of G (jω) H (jω) for a closed loop system passes through (-2, j0) point in GH plane, what would be the value of gain margin of the system in dB?**

a) 0 dB

b) 2.0201 dB

c) 4 dB**d) 6.0205 dB****Answer: d****Explanation: Gain Margin is calculated by taking inverse of the gain where the Nyquist plot cuts the real axis.****3. For Nyquist contour, the size of radius is _______**

a) 25

b) 0

c) 1**d) ∞****Answer: d****Explanation: For Nyquist contour, the size of radius is ∞.****4. Consider a feedback system with gain margin of about 30. At what point does Nyquist plot crosses negative real axis?**

a) -3**b) -0.3**

c) -30

d) -0.03**Answer: b****Explanation: Gain Margin is always inverse of the point which cuts the Nyquist on the real axis.****5. According to Nyquist stability criterion, where should be the position of all zeros of q(s) corresponding to s-plane?****a) On left half**

b) At the center

c) On right half

d) Random**Answer: a****Explanation: According to Nyquist stability criterion zeroes must lie on the left half on the s plane.****6. If the system is represented by G(s) H(s) = k (s+7) / s (s +3) (s + 2), what would be its magnitude at ω = ∞?****a) 0**

b) ∞

c) 7/10

d) 21**Answer: a****Explanation: On calculating the magnitude of the system and putting the value of frequency one gets the magnitude as 0.****7. Consider the system represented by the equation given below. What would be the total phase value at ω = 0?****200/[s3 (s + 3) (s + 6) (s + 10)].**

a) -90°

b) -180°**c) -270°**

d) -360°**Answer: c****Explanation: The phase can be calculated by the basic formula for calculating phase angle.****8. Due to an addition of pole at origin, the polar plot gets shifted by ___ at ω = 0 ?**

a) -45°

b) -60°**c) -90°**

d) -180°**Answer: c****Explanation: Addition of pole causes instability to the system.****9. In polar plots, if a pole is added at the origin, what would be the value of the magnitude at Ω = 0?**

a) Zero**b) Infinity**

c) Unity

d) Unpredictable**Answer: b****Explanation: Addition of pole causes instability to the system.****10. In polar plots, what does each and every point represent w.r.t magnitude and angle?**

a) Scalar

b) Vector**c) Phasor**

d) Differentiator**Answer: c****Explanation: Each and every point on the polar plot is the phasor where value of frequency varies.**

**Time Domain Analysis**

**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****Explanation: 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****Explanation: 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****Explanation: 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****Explanation: 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****Explanation: 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****Explanation: 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****Explanation: 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****Explanation: 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****Explanation: 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****Explanation: 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.**

**Assessment of Relative Stability Using Nyquist Criterion**

**1. The phase margin (in degrees) of a system having the loop transfer function G(s) H(s)=2√3/s(s+1) is:**

a) 45°

b) -30°

c) 60°**d) 30°****Answer: d****Explanation: Phase margin is calculated at gain cross over frequency where magnitude of the transfer function is 1.****2. The system with the open loop transfer function G(s) H(s) =1/s(s ^{^}2+s+1) has the gain margin of :**

a) -6 dB

**b) 0 dB**

c) 3.5 dB

d) 6 dB

**Answer: b**

**Explanation: Gain margin is calculated at phase cross over frequency where the phase is 180°.**

**3. The phase angle of the system, G(s) =s+5/s**

^{2}+4s+9, varies between :**a) 0° and 90°**

b) 0° and -90°

c) 0° and -180°

d) -90° and -180°

**Answer: a**

**Explanation: As it is the type 0 system so the phase angle can be 0° and 90°.**

**4. The polar plot of the transfer function G(s) = 10(s+1)/s+10 will be in the :**

a) First quadrant

b) Second quadrant

c) Third quadrant

**d) Fourth quadrant**

**Answer: d**

**Explanation: Polar plot of the given transfer function lies in the fourth quadrant.**

**5. As the polar plot moves toward the point (-1, 0) then the system becomes :**

a) Stable

b) Marginally stable

c) Conditionally stable

**d) Unstable**

**Answer: d**

**Explanation: As the polar plot moves toward the point (-1, 0) then the system becomes unstable.**

**6. Polar plots moving toward the imaginary axis makes the system:**

a) Stable

b) Marginally stable

c) Conditionally stable

**d) Unstable**

**Answer: d**

**Explanation: Polar plots moving toward the imaginary axis makes the system unstable.**

**7. The concepts used to measure relative stability are:**

a) Phase margin

b) Gain margin

**c) Phase and Gain margin**

d) Stable

**Answer: c**

**Explanation: The concepts used to measure relative stability are phase margin and gain margin.**

**8. Phase and gain margin are applicable to open and closed loop systems both.**

a) True

**b) False**

**Answer: b**

**Explanation: Phase and gain margin are applicable only to open loop systems.**

**9. Gain margin is:**

a) It is a factor by which the system gain can be increased to drive it to the verge of instability

b) It is calculated at gain cross over frequency

c) It is calculated at phase cross over frequency

**d) Both a and c**

**Answer: d**

**Explanation: Gain margin is a factor by which the system gain can be increased to drive it to the verge of instability and is calculated at phase cross over frequency.**

**10. Phase margin is:**

a) It is amount of additional phase lag at the gain cross over frequency required to bring the system to the verge of instability

b) It is always positive for stable feedback systems

c) It is calculated at gain cross over frequency

**d) All of the mentioned**

**Answer: d**

**Explanation: Phase margin is the measure of relative stability which is always positive for stable systems.**

**Closed-Loop Frequency Response**

**1. Closed loop frequency response is very useful as :**

a) It approximately predicts the time response of the systems

b) Time response are converted into time domain specifications

c) After design time domain specification is converted into frequency domain**d) All of the mentioned****Answer: d****Explanation: Closed loop frequency response is very useful as it enables to use second order correlations between frequency and transient response.****2. Maximum peak overshoot in time domain corresponds to :****a) Resonance peak**

b) Resonant frequency

c) Bandwidth

d) Cut-off rate**Answer: a****Explanation: Resonance peak in frequency domain correspond to maximum peak overshoot in time domain.****3. Frequency of oscillation in time domain correspond to :**

a) Resonance peak**b) Resonant frequency**

c) Bandwidth

d) Cut-off rate**Answer: b****Explanation: Resonant frequency in frequency domain correspond to frequency of oscillation in time domain.****4. Bandwidth is :**

a) Range of frequencies for which the system gain is more than-3dB

b) This is considered good range for transmission of signals

c) For better communication bandwidth of signal must be less**d) All of the mentioned****Answer: d****Explanation: Bandwidth of a signal must be less but channel must be more foe better transmission or communication.****5. Cut-off rate is the ability of the system to distinguish the signal from _____________**

a) Bandwidth**b) Noise**

c) Resonance peak

d) Magnitude**Answer: b****Explanation: Cut-off rate is the ability of the system to distinguish the signal from noise.****6. The important figures of merit to the system in frequency domain are :**

a) Maximum value of resonant peak

b) Value of resonance frequency**c) Maximum value of resonant peak and Value of resonance frequency**

d) Minimum value of resonance frequency**Answer: c****Explanation: The important figures of merit to the system in frequency domain are maximum value of resonance peak and frequency at which it occurs.****7. In q(s) plane Nyquist plot is symmetrical about the :**

a) Imaginary axis**b) Real axis**

c) Origin

d) None of the mentioned**Answer: b****Explanation: By definition, In q(s) plane Nyquist plot is symmetrical about the real axis.****8. A polar plot intersects the unit circle at a point making -45° to the negative real axis then the phase margin of the system is :**

a) -45°**b) 45°**

c) 180°-45°

d) 180°+45°**Answer: b****Explanation: As the angle is with the negative real axis hence the Phase margin will be 45°.****9. The parameter which is constant along the constant N circle :**

a) Frequency**b) Phase angle**

c) Magnitude

d) Open loop gain**Answer: b****Explanation: Phase angle remains constant in constant N-circle.****10. In second order system gain margin is :**

a) Zero value

b) Finite value**c) Infinite value**

d) None of the mentioned**Answer: c****Explanation: Gain margin is defined generally for systems with order greater than 3.**