Control system MCQ Questions and Answers with explanation -2021

Ques 41. The output of a feedback control system must be a function of

  1. Reference and output
  2. Reference and input
  3. Input and feedback signal
  4. Output and feedback signal
Answer.1. Reference and output

Explanation:

Closed-Loop Control

  • A closed-loop control system utilizes a measure of the actual output to compare the actual output with the desired output response.
  • The measure of the output is called the feedback signal. The elements of a general closed-loop feedback control system are shown in Figure.

Closed loop system

  • A closed-loop control system compares the measurement of the output with the desired output (reference or command input).
  • The difference between the two quantities (the error signal) is then used to drive the output closer to the reference input through the controller and actuator.
  • Often the difference between the output of the process under control and the reference input is amplified and used to control the process so that the difference is continually reduced.

 

Advantages of closed-loop Systems

  1. Closed-loop systems have the following advantages:
  2. Faster response to an input signal.
  3. Effective disturbance rejection
  4. Better tracking of references
  5. Low sensitivity to system parameter errors (e.g., errors in plant or controller gains)
  6. Low sensitivity to changes in calibration errors (recalibration is unnecessary)
  7. More accurate control of plants under disturbances and internal variations.
  8. Effective and flexible control tuning by varying the control gain is Used to stabilize systems that are inherently unstable in the open-loop form.

Disadvantages of Closed-Loop Systems

The following are some of the disadvantages of closed-loop systems:

  1. Require the use of sensors which increase the system costs Involve more components which leads to more costs and complexity.
  2. The power costs (due to high gains) are high.
  3. More complex design, harder to build.
  4. Sometimes obtaining the output measurement is either hard or not economically feasible.
  5. Initial tuning is more difficult, especially if the bandwidth is narrow.
  6. There is always a steady-state error (with proportional controllers).
  7. The system tends to become unstable as the gain is increased beyond certain limits.
  8. Closed-loop control methods are unnecessary when system inputs and the plant model are known with total certainty, and there are no external disturbances
  9. Closed-loop systems are not always controllable.

Essentially, the advantages of closed-loop systems are the disadvantages of open-loop systems, and the disadvantages of closed-loop systems are the advantages of open-loop systems. The introduction of feedback enables the engineer to control the desired output and improve accuracy, but it requires attention to the issue of stability of response. Feedback is used for the purpose of reducing the error between the reference input and the system output. However, the significance of the effects of feedback in control systems is more complex. The reduction of system error is merely one of the many important effects that feedback may have upon a system.

 

Ques 42. The transfer function of a system is used to calculate which of the following?

  1. The order of the system
  2. The time constant
  3. The output for any given input
  4. The steady state gain
Answer.3. The output for any given input

Explanation:

The transfer function of a linear, time-invariant system is defined as the ratio of the Laplace transform of the output to the Laplace transform of the input with all initial conditions being zero.

The transfer function is a frequency-domain concept that is used to calculate the output of the linear system to any input.

$TF = \frac{{C\left( s \right)}}{{R\left( s \right)}}$

or

Transfer function = (Transform of o/p signal)/(Transform of i/p signal)

So that transfer function of the system is used to calculate the output for a given input.

  • The transfer function H(s) is defined as the ratio C(s)/R(s), where C(s) is the Laplace transform of the output signal c(t), and R(s) is the Laplace transform of the input signal r(t), and it defines the properties of the dynamic system.
  • The poles of the system, i.e., the roots of the denominator in H(s)  give the frequencies where the system has free vibrations (if it is a transfer function of a mechanical system).
  • The transfer function can (in the theoretical analysis) be used to find the solutions (responses) for any input (force) by using the inverse Laplace transform.

For unit impulse input i.e. r(t) = δ(t)

⇒ R(s) = δ(s) = 1

Now transfer function = C(s)

Therefore, the transfer function is also known as the impulse response of the system.

Transfer function = L[IR]

IR = L-1 [TF]

 

Ques 43. In an amplifier with the negative feedback, bandwidth is _________ and voltage gain is _________.

  1. Bandwidth is decreased by a factor (1+Aβ) and voltage gain decreases
  2. Bandwidth is decreased by factor β and voltage gain remains same
  3. Bandwidth is increased by the factor (1+Aβ) and voltage gain is reduced
  4. Bandwidth remains the same and voltage gain increases
Answer.3. Bandwidth is increased by the factor (1+Aβ) and voltage gain is reduced

Explanation:

Negative (degenerative) feedback

When the output energy (voltage or current) is applied such that it decreases the input, i.e. the feedback is out of phase of the input signal, such feedback is called negative, inverse or degenerative feedback. This feedback reduces gain but has a number of other merits like stability in gain, less distortion, etc. This feedback is used in amplifiers and reduction in gain can be compensated by increasing the number of amplification stages.

negative feedback

Properties of Negative feedback

Gain Desensitivity

With the introduction of negative feedback, the gain of an amplifier is reduced:

$A = \frac{{{A_0}}}{{1 + {A_0}\beta }}$

The Bandwidth at the same time increases by the same amount, resulting in the gain-bandwidth product which is constant.

Increase in Bandwidth

For amplifier having negative feedback, the upper cut-off frequency is increased by a factor of (1 + Aβ) . that is the amount of feedback.

Noise Reduction

Negative feedback when used in amplifiers increases the signal to the noise ratio or causes a reduction in noise.

Non-linear Distortion Reduction

Application of negative feedback to amplifiers causes the amplifier characteristics to be less non-linear or more linearized and the distortion gets reduced by a factor of  $\frac{1}{{1 + A\beta }}$

Increase in Input Impedance

Negative feedback increases the input impedance of amplifiers which is generally preferred in multistage amplifiers to reduce the loading effect.

Decrease in Output Impedance

Negative feedback decreases the output impedance of an amplifier which is generally preferred as low output impedance helps in higher power transfer to load.

 

Ques 44. The transient response, with feedback system

  1. Rises slowly
  2. Rises quickly
  3. Decays slowly
  4. Decays quickly
Answer.4. Decays Quickly

Explanation:

Closed-Loop Control

  • A closed-loop control system utilizes a measure of the actual output to compare the actual output with the desired output response.
  • The measure of the output is called the feedback signal. The elements of a general closed-loop feedback control system are shown in Figure.

Closed loop system

  • A closed-loop control system compares the measurement of the output with the desired output (reference or command input).
  • The difference between the two quantities (the error signal) is then used to drive the output closer to the reference input through the controller and actuator.
  • Often the difference between the output of the process under control and the reference input is amplified and used to control the process so that the difference is continually reduced.

Transient Response

After applying an input to the control system, the output takes a certain time to reach a steady-state. So, the output will be in a transient state till it goes to a steady state. Therefore, the response of the control system during the transient state is known as the transient response.

Transient response

Settling time:

It is time required for the response to use and reach to the tolerance band.

For 2% tolerance band:

${t_s} = 4\tau = \frac{4}{{\xi \:{\omega _n}}}$

For 5% tolerance band:

${t_s} = 4\tau = \frac{3}{{\xi \:{\omega _n}}}$

Thus due to negative feedback transient responses decay very fast. 

Advantages of closed-loop Systems

Closed-loop systems have the following advantages:

  1. Faster response to an input signal.
  2. Effective disturbance rejection
  3. Better tracking of references
  4. Low sensitivity to system parameter errors (e.g., errors in plant or controller gains)
  5. Low sensitivity to changes in calibration errors (recalibration is unnecessary)
  6. More accurate control of plants under disturbances and internal variations.
  7. Effective and flexible control tuning by varying the control gain is used to stabilize systems that are inherently unstable in the open-loop form.
  8. These systems have high bandwidth i.e., high operating frequency zone than the open-loop system.
  9. The transient response in the closed-loop system decays more quickly than in the open-loop system.

The feedback reduces the time constant, lesser the time constant faster the response. Hence the transient response decay more quickly.

 

Ques 45. The first element of each of the following row of a Routh-Hurwitz stability test showed the signs as follows

Row I II III IV V
Sign + +

Consider the following statements:

  1. The system has three roots in the right-half of s-plane
  2. The system has three roots in the left -half of s-plane
  3. The system is stable
  4. The system is unstable

Which of the above statements about the system are correct?

  1. A  and C
  2. A and D
  3. B and C
  4. B and D
Answer.2. A and D

Explanation:

Stable System: If all the roots of the characteristic equation lie on the left half of the ‘s’ plane then the system is said to be a stable system.

Unstable System: If some of the roots of the system lie on the right half of the ‘s’ plane then the system is said to be an unstable system.

Routh- Hurwitz Criterion:

Routh Hurwitz criterion states that any system can be stable if and only if all the roots of the first column have the same sign and if it does not has the same sign or there is a sign change then the number of sign changes in the first column is equal to the number of roots of the characteristic equation in the right half of the s-plane i.e. equals to the number of roots with positive real parts.

Application:

Number of sign changes in the given table = 3

Number of poles on right half of s-plane = 3

Number of poles on left half of s-plane = 5 – 3 = 2

As there are three poles on the right half of the s-lane, the system is unstable.

Number of sign change = Number of Poles Lies In RHS of S plane = 2

Hence there are two negative roots, therefore, the system is unstable

 

Ques 46. Consider the following statements regarding the advantages of closed-loop negative feedback control systems over open-loop systems:

  1. The overall reliability of the closed-loop systems is more than that of the open-loop systems.
  2. The transient response in the closed-loop system decays more quickly than in the open-loop system.
  3. In an open-loop system, closing the loop increases the overall gain of the system.
  4. In the closed-loop system, the effect of variation of component parameters on its performance is reduced.

Which of the following statements are correct?

  1. A and C
  2. A and B
  3. B and D
  4. A and D
Answer.3. A and D

Explanation:

Open Loop Control System:- When the control action of a system is independent of the output, the system is said to be an open-loop control system.

Closed-loop Control System:- If the control action is somehow dependent on the output, the system is called a Closed-loop or Feedback control system.

Difference Between Open-loop and Closed-Loop Control System

Open Loop Control System Closed-Loop Control System
In this system, the controlled action is free from the output In this system, the output mainly depends on the controlled act of the system.
This control system is also called a Non feedback control system This type of control system is also called a feedback control system
The components of this system include a controlled process and controller. The components of this kind of system include an amplifier, controlled process, controller, and feedback
The construction of this system is simple The construction of this system is complex
The accuracy of this system mainly depends on the calibration These are accurate due to feedback
The stability of these systems are stable The stability of these systems are less stable
Sensitivity high Less sensitive
The optimization in this system is not possible The optimization in this system is  possible
The transient response decay slowly The transient response decay fast
The calibration of this system is difficult The calibration of this system is easy
The disturbance of this system will be affected The disturbance of this system will  not be affected
These systems are non-linear These systems are linear
The best examples of this control system are automatic washing machine, traffic light, TV remote, immersion rod,  etc. Examples of this kind of control system are AC, control systems for temperature, pressure and speed, toaster, and refrigerator

 

Ques 47. Which of the following transfer functions is/are minimum phase transfer functions(s)?

  1. $\frac{1}{{(S – 1)}}$
  2. $\frac{{(S – 1)}}{{(S + 3)(S + 4)}}$
  3. $\frac{{(S + 2)}}{{(S + 3)(S – 4)}}$

Select the correct answer using the codes given below:

  1. A and C
  2. A only
  3. B and C
  4. None of these
Answer.D. None of these

Explanation:

The transfer functions having no poles or zeros in the left half of the s-plane are minimum-phase transfer functions;. It is the stable transfer function.

The transfer functions having poles and/or zeros in the right-half of the S-plane are non-minimum phase transfer functions.

It can easily be established that a proper rational transfer function is a minimum phase transfer function if all of its zeros lie in the left half s-plane.

Calculation:- 

For minimum phase transfer functions, the number of poles and zero must be on left side of s-plane and In the given question the transfer functions have at least one pole or zero in R.H.S -plane

 

Ques 48. Which of the following statements is correct for a system with the gain margin close to unity or a phase margin close to zero?

  1. The system is relatively stable
  2. The system is highly stable
  3. The system is highly oscillatory
  4. None of the above
Answer.3. The system is high oscillatory

Explanation:

The stability of a feedback system can be determined from the Bode plot of the Frequency response of the open-loop system. This stability is usually based upon the Nyquist criterion for stability.

Gain margin (GM): The gain margin of the system defines by how much the system gain can be increased so that the system moves on the edge of stability.

A large gain margin or a large phase margin indicates a very stable feedback system but usually a very sluggish response.

If the open-loop frequency response shows gain greater than or equal to unity when the phase shift is -180° then the closed-loop system is not stable or highly oscillatory.

If the phase shift of the open-loop response is -180° or more negative than -180° when the gain is unity then the closed-loop system is unstable.

Gain margin and phase margin are frequently used for frequency response specifications by designers. Usually a Gain margin of about 6 dB or a Phase margin of 30 – 35° results in a reasonably good degree of relative stability.

 

Ques 49. Due to which of the following reasons excessive bandwidth in control systems should be avoided?

  1. It leads to slow speed of response
  2. It leads to low relative stability
  3. Noise is proportional to bandwidth
  4. None of the above
Answer.3. Noise is proportional to bandwidth

Explanation:

The noise power is evenly distributed over all RF and microwave frequencies are called white noise. The power
spectral density of white noise is constant over frequency, which implies that noise power is proportional to bandwidth. So if the measurement bandwidth is doubled, the detected noise power will double.

Thermal white noise power is defined by

N=kTB

where N is the noise power

k = 1.380 x 10-23 J/K is Boltzmann’s constant

T is the temperature

B is the noise bandwidth

  • Excessive Bandwidth causes increase in the noise with the same proportion as the bandwidth.
  • Hence, noise is not good for any signal therefore the excessive bandwidth is not desirable.

 

Ques 50. In a stable control system backlash can cause which of the following?

  1. Underdamping
  2. Overdamping
  3. Poor stability at reduced values of open loop gain
  4. Low-level oscillations
Answer.4. Low-level oscillations

Explanation:

Backlash or gear play arises in the mechanical system involving gear trains.

  1. If an input sinusoid is used, then the output of a backlash will be periodic, but the output will remain constant whilst the input changes from being increasing to decreasing.
  2. The main difficulty is the phase shift which is introduced by the backlash that can cause stability problems in feedback control loops.
  3. An interesting feature of backlash is its multi-valued behaviour, since for each input there are two possible values for the output of the nonlinearity.
  4. The output that is appropriate depends upon the previous motion of the input signal, and hence the output depends upon the history of the input signal movements.
  5. If backlash occurs the analysis will be non-linear because the backlash can cause undesired low-level oscillation in the feedback control system.

Note:- The gear meshes are manufactured for minimal backlash, but the resulting increase in the friction between gear teeth thus reduces the efficiency of the system. Backlash can be useful sometimes as it increases the damping.

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