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Controllers & Compensators MCQs for Electrical Engineering (EE) Exam
It covers all Important Questions with answers on Controllers & Compensators for the Electrical Engineering (EE) exam. The questions are based on important topics. Details about the questions:- Topic: Controllers & Compensators
- Type of Questions: MCQs with solutions
- Number of Questions: 50
- You can attempt them on EduRev to score high in Electrical Engineering (EE) exam.
Direction: The following item consists of two statements, one labelled as ‘Statement (I)’ and the other as ‘Statement (II)’. Examine these two statements carefully and select the answers to these items using the code given below:Statement I: For type-II or higher systems, lead compensator may be used.
Statement II: Lead compensator increases the margin of stability.- a)Both Statement I and Statement II are individually true and Statement II is the correct explanation of Statement I
- b)Both Statement I and Statement II are individually true but Statement II is not the correct explanation of Statement I
- c)Statement I is true but Statement II is false
- d)Statement I is false but Statement II is true
Correct answer is option 'A'. Can you explain this answer?
Direction: The following item consists of two statements, one labelled as ‘Statement (I)’ and the other as ‘Statement (II)’. Examine these two statements carefully and select the answers to these items using the code given below:
Statement I: For type-II or higher systems, lead compensator may be used.
Statement II: Lead compensator increases the margin of stability.
Statement II: Lead compensator increases the margin of stability.
a)
Both Statement I and Statement II are individually true and Statement II is the correct explanation of Statement I
b)
Both Statement I and Statement II are individually true but Statement II is not the correct explanation of Statement I
c)
Statement I is true but Statement II is false
d)
Statement I is false but Statement II is true
 | Pioneer Academy answered |
In general, there are two situations in which compensation is required.
- In the first case, the system is absolutely unstable, and the compensation is required to stabilize it as well as to achieve a specified performance.
- In the second case, the system is stable, but the compensation is required to obtain the desired performance.
The systems which are of type-2 or higher are usually absolutely unstable. For type-2 or higher systems, only the lead compensator is required because only the lead compensator improves the margin of stability.
Both Statement I and Statement II are individually true and Statement II is the correct explanation of Statement I
Note: In type-1 and type-0 systems, stable operation is always possible if the gain is sufficiently reduced. In such cases, any of the three compensators, lead, lag, lag-lead may be used to obtain the desired performance.
Both Statement I and Statement II are individually true and Statement II is the correct explanation of Statement I
Note: In type-1 and type-0 systems, stable operation is always possible if the gain is sufficiently reduced. In such cases, any of the three compensators, lead, lag, lag-lead may be used to obtain the desired performance.
In the phase lead compensation network, the phase of ______ leads the phase of ______.- a)input voltage, output voltage
- b)input voltage, input voltage
- c)output voltage, input voltage
- d)output voltage, output voltage
Correct answer is option 'C'. Can you explain this answer?
In the phase lead compensation network, the phase of ______ leads the phase of ______.
a)
input voltage, output voltage
b)
input voltage, input voltage
c)
output voltage, input voltage
d)
output voltage, output voltage
 | Machine Experts answered |
Lead compensator:
Transfer function:
Transfer function:
If it is in the form of 
then a < 1
then a < 1If it is in the form of 
then a > b
In the frequency domain,
Phase angle, ∠G (jω) = tan−1ωαT − tan−1ωT
then a > bIn the frequency domain,
Phase angle, ∠G (jω) = tan−1ωαT − tan−1ωT
ϕ = tan-1 ωaT – tan-1 ωT
As a > 1 always (from the definition), ϕ is positive
Hence, it is clear that the phase of output voltage leads the phase of the input voltage.
As a > 1 always (from the definition), ϕ is positive
Hence, it is clear that the phase of output voltage leads the phase of the input voltage.
Which of the following is NOT the disadvantage of lag compensator in a control system?- a)In lag compensator, the attenuation offered by it shifts the gain crossover frequency to a lower point, thereby decreasing the bandwidth.
- b)The lag network offers a reduction in bandwidth, and this gives shorter rise time and settling time and so the transient response.
- c)A lag compensator somewhat acts as a proportional plus integral controller, hence adversely affects the stability of the system.
- d)Though the system response is longer due to decreased bandwidth, the response is quite slow
Correct answer is option 'B'. Can you explain this answer?
Which of the following is NOT the disadvantage of lag compensator in a control system?
a)
In lag compensator, the attenuation offered by it shifts the gain crossover frequency to a lower point, thereby decreasing the bandwidth.
b)
The lag network offers a reduction in bandwidth, and this gives shorter rise time and settling time and so the transient response.
c)
A lag compensator somewhat acts as a proportional plus integral controller, hence adversely affects the stability of the system.
d)
Though the system response is longer due to decreased bandwidth, the response is quite slow
 | Zoya Sharma answered |
Advantages of Lag Compensator:
- A phase lag network offers high gain at low frequency. Thus, it performs the function of a low pass filter.
- The introduction of this network increases the steady-state performance of the system.
- The lag network offers a reduction in bandwidth and this provides longer rise time and settling time and so the transient response.
- The angular contribution of the pole is more than that of the compensator zero because the pole dominates the zero in the lag compensator.
Advantages of Lead Compensator:
- It improves the damping of the overall system.
- The enhanced damping of the system supports less overshoot along with less rise time and settling time. Therefore, the transient response gets improved.
- The addition of a lead network improves the phase margin.
- A system with a lead network provides a quick response as it increases bandwidth thereby providing a faster response.
- Lead networks do not disturb the steady-state error of the system.
- It maximizes the velocity constant of the system.
The compensator required to improve the steady state response of a system is- a)Lag
- b)Lead
- c)Lag-lead
- d)Zero
Correct answer is option 'A'. Can you explain this answer?
The compensator required to improve the steady state response of a system is
a)
Lag
b)
Lead
c)
Lag-lead
d)
Zero
 | Cstoppers Instructors answered |
Lag compensator:
Transfer function:
Transfer function:
If it is in the form of 
then a < 1
then a < 1If it is in the form of 
then a > b
Maximum phase lag frequency:
ωm = 1√Ta
Maximum phase lag::
then a > bMaximum phase lag frequency:
ωm = 1√Ta
Maximum phase lag::
ϕm is negative
Pole zero plot:
The pole is nearer to the origin.
Filter: It is a low pass filter (LPF)
Effect on the system:
Filter: It is a low pass filter (LPF)
Effect on the system:
- Rise time and settling time increases and Bandwidth decreases
- The transient response becomes slower
- The steady-state response is improved
- Stability decreases
What is the full form of PID?- a)Proportional Integral Derivative
- b)Proportional Integral Device
- c)Programmable Integral Device
- d)Programmable Integral Derivative
Correct answer is option 'A'. Can you explain this answer?
What is the full form of PID?
a)
Proportional Integral Derivative
b)
Proportional Integral Device
c)
Programmable Integral Device
d)
Programmable Integral Derivative
 | Pooja Patel answered |
Proportion + Integral + Derivative (PID):
The PID controller produces on output, which is the combination of outputs of proportional, integral, and derivative controllers.
This is defined in terms of differential equations as:
Applying Laplace transform, we get:
Transfer function will be:
Integral control:
It is the control mode where the controller Output is proportional to the integral of the error with respect to time.
Applying Laplace transform, we get:
Transfer function will be:
Integral control:
It is the control mode where the controller Output is proportional to the integral of the error with respect to time.
Integral controller output = k × integral of error with time, i.e.
Proportional + Derivate:
Proportional + Derivate:
The additive combination of proportional & Derivative control is known as P-D control.
Overall transfer function for a PD controller is given by:
It is equivalent to a High-pass filter.
It is equivalent to a High-pass filter.
Given a badly underdamped control system, the type of cascade compensator to be used to improve its damping is- a)phase-lag
- b)phase-lead-lag
- c)phase-lead
- d)notch filter
Correct answer is option 'C'. Can you explain this answer?
Given a badly underdamped control system, the type of cascade compensator to be used to improve its damping is
a)
phase-lag
b)
phase-lead-lag
c)
phase-lead
d)
notch filter
 | Aniket Shah answered |
Improving Damping in a Badly Underdamped Control System
Underdamped control systems often exhibit oscillatory behavior, which can lead to instability and poor performance. To improve the damping of such a system, a cascade compensator can be used. Among the given options, the appropriate type of cascade compensator to be used is a phase-lead compensator.
The phase-lead compensator is designed to increase the phase margin of the system, which helps improve stability and damping. It achieves this by introducing a phase lead at the desired frequency range. The phase lead compensator consists of a high-pass filter and a gain element.
Below are the reasons why the phase-lead compensator is the correct choice in this scenario:
1. Phase Margin Improvement:
The phase-lead compensator increases the phase margin of the system. The phase margin is the amount by which the phase of the system lags behind -180 degrees at the gain crossover frequency. By increasing the phase margin, the system becomes more stable and better damped.
2. Introduction of Phase Lead:
The phase-lead compensator introduces a phase lead at the desired frequency range. This additional phase lead helps to counteract the phase lag caused by the poorly damped system. By adding a phase lead, the system's phase response is shifted in a way that improves damping and stability.
3. Frequency Response Shaping:
The phase-lead compensator also shapes the frequency response of the system. It allows for boosting the gain at certain frequencies while maintaining stability. This control over the frequency response helps to improve the overall performance of the system by reducing oscillations and overshoot.
4. Stability Enhancement:
By increasing the phase margin and introducing a phase lead, the phase-lead compensator enhances the stability of the system. It helps to suppress oscillations and prevent the system from becoming unstable. This is crucial in underdamped systems where the lack of damping can lead to erratic behavior and instability.
In summary, to improve the damping of a badly underdamped control system, a phase-lead compensator is the most suitable type of cascade compensator. It increases the phase margin, introduces a phase lead, shapes the frequency response, and enhances stability.
Underdamped control systems often exhibit oscillatory behavior, which can lead to instability and poor performance. To improve the damping of such a system, a cascade compensator can be used. Among the given options, the appropriate type of cascade compensator to be used is a phase-lead compensator.
The phase-lead compensator is designed to increase the phase margin of the system, which helps improve stability and damping. It achieves this by introducing a phase lead at the desired frequency range. The phase lead compensator consists of a high-pass filter and a gain element.
Below are the reasons why the phase-lead compensator is the correct choice in this scenario:
1. Phase Margin Improvement:
The phase-lead compensator increases the phase margin of the system. The phase margin is the amount by which the phase of the system lags behind -180 degrees at the gain crossover frequency. By increasing the phase margin, the system becomes more stable and better damped.
2. Introduction of Phase Lead:
The phase-lead compensator introduces a phase lead at the desired frequency range. This additional phase lead helps to counteract the phase lag caused by the poorly damped system. By adding a phase lead, the system's phase response is shifted in a way that improves damping and stability.
3. Frequency Response Shaping:
The phase-lead compensator also shapes the frequency response of the system. It allows for boosting the gain at certain frequencies while maintaining stability. This control over the frequency response helps to improve the overall performance of the system by reducing oscillations and overshoot.
4. Stability Enhancement:
By increasing the phase margin and introducing a phase lead, the phase-lead compensator enhances the stability of the system. It helps to suppress oscillations and prevent the system from becoming unstable. This is crucial in underdamped systems where the lack of damping can lead to erratic behavior and instability.
In summary, to improve the damping of a badly underdamped control system, a phase-lead compensator is the most suitable type of cascade compensator. It increases the phase margin, introduces a phase lead, shapes the frequency response, and enhances stability.
Match the following :-
- a)1 - b, 2 - a, 3 - d, 4 - c
- b)1 - a, 2 - b, 3 - c, 4 - d
- c)1 - c, 2 - d, 3 - b, 4 - a
- d)1 - a, 2 - d, 3 - c, 4 - b
Correct answer is option 'A'. Can you explain this answer?
Match the following :-
a)
1 - b, 2 - a, 3 - d, 4 - c
b)
1 - a, 2 - b, 3 - c, 4 - d
c)
1 - c, 2 - d, 3 - b, 4 - a
d)
1 - a, 2 - d, 3 - c, 4 - b
| | Machine Experts answered |
Sink node:
- A local sink is a node of a directed graph with no exiting edges, also called a terminal.
- It is the output node in the signal flow graph. It is a node, which has only incoming branches.
Lag Compensator:
- Phase lag network offers high gain at low frequency.
- Thus, it performs the function of a low pass filter.
- The introduction of this network increases the steady-state performance of the system.
Damping Ratio:
- The damping ratio gives the level of damping in the control system related to critical damping.
- The damping ratio is defined as the ratio of actual damping to the critical damping of the system.
- It is the ratio of the damping coefficient of a differential equation of a system to the damping coefficient of critical damping.
- ζ = actual damping / critical damping
Cut-off rate: It is the slope of the log-magnitude curve near the cut-off region of the Bode-plot.
Consider the following statements regarding a control system:(a) Addition of pole to left half of s-plane reduce the relative stability(b) Addition of zero to left half of s-plane increase the damping factor(c) Integral controller reduces the steady state error(d) Derivate controller cannot be used in isolationWhich of the above statements are true?- a)(a) & (c) only
- b)(b) & (d) only
- c)(a), (b), (d) only
- d)All (a), (b), (c), (d)
Correct answer is option 'D'. Can you explain this answer?
Consider the following statements regarding a control system:
(a) Addition of pole to left half of s-plane reduce the relative stability
(b) Addition of zero to left half of s-plane increase the damping factor
(c) Integral controller reduces the steady state error
(d) Derivate controller cannot be used in isolation
Which of the above statements are true?
a)
(a) & (c) only
b)
(b) & (d) only
c)
(a), (b), (d) only
d)
All (a), (b), (c), (d)
| | Cstoppers Instructors answered |
(a) Addition of pole reduces stability
Consider system =
Adding Pole [say at origin]
(b) Addition of zero increase ξ
Consider system with Transfer function
Now add one zero to left half say at -2
(c) Integral controller adds one pole at origin
Now add one zero to left half say at -2
(c) Integral controller adds one pole at origin
As type of system increase steady state error reduce
(d) Derivative controllers are not used Alone because with sudden changes in the system the derivative controller will compensate the output fast therefore in long term effects the isolated controller will produce huge steady state errors.
Phase lead compensation- a)increases bandwidth and increases steady-state error
- b)decreases bandwidth and decreases steady-state error
- c)will not affect bandwidth but decreases steady-state error
- d)increases bandwidth but will not affect steady-state error
Correct answer is option 'D'. Can you explain this answer?
Phase lead compensation
a)
increases bandwidth and increases steady-state error
b)
decreases bandwidth and decreases steady-state error
c)
will not affect bandwidth but decreases steady-state error
d)
increases bandwidth but will not affect steady-state error
 | Aman Datta answered |
Phase lead compensation is a technique used in control systems to improve the performance of the system. It involves adding a lead compensator to the open-loop transfer function of the system. The lead compensator introduces a phase lead at a specific frequency, which helps to increase the overall phase margin of the system.
Effect on Bandwidth:
Adding a phase lead compensator increases the bandwidth of the system. The bandwidth of a system is the range of frequencies over which the system can respond effectively. By introducing a phase lead at a specific frequency, the phase lead compensator helps to extend the range of frequencies over which the system can operate accurately. This increase in bandwidth allows the system to respond more quickly to changes in the input signal.
Effect on Steady-State Error:
Steady-state error is a measure of the difference between the desired output and the actual output of a system when the input signal is constant. Adding a phase lead compensator does not have a direct effect on the steady-state error of the system. The steady-state error is mainly determined by other factors such as the type of system (e.g., type 0, type 1, etc.), the presence of disturbances, and the gain of the system.
Conclusion:
Based on the given options, the correct answer is option 'D' - adding a phase lead compensator increases the bandwidth but will not affect the steady-state error. This is because the phase lead compensator primarily improves the system's stability and response time by increasing the phase margin and bandwidth. However, it does not directly influence the steady-state error, which is determined by other factors.
Effect on Bandwidth:
Adding a phase lead compensator increases the bandwidth of the system. The bandwidth of a system is the range of frequencies over which the system can respond effectively. By introducing a phase lead at a specific frequency, the phase lead compensator helps to extend the range of frequencies over which the system can operate accurately. This increase in bandwidth allows the system to respond more quickly to changes in the input signal.
Effect on Steady-State Error:
Steady-state error is a measure of the difference between the desired output and the actual output of a system when the input signal is constant. Adding a phase lead compensator does not have a direct effect on the steady-state error of the system. The steady-state error is mainly determined by other factors such as the type of system (e.g., type 0, type 1, etc.), the presence of disturbances, and the gain of the system.
Conclusion:
Based on the given options, the correct answer is option 'D' - adding a phase lead compensator increases the bandwidth but will not affect the steady-state error. This is because the phase lead compensator primarily improves the system's stability and response time by increasing the phase margin and bandwidth. However, it does not directly influence the steady-state error, which is determined by other factors.
Assertion (A): Introduction of phase lag network in forward path increases the phase shift.
Reason (R): A phase lag network has pole nearer to the imaginary axis as compared to zero.- a)Both A and R are true and R is a correct explanation of A.
- b)Both A and R are true but R is not a correct explanation of A.
- c)A is true but R is false.
- d)A is false but R is true.
Correct answer is option 'D'. Can you explain this answer?
Assertion (A): Introduction of phase lag network in forward path increases the phase shift.
Reason (R): A phase lag network has pole nearer to the imaginary axis as compared to zero.
Reason (R): A phase lag network has pole nearer to the imaginary axis as compared to zero.
a)
Both A and R are true and R is a correct explanation of A.
b)
Both A and R are true but R is not a correct explanation of A.
c)
A is true but R is false.
d)
A is false but R is true.
 | Mira Mukherjee answered |
Understanding Phase Lag Networks
In control systems, the behavior of phase lag networks is crucial for understanding their effects on system stability and response.
Assertion (A)
- The assertion claims that introducing a phase lag network in the forward path increases the phase shift.
- This statement is false because a phase lag network actually decreases the phase shift in a system.
- Phase lag networks introduce a delay in the response, leading to a reduction in the overall phase.
Reason (R)
- The reason states that a phase lag network has a pole nearer to the imaginary axis compared to a zero.
- This statement is true as phase lag networks are characterized by having a specific configuration of poles and zeros that influences the phase response.
- The pole being closer to the imaginary axis signifies that it contributes less to the phase shift than a zero would, validating the nature of phase lag networks.
Conclusion
- Since Assertion (A) is false and Reason (R) is true, the correct option is D: "A is false but R is true."
- Understanding these concepts helps in designing systems with desired stability and performance characteristics.
Key Takeaway
- In control systems, it is essential to recognize the implications of phase lag networks on phase shifts to ensure effective system design and analysis.
In control systems, the behavior of phase lag networks is crucial for understanding their effects on system stability and response.
Assertion (A)
- The assertion claims that introducing a phase lag network in the forward path increases the phase shift.
- This statement is false because a phase lag network actually decreases the phase shift in a system.
- Phase lag networks introduce a delay in the response, leading to a reduction in the overall phase.
Reason (R)
- The reason states that a phase lag network has a pole nearer to the imaginary axis compared to a zero.
- This statement is true as phase lag networks are characterized by having a specific configuration of poles and zeros that influences the phase response.
- The pole being closer to the imaginary axis signifies that it contributes less to the phase shift than a zero would, validating the nature of phase lag networks.
Conclusion
- Since Assertion (A) is false and Reason (R) is true, the correct option is D: "A is false but R is true."
- Understanding these concepts helps in designing systems with desired stability and performance characteristics.
Key Takeaway
- In control systems, it is essential to recognize the implications of phase lag networks on phase shifts to ensure effective system design and analysis.
A phase lead compensation network- a)speeds up the dynamic response
- b)decreases the system bandwidth
- c)reduces the steady state error
- d)is applied when error constants are specified
Correct answer is option 'D'. Can you explain this answer?
A phase lead compensation network
a)
speeds up the dynamic response
b)
decreases the system bandwidth
c)
reduces the steady state error
d)
is applied when error constants are specified
 | Sarthak Sharma answered |
Phase Lead Compensation Network: Explanation of Answer D
Introduction:
Phase lead compensation is a type of frequency domain compensation technique used in control systems to stabilize the closed-loop system, increase its phase margin, and improve its transient response. A phase lead compensation network is a circuit that introduces a phase lead in the transfer function of the plant to improve its stability and performance.
Answer Explanation:
The correct answer is option D, which states that the phase lead compensation network is applied when error constants are specified.
Explanation:
Error constants are the steady-state errors of a control system, which indicate the difference between the desired output and the actual output of the system. The error constants are used to measure the accuracy and precision of the control system. The phase lead compensation network is used to reduce the steady-state error of the system, which means that the output of the system will be closer to the desired output. Therefore, the phase lead compensation network is applied when error constants are specified to achieve better accuracy and precision of the system.
Other Options:
Option A: Speeding up the dynamic response is the purpose of phase lag compensation, which introduces a phase lag in the transfer function of the plant to reduce the overshoot and the settling time of the system.
Option B: Decreasing the system bandwidth is the purpose of low-pass filters, which attenuate the high-frequency components of the input signal to reduce the noise and the distortion in the output signal.
Option C: Reducing the steady-state error is the purpose of integral compensation, which introduces an integrator in the transfer function of the plant to eliminate the steady-state error of the system.
Conclusion:
In conclusion, the phase lead compensation network is applied when error constants are specified to reduce the steady-state error of the control system. The other options are not correct because they describe different compensation techniques with different purposes.
Introduction:
Phase lead compensation is a type of frequency domain compensation technique used in control systems to stabilize the closed-loop system, increase its phase margin, and improve its transient response. A phase lead compensation network is a circuit that introduces a phase lead in the transfer function of the plant to improve its stability and performance.
Answer Explanation:
The correct answer is option D, which states that the phase lead compensation network is applied when error constants are specified.
Explanation:
Error constants are the steady-state errors of a control system, which indicate the difference between the desired output and the actual output of the system. The error constants are used to measure the accuracy and precision of the control system. The phase lead compensation network is used to reduce the steady-state error of the system, which means that the output of the system will be closer to the desired output. Therefore, the phase lead compensation network is applied when error constants are specified to achieve better accuracy and precision of the system.
Other Options:
Option A: Speeding up the dynamic response is the purpose of phase lag compensation, which introduces a phase lag in the transfer function of the plant to reduce the overshoot and the settling time of the system.
Option B: Decreasing the system bandwidth is the purpose of low-pass filters, which attenuate the high-frequency components of the input signal to reduce the noise and the distortion in the output signal.
Option C: Reducing the steady-state error is the purpose of integral compensation, which introduces an integrator in the transfer function of the plant to eliminate the steady-state error of the system.
Conclusion:
In conclusion, the phase lead compensation network is applied when error constants are specified to reduce the steady-state error of the control system. The other options are not correct because they describe different compensation techniques with different purposes.
The action of a PD controller is to- a)increase the rise time and steady state error of the system.
- b)reduce the rise time and increase the steady error of the system.
- c)maintain a constant value of rise time and reduce the steady state error of the system.
- d)reduce the rise time and maintain a constant value of steady state error of the system.
Correct answer is option 'D'. Can you explain this answer?
The action of a PD controller is to
a)
increase the rise time and steady state error of the system.
b)
reduce the rise time and increase the steady error of the system.
c)
maintain a constant value of rise time and reduce the steady state error of the system.
d)
reduce the rise time and maintain a constant value of steady state error of the system.
 | Aniket Choudhury answered |
Due to PD controller, a zero is added to the forward path which results in a lead compensator. Therefore, steady state error remais the same whiie rise time of the system is reduced (i.e. stability is increased).
The pole-zero plot shown below represents a
- a)Lag-lead compensating network
- b)PD controller
- c)PID controller
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
The pole-zero plot shown below represents a
a)
Lag-lead compensating network
b)
PD controller
c)
PID controller
d)
None of the above
| | Zoya Sharma answered |
Concept:
The speed of response and, the steady-state error can be simultaneously improved if both phase-lag and phase-lead compensation networks are used. However, instead of using two separate lag and lead networks, a single network combining both can be used.
The speed of response and, the steady-state error can be simultaneously improved if both phase-lag and phase-lead compensation networks are used. However, instead of using two separate lag and lead networks, a single network combining both can be used.
Lag-lead compensator:
In the lag-lead compensator network, the lag compensator is nearer to the origin.
In the lag-lead compensator network, the lag compensator is nearer to the origin.
Lead-lag compensator:
In the lead-lag compensator network, the lead compensator is nearer to the origin.
A first order dynamic linear system with a proportional controller exhibits an offset to a unit step input. The offset can be reduced by- a)increasing the proportional gain
- b)adding derivative mode
- c)adding integral mode
- d)decreasing the porportional gain
Correct answer is option 'C'. Can you explain this answer?
A first order dynamic linear system with a proportional controller exhibits an offset to a unit step input. The offset can be reduced by
a)
increasing the proportional gain
b)
adding derivative mode
c)
adding integral mode
d)
decreasing the porportional gain
| | Kritika Gupta answered |
One of the disadvantage of a proportional controller is that it exhibits a permanent residual error at its operating point known as offset and
given by
The offset can be
reduced by adding integral mode.
given by
The offset can bereduced by adding integral mode.
Which of the following is not correct with respect to a phase-lead compensation network?- a)It increases system bandwidth
- b)It increases gain at higher frequencies
- c)It is used when fast transient response is required
- d)It is used when decrease rapidly near crossover frequency
Correct answer is option 'D'. Can you explain this answer?
Which of the following is not correct with respect to a phase-lead compensation network?
a)
It increases system bandwidth
b)
It increases gain at higher frequencies
c)
It is used when fast transient response is required
d)
It is used when decrease rapidly near crossover frequency
| | Shivam Das answered |
Understanding Phase-Lead Compensation
Phase-lead compensation is a technique used in control systems to improve stability and performance. Let's analyze why option 'D' is incorrect.
Key Characteristics of Phase-Lead Compensation:
- Increases System Bandwidth:
- Phase-lead compensation increases the bandwidth of the system. This allows the system to respond more quickly to changes in input.
- Increases Gain at Higher Frequencies:
- It provides an increase in gain at higher frequencies, which enhances the system's ability to track fast changes in input signals.
- Fast Transient Response:
- This compensation technique is particularly beneficial when fast transient responses are desired. It reduces the settling time and improves the overall responsiveness of the system.
Why Option 'D' is Incorrect:
- Decrease Rapidly Near Crossover Frequency:
- This statement is misleading. In a phase-lead compensation network, the phase margin is increased, and the gain does not decrease rapidly near the crossover frequency. Instead, the network is designed to maintain or even enhance the gain within the crossover region, leading to a more stable and responsive system.
Conclusion:
In summary, phase-lead compensation is characterized by its ability to enhance system performance. It does not lead to a rapid decrease in gain near the crossover frequency, making option 'D' the incorrect statement.
Phase-lead compensation is a technique used in control systems to improve stability and performance. Let's analyze why option 'D' is incorrect.
Key Characteristics of Phase-Lead Compensation:
- Increases System Bandwidth:
- Phase-lead compensation increases the bandwidth of the system. This allows the system to respond more quickly to changes in input.
- Increases Gain at Higher Frequencies:
- It provides an increase in gain at higher frequencies, which enhances the system's ability to track fast changes in input signals.
- Fast Transient Response:
- This compensation technique is particularly beneficial when fast transient responses are desired. It reduces the settling time and improves the overall responsiveness of the system.
Why Option 'D' is Incorrect:
- Decrease Rapidly Near Crossover Frequency:
- This statement is misleading. In a phase-lead compensation network, the phase margin is increased, and the gain does not decrease rapidly near the crossover frequency. Instead, the network is designed to maintain or even enhance the gain within the crossover region, leading to a more stable and responsive system.
Conclusion:
In summary, phase-lead compensation is characterized by its ability to enhance system performance. It does not lead to a rapid decrease in gain near the crossover frequency, making option 'D' the incorrect statement.
If r = 1 in the G(s) = 
then the compensator can give the minimum phase at a frequency of- a)
- b)0.777 rad / s
- c)1 rad / s
- d)
Correct answer is option 'D'. Can you explain this answer?
If r = 1 in the G(s) = then the compensator can give the minimum phase at a frequency of
then the compensator can give the minimum phase at a frequency ofa)
b)
0.777 rad / s
c)
1 rad / s
d)
| | Machine Experts answered |
Concept:
Lead and Lag compensators:
Gc(s) = (1 + aTs) / (1 + Ts) where a and T > 0, a > 1 (lead) & a < 1 (lag)
∠Gc(s) = ϕ = tan-1 ωaT – tan-1 ωT
ωm is the geometric mean of the two corner frequencies 1/T and 1/aT
ωm = 1/T√α
Lead and Lag compensators:
Gc(s) = (1 + aTs) / (1 + Ts) where a and T > 0, a > 1 (lead) & a < 1 (lag)
∠Gc(s) = ϕ = tan-1 ωaT – tan-1 ωT
ωm is the geometric mean of the two corner frequencies 1/T and 1/aT
ωm = 1/T√α
Calculations:
Given Gc(s) =
r = 1
By substituting r value we get Gc(s) =
Here T = 1 and a = 0.1
Given Gc(s) =
r = 1
By substituting r value we get Gc(s) =
Here T = 1 and a = 0.1
The transfer function 
represents a- a)lag network
- b)lead network
- c)lag-lead network
- d)proportional controller
Correct answer is option 'A'. Can you explain this answer?
The transfer function represents a
represents aa)
lag network
b)
lead network
c)
lag-lead network
d)
proportional controller
| | Zoya Sharma answered |
Concept:
Lag compensator:
Transfer function:
If it is in the form of
then a < 1
If it is in the form of
then a > b
Maximum phase lag frequency:
ωm = 1/T√a
Maximum phase lag: ϕm = sin−1(α−1/α+1)
ϕm is negative
Pole zero plot:
The pole is nearer to the origin.
Given:
Zero = -2
Pole = -1
Analysis:
The pole-zero plot of T(s) is as shown:
Since the pole is closer to the origin than zero.
It is a lag compensator.
Lag compensator:
Transfer function:
If it is in the form of
then a < 1If it is in the form of
then a > bMaximum phase lag frequency:
ωm = 1/T√a
Maximum phase lag: ϕm = sin−1(α−1/α+1)
ϕm is negative
Pole zero plot:
The pole is nearer to the origin.
Given:
Zero = -2
Pole = -1
Analysis:
The pole-zero plot of T(s) is as shown:
Since the pole is closer to the origin than zero.
It is a lag compensator.
A system employing proportional plus error rate control is shown in figure below.
The value of error rate control (Ke) and 2% settling time for a damping ratio of 0.5 are respectively- a)0.116 and 2.53 sec
- b)0.265 and 0.116 sec
- c)0.116 and 0.265 sec
- d)0.265 and 2.53 se
Correct answer is option 'A'. Can you explain this answer?
A system employing proportional plus error rate control is shown in figure below.
The value of error rate control (Ke) and 2% settling time for a damping ratio of 0.5 are respectively
The value of error rate control (Ke) and 2% settling time for a damping ratio of 0.5 are respectively
a)
0.116 and 2.53 sec
b)
0.265 and 0.116 sec
c)
0.116 and 0.265 sec
d)
0.265 and 2.53 se
 | Prisha Sen answered |
The forward path gain of the given system is:
∴ Characteristic equation is
1 + G(s)H(s) = 0
or
or, s2 + (2 + 10 Ke)s +10 = 0
Here,
ωn = √10 rad/s
and 2ξωn = (2 + 10Ke)
Given, ξ = 0.5
So, 2 x 0.5 x √10 = (2 + 10Ke)
or,
= 1.16/10 = 0.116
Also, 2% settling time
∴ Characteristic equation is
1 + G(s)H(s) = 0
or
or, s2 + (2 + 10 Ke)s +10 = 0
Here,
ωn = √10 rad/s
and 2ξωn = (2 + 10Ke)
Given, ξ = 0.5
So, 2 x 0.5 x √10 = (2 + 10Ke)
or,
= 1.16/10 = 0.116
Also, 2% settling time
Which of the following is a correct statement?- a)PI controllers improves steady state response
- b)PD controllers improves transient response
- c)Both (a) & (b)
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Which of the following is a correct statement?
a)
PI controllers improves steady state response
b)
PD controllers improves transient response
c)
Both (a) & (b)
d)
None of these
| | Pooja Patel answered |
Concept:
Proportional + Derivate(PD):
The additive combination of proportional & Derivative control is known as P-D control.
Proportional + Derivate(PD):
The additive combination of proportional & Derivative control is known as P-D control.
The overall transfer function for a PD controller is given by:
PD controller is nothing but a differentiator (or) a High Pass Filter.
PD controller is nothing but a differentiator (or) a High Pass Filter.
The frequency of noise is very high.
So this high pass filter will allow noise into the system which results in noise amplification.
PD Controllers reduce the response time and thus improve transient response
Effects of Proportional Derivative (PD) controllers:
- Decreases the type of the system by one
- Reduces the rise time and settling time
- It has high sensitivity.
- Rise time and settling time decreases and Bandwidth increases
- The speed of response is increased i.e. the transient response is improved
- Improves gain margin, phase margin, and resonant peak
- Increases the input noise
- Improves the stability
Proportional Integral Controller:
This controller resembles the combination of the proportional and integral controller.
The structure of this controller is shown below:
This is used to decrease the steady-state error without affecting the stability of the system.
The transfer function is defined as:
Analysis:
Analysis:
The transfer function of the system is calculated as:
Disadvantages: Slow reaction to the disturbances.
Disadvantages: Slow reaction to the disturbances.
Advantages:
- It provides the zero control error
- It is insensitive to the interference of the measurement channel.
- PI Controllers increase the type of the system and thus reduce steady-state error and improve steady state
response
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