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In a second order system with a unit step input, the speed of response is high if system is
- a)overdamped
- b)undamped system
- c)critically damped
- d)underdamped
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In a second order system with a unit step input, the speed of response...
An underdamped system with damping factor slightly less than 1 gives high speed of response.
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In a second order system with a unit step input, the speed of response...
Underdamped System:
An underdamped system is characterized by oscillatory behavior in its response to a unit step input. The transient response of an underdamped system includes oscillations before settling down to the final value.
Speed of Response:
The speed of response refers to how quickly a system reaches its steady-state value after a change in input. In the case of a second-order system with a unit step input, a high speed of response indicates that the system quickly settles at the final value without excessive oscillations or delays.
Relation to Underdamped System:
In the context of the given options, an underdamped system exhibits a faster speed of response compared to overdamped and critically damped systems. This is because the oscillatory behavior in an underdamped system helps in quickly reaching the final value without prolonged settling times.
Impact on System Performance:
A high speed of response is desirable in many control systems applications where quick and accurate responses are required. For example, in systems that involve tracking or regulating a variable, a fast response helps in maintaining stability and meeting performance requirements.
Conclusion:
In summary, an underdamped system is associated with a high speed of response in the context of a second-order system with a unit step input. This behavior is beneficial for systems that require rapid and precise adjustments to changes in input signals.
An underdamped system is characterized by oscillatory behavior in its response to a unit step input. The transient response of an underdamped system includes oscillations before settling down to the final value.
Speed of Response:
The speed of response refers to how quickly a system reaches its steady-state value after a change in input. In the case of a second-order system with a unit step input, a high speed of response indicates that the system quickly settles at the final value without excessive oscillations or delays.
Relation to Underdamped System:
In the context of the given options, an underdamped system exhibits a faster speed of response compared to overdamped and critically damped systems. This is because the oscillatory behavior in an underdamped system helps in quickly reaching the final value without prolonged settling times.
Impact on System Performance:
A high speed of response is desirable in many control systems applications where quick and accurate responses are required. For example, in systems that involve tracking or regulating a variable, a fast response helps in maintaining stability and meeting performance requirements.
Conclusion:
In summary, an underdamped system is associated with a high speed of response in the context of a second-order system with a unit step input. This behavior is beneficial for systems that require rapid and precise adjustments to changes in input signals.
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In a second order system with a unit step input, the speed of response is high if system isa)overdampedb)undamped systemc)critically dampedd)underdampedCorrect answer is option 'D'. Can you explain this answer?
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