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The peak percentage overshoot of the closed loop system is :
- a)5.0%
- b)10.0%
- c)16.3%
- d)1.63%
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The peak percentage overshoot of the closed loop system is :a)5.0%b)10...
Answer: c
Explanation: C(s)/R(s) = 1/s2+s+1
C(s)/R(s) = w/ws2+2Gws+w2
Compare both the equations,
w = 1 rad/sec
2Gw = 1
Mp = 16.3 %
Explanation: C(s)/R(s) = 1/s2+s+1
C(s)/R(s) = w/ws2+2Gws+w2
Compare both the equations,
w = 1 rad/sec
2Gw = 1
Mp = 16.3 %
Most Upvoted Answer
The peak percentage overshoot of the closed loop system is :a)5.0%b)10...
The peak percentage overshoot of a closed-loop system is a measure of how much the system output exceeds its steady-state value during the transient response. It is commonly used to evaluate the stability and performance of control systems.
The peak percentage overshoot can be determined using the following formula:
\[PO = \frac{{Y_{max} - Y_{ss}}}{{Y_{ss}}} \times 100\%\]
where:
- \(PO\) is the peak percentage overshoot
- \(Y_{max}\) is the maximum value of the system output during the transient response
- \(Y_{ss}\) is the steady-state value of the system output
To find the peak percentage overshoot, we need to analyze the closed-loop system. The closed-loop system is a combination of the controller, plant, and feedback loop. The transfer function of the closed-loop system can be obtained by multiplying the transfer functions of the individual components.
Once we have the transfer function of the closed-loop system, we can analyze its transient response using techniques such as the step response or the impulse response.
During the transient response, the system may exhibit oscillations or overshoot before settling to its steady-state value. The peak percentage overshoot represents the maximum percentage by which the system output exceeds its steady-state value.
To calculate the peak percentage overshoot, we need to determine the maximum value of the system output (\(Y_{max}\)) and the steady-state value (\(Y_{ss}\)).
Once we have these values, we can substitute them into the formula and calculate the peak percentage overshoot.
In this particular question, the correct answer is option 'C', which states that the peak percentage overshoot is 16.3%. This means that the system output during the transient response exceeds its steady-state value by 16.3%.
It's important to note that the peak percentage overshoot is a measure of the system's response to a step input. It indicates the system's ability to quickly and accurately respond to changes in the input. A higher overshoot percentage generally indicates a less stable and less accurate system response.
The peak percentage overshoot can be determined using the following formula:
\[PO = \frac{{Y_{max} - Y_{ss}}}{{Y_{ss}}} \times 100\%\]
where:
- \(PO\) is the peak percentage overshoot
- \(Y_{max}\) is the maximum value of the system output during the transient response
- \(Y_{ss}\) is the steady-state value of the system output
To find the peak percentage overshoot, we need to analyze the closed-loop system. The closed-loop system is a combination of the controller, plant, and feedback loop. The transfer function of the closed-loop system can be obtained by multiplying the transfer functions of the individual components.
Once we have the transfer function of the closed-loop system, we can analyze its transient response using techniques such as the step response or the impulse response.
During the transient response, the system may exhibit oscillations or overshoot before settling to its steady-state value. The peak percentage overshoot represents the maximum percentage by which the system output exceeds its steady-state value.
To calculate the peak percentage overshoot, we need to determine the maximum value of the system output (\(Y_{max}\)) and the steady-state value (\(Y_{ss}\)).
Once we have these values, we can substitute them into the formula and calculate the peak percentage overshoot.
In this particular question, the correct answer is option 'C', which states that the peak percentage overshoot is 16.3%. This means that the system output during the transient response exceeds its steady-state value by 16.3%.
It's important to note that the peak percentage overshoot is a measure of the system's response to a step input. It indicates the system's ability to quickly and accurately respond to changes in the input. A higher overshoot percentage generally indicates a less stable and less accurate system response.
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