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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
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A third order system is approximated to an equivalent second order sys...
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.
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.
Most Upvoted Answer
A third order system is approximated to an equivalent second order sys...
Introduction:
In control systems, the rise time is defined as the time taken by the system's response to rise from 10% to 90% of its final value. The rise time is an important parameter that determines the transient response of a system. In this question, we are given a third-order system and asked to determine the rise time of an equivalent second-order approximation of the system.
Explanation:
When a higher-order system is approximated to a lower-order system, some of the dynamics of the original system are lost. This means that the approximation may not accurately represent the behavior of the original system for all inputs. In the given question, we are assuming that the approximation accurately represents the original system for any input.
Effect of Order on Rise Time:
The order of a system determines its complexity and the number of poles it has. In general, higher-order systems have more poles, which can result in slower rise times. As the order of the system increases, the number of poles increases, leading to more complex dynamics and slower response times.
Second-Order Approximation:
When a third-order system is approximated to a second-order system, some of the poles of the original system are neglected. This simplification can result in a faster response time, as the neglected poles would have contributed to the system's overall response time.
Conclusion:
Based on the above analysis, we can conclude that the rise time of the approximated second-order system will be smaller than the original third-order system for any input. This is because the approximation neglects some of the poles of the original system, resulting in a simpler and faster response. However, it is important to note that the approximation may not accurately represent the behavior of the original system for all inputs, especially in cases where the neglected poles significantly impact the system's response.
In control systems, the rise time is defined as the time taken by the system's response to rise from 10% to 90% of its final value. The rise time is an important parameter that determines the transient response of a system. In this question, we are given a third-order system and asked to determine the rise time of an equivalent second-order approximation of the system.
Explanation:
When a higher-order system is approximated to a lower-order system, some of the dynamics of the original system are lost. This means that the approximation may not accurately represent the behavior of the original system for all inputs. In the given question, we are assuming that the approximation accurately represents the original system for any input.
Effect of Order on Rise Time:
The order of a system determines its complexity and the number of poles it has. In general, higher-order systems have more poles, which can result in slower rise times. As the order of the system increases, the number of poles increases, leading to more complex dynamics and slower response times.
Second-Order Approximation:
When a third-order system is approximated to a second-order system, some of the poles of the original system are neglected. This simplification can result in a faster response time, as the neglected poles would have contributed to the system's overall response time.
Conclusion:
Based on the above analysis, we can conclude that the rise time of the approximated second-order system will be smaller than the original third-order system for any input. This is because the approximation neglects some of the poles of the original system, resulting in a simpler and faster response. However, it is important to note that the approximation may not accurately represent the behavior of the original system for all inputs, especially in cases where the neglected poles significantly impact the system's response.
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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 inputb)Smaller than the original system for any inputc)Larger than the original system for any inputd)Larger or smaller depending on the inputCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2026 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about 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 inputb)Smaller than the original system for any inputc)Larger than the original system for any inputd)Larger or smaller depending on the inputCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 inputb)Smaller than the original system for any inputc)Larger than the original system for any inputd)Larger or smaller depending on the inputCorrect answer is option 'B'. Can you explain this answer?.
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 inputb)Smaller than the original system for any inputc)Larger than the original system for any inputd)Larger or smaller depending on the inputCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2026 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about 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 inputb)Smaller than the original system for any inputc)Larger than the original system for any inputd)Larger or smaller depending on the inputCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 inputb)Smaller than the original system for any inputc)Larger than the original system for any inputd)Larger or smaller depending on the inputCorrect answer is option 'B'. Can you explain this answer?.
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