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The output in response to a unit step input for a particular continuous control system is c(t)= 1-e-t. What is the delay time Td?
- a)0.36
- b)0.18
- c)0.693
- d)0.289
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The output in response to a unit step input for a particular continuou...
The output is given as a function of time. The final value of the output is limn->∞c(t) = 1; .
Hence Td (at 50% of the final value) is the solution of 0.5 = 1-e-Td, and is equal to ln 2 or 0.693 sec.
Most Upvoted Answer
The output in response to a unit step input for a particular continuou...
Delay Time Calculation:
1. The delay time (Td) is the time taken for the response of the system to reach 50% of its final value after a step input.
2. Given the output response c(t) = 1 - e^(-t), we need to find the time at which c(t) = 0.5.
3. Setting c(t) = 0.5 and solving for t:
1 - e^(-t) = 0.5
e^(-t) = 0.5
-t = ln(0.5)
t = -ln(0.5)
4. Calculating the value of t:
t ≈ 0.693
5. Therefore, the delay time (Td) for the given continuous control system is approximately 0.693.
Thus, the correct answer is option 'C' - 0.693.
1. The delay time (Td) is the time taken for the response of the system to reach 50% of its final value after a step input.
2. Given the output response c(t) = 1 - e^(-t), we need to find the time at which c(t) = 0.5.
3. Setting c(t) = 0.5 and solving for t:
1 - e^(-t) = 0.5
e^(-t) = 0.5
-t = ln(0.5)
t = -ln(0.5)
4. Calculating the value of t:
t ≈ 0.693
5. Therefore, the delay time (Td) for the given continuous control system is approximately 0.693.
Thus, the correct answer is option 'C' - 0.693.
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The output in response to a unit step input for a particular continuou...
The output is given as a function of time. The final value of the output is limn->∞c(t) = 1; .
Hence Td (at 50% of the final value) is the solution of 0.5 = 1-e-Td, and is equal to ln 2 or 0.693 sec.
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