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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...
Answer: c
Explanation: 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.
Explanation: 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...
Given information:
The output of a continuous control system in response to a unit step input is given by c(t) = 1 - e^(-t).
To find:
The delay time (Td) of the system.
Explanation:
The delay time (Td) of a system is the time it takes for the system output to reach a certain fraction of its final value after applying a unit step input. In this case, we need to find the time it takes for the output c(t) to reach 0.63 (or 63%) of its final value.
Step 1:
We can set up the equation c(t) = 0.63 and solve for t.
1 - e^(-t) = 0.63
Step 2:
Rearrange the equation to isolate e^(-t).
e^(-t) = 1 - 0.63
e^(-t) = 0.37
Step 3:
Take the natural logarithm of both sides to solve for t.
ln(e^(-t)) = ln(0.37)
-t = ln(0.37)
t = -ln(0.37)
Step 4:
Evaluate the value of t using a calculator.
t ≈ 0.693
Therefore, the delay time Td is approximately equal to 0.693. Hence, the correct answer is option C.
The output of a continuous control system in response to a unit step input is given by c(t) = 1 - e^(-t).
To find:
The delay time (Td) of the system.
Explanation:
The delay time (Td) of a system is the time it takes for the system output to reach a certain fraction of its final value after applying a unit step input. In this case, we need to find the time it takes for the output c(t) to reach 0.63 (or 63%) of its final value.
Step 1:
We can set up the equation c(t) = 0.63 and solve for t.
1 - e^(-t) = 0.63
Step 2:
Rearrange the equation to isolate e^(-t).
e^(-t) = 1 - 0.63
e^(-t) = 0.37
Step 3:
Take the natural logarithm of both sides to solve for t.
ln(e^(-t)) = ln(0.37)
-t = ln(0.37)
t = -ln(0.37)
Step 4:
Evaluate the value of t using a calculator.
t ≈ 0.693
Therefore, the delay time Td is approximately equal to 0.693. Hence, the correct answer is option C.
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