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A control system whose step response is -0.5(1+e-2t) is cascaded to another control block whose impulse response is e-t. What is the transfer function of the cascaded combination?
- a)1/(s+2)(s+1)
- b)1/(s+1)s
- c)1/(s+3)
- d)0.5/(s+1)(s+2)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A control system whose step response is -0.5(1+e-2t) is cascaded to an...
Let's first find the transfer function of the first control system. We know that the step response is given by: y(t) = -0.5(1+e^(-2t))
Taking the Laplace transform of both sides, we get: Y(s) = -0.5(1/s + 1/(s+2))
The transfer function of the first control system is therefore: G1(s) = Y(s)/U(s) = -0.5/(s(s+2))
Now let's find the transfer function of the second control block. We know that the impulse response is given by: h(t) = e^(-t)
Taking the Laplace transform of both sides, we get: H(s) = 1/(s+1)
The transfer function of the second control system is therefore: G2(s) = H(s)/U(s) = 1/(s+1)
The transfer function of the cascaded combination is given by the product of the individual transfer functions: G(s) = G1(s) * G2(s) = [-0.5/(s(s+2))] * [1/(s+1)] = -0.5/(s(s+2)(s+1))
Therefore, the correct answer is: 1/(s+2)(s+1).
This question is part of UPSC exam. View all Electronics and Communication Engineering (ECE) courses
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A control system whose step response is -0.5(1+e-2t) is cascaded to an...
Community Answer
A control system whose step response is -0.5(1+e-2t) is cascaded to an...
Given:
Step response of first control system = -0.5(1 e-2t)
Impulse response of second control system = e-t
To find: Transfer function of cascaded combination
Approach:
The transfer function of a control system is given by the Laplace transform of its impulse response (for an impulse input) or step response (for a step input).
The given step response can be converted into an impulse response using the fact that the Laplace transform of a step response is 1/s times the Laplace transform of the corresponding impulse response.
Then, the transfer function of the cascaded system can be found by multiplying the transfer functions of the individual systems.
Calculation:
Step response of first control system = -0.5(1 e-2t)
Taking Laplace transform on both sides, we get:
G1(s) = -0.5/(s + 2)
Impulse response of second control system = e-t
Taking Laplace transform on both sides, we get:
G2(s) = 1/(s + 1)
Transfer function of cascaded system = G1(s) * G2(s)
= (-0.5/(s + 2)) * (1/(s + 1))
= -0.5/(s^2 + 3s + 2)
= -0.5/[(s + 1) (s + 2)]
Therefore, the correct answer is option A.
Step response of first control system = -0.5(1 e-2t)
Impulse response of second control system = e-t
To find: Transfer function of cascaded combination
Approach:
The transfer function of a control system is given by the Laplace transform of its impulse response (for an impulse input) or step response (for a step input).
The given step response can be converted into an impulse response using the fact that the Laplace transform of a step response is 1/s times the Laplace transform of the corresponding impulse response.
Then, the transfer function of the cascaded system can be found by multiplying the transfer functions of the individual systems.
Calculation:
Step response of first control system = -0.5(1 e-2t)
Taking Laplace transform on both sides, we get:
G1(s) = -0.5/(s + 2)
Impulse response of second control system = e-t
Taking Laplace transform on both sides, we get:
G2(s) = 1/(s + 1)
Transfer function of cascaded system = G1(s) * G2(s)
= (-0.5/(s + 2)) * (1/(s + 1))
= -0.5/(s^2 + 3s + 2)
= -0.5/[(s + 1) (s + 2)]
Therefore, the correct answer is option A.
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A control system whose step response is -0.5(1+e-2t) is cascaded to another control block whose impulse response is e-t. What is the transfer function of the cascaded combination?a)1/(s+2)(s+1)b)1/(s+1)sc)1/(s+3)d)0.5/(s+1)(s+2)Correct answer is option 'A'. Can you explain this answer?
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