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An open loop control system results in a response of
(10e-2t - 3e-t) u(t)
For an unit impulse input. The D.C. gain of control system is….....?
(Important - Enter only the numerical value in the answer)
Correct answer is '2'. Can you explain this answer?
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An open loop control system resultsin a response of(10e-2t - 3e-t) u(t...
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An open loop control system resultsin a response of(10e-2t - 3e-t) u(t...
To find the DC gain of the control system, we need to determine the value of the response when the input is a unit impulse.
The unit impulse function, denoted as δ(t), is defined as a function that is zero for all values of t except when t = 0, where it has an infinite magnitude such that its integral over any interval containing t = 0 is equal to 1.
For an open-loop control system, the response to a unit impulse input is given by the Laplace transform of the transfer function, evaluated at s = 0.
The Laplace transform of the given response, R(s), is:
R(s) = 10e^(-2s)/(s+2) - 3e^(-s)/s
To find the value of the response when the input is a unit impulse, we substitute s = 0 into the Laplace transform:
R(0) = 10e^(-2*0)/(0+2) - 3e^(-0)/0
= 10/2 - 3/0 (Note: e^0 = 1)
= 5 - undefined
Therefore, the DC gain of the control system is undefined.
The unit impulse function, denoted as δ(t), is defined as a function that is zero for all values of t except when t = 0, where it has an infinite magnitude such that its integral over any interval containing t = 0 is equal to 1.
For an open-loop control system, the response to a unit impulse input is given by the Laplace transform of the transfer function, evaluated at s = 0.
The Laplace transform of the given response, R(s), is:
R(s) = 10e^(-2s)/(s+2) - 3e^(-s)/s
To find the value of the response when the input is a unit impulse, we substitute s = 0 into the Laplace transform:
R(0) = 10e^(-2*0)/(0+2) - 3e^(-0)/0
= 10/2 - 3/0 (Note: e^0 = 1)
= 5 - undefined
Therefore, the DC gain of the control system is undefined.
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