An open loop control system resultsin a response of(10e-2t - 3e-t) u(t)For an unitimpulse input. The D.C. gain ofcontrol system is….....?(Important - Enter only the numerical value in the answer)Correct answer is '2'. Can you explain this answer?

Question

An open loop control system resultsin a response of(10e-2t - 3e-t) u(t)For an unitimpulse input. The D.C. gain ofcontrol system is&hellip;.....?(Important - Enter only the numerical value in the answer)Correct answer is '2'. Can you explain this answer?

Answer

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.

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