-
A control system whose step responses is – 0.5 (1+ e–2t) u (t) is cascaded to another control block whose impulse response is e–t. The transfer function of the cascaded combination is—
-
-
1 (s + 1) (s + 2)
-
1 (s + 1)
-
1 s(s + 2) -
– 0·5s (s + 1) (s + 2)
-
Correct Option: A
Given step response of first control block (b) = – 0.5 (1 + e–2t) u(t) and impulse response of second control block = e– t since both the control system are put in the cascaded form, so we with calculate T.F. of both control function either in the impulse response form or in step response form. Also we know that impulse response is the derivative of step response
| i.e., | [– 0.5 (1 + e2t) u(t)] = – e–2t | |
| dt |
or
| H1(s) = | |
| (s + 1) |
Similarly
| H2(s) = [e–1] = | |
| (s + 1) |
∴ H(s)=H1(s) × H2(s)
| = | . | ||
| (s + 2) | (s + 1) |
| = | |
| (s + 2)(s + 1) |
| = | |
| (s + 2)(s + 1) |
