Question

What is the impulse response till t=16 unit in time of a system whose transfer function is that of the following?

(a) ^3⁄4*r(t-4) + ^3⁄4*r(t-16)+u(t-16)

(b) ^3⁄4*r(t-4) – ^3⁄4*r(t+16)-u(t-16)

(c) ^3⁄4*r(t-4) – ^3⁄4*r(t-16)-u(t-16)

(d) ^3⁄4*r(t-4) – ^3⁄4*r(t+16)-u(t+16)

This question was posed to me in my homework.

Query is from Impulse Response in division Control System Applications of MATLAB

Answer 1

The correct choice is (c) ^3⁄4*r(t-4) – ^3⁄4*r(t-16)-u(t-16)

Best explanation: The correct representation of the signal shown in the graph is ^3⁄4*r(t-4) – ^3⁄4*r(t-16)-u(t-16). This is because the ramp function, starting from t=4 units in time, has a slope of ^3⁄4 and it’s shown to end at t=16. So, there it faces a slope change to 0, so the 2^nd term happens and finally, the amplitude becomes 0 which is why, the 3^rd term happens.