Question

The transfer function is

Hyr= 36/(s+3)²
The steady-state output is yss=12cos(√3t−30⁰)
What is the input r(t), t≥0 that creates this steady-state output?

a. r(t)=36cos(√3t),t≥0
b. r(t)=3cos(√3t−30⁰),t≥0
c. r(t)=4cos(√3t+30⁰),t≥0 r
d. (t)=3,t≥0

Answer 1

The input r(t) that creates the given steady-state output y(t) can be calculated by taking the inverse Laplace transform of the transfer function.

Step-by-step explanation:

To create the steady-state output y(t)=12cos(√3t-30°), the input r(t) can be found by rearranging the transfer function and equating it to the steady-state output. By comparing the given expression with the standard form of the transfer function, Hyr = K/(s+a)^2, we can see that K = 36 and a = 3. The input r(t) can be calculated by taking the inverse Laplace transform of the transfer function: r(t) = 36cos(√3t).