Final answer:
The step response of the first-order control system with transfer function G(s) = 44 / (3s + 1) is y(t) = 44 * (1 - e^{-t/3}), which shows an exponential approach to the final value of 44 over time.
Step-by-step explanation:
To find the step response of a first-order control system described by G(s) = 44 / (3s + 1), you need to determine the Inverse Laplace transform. Assume that we are subjecting the system to a unit step input, which is U(s) = 1 / s in the Laplace domain. To get the output, we multiply the transfer function by the input, which gives us Y(s) = G(s) * U(s) = (44 / (3s + 1)) * (1 / s). Then we look for the inverse Laplace transform to find y(t), which is the step response in the time domain.
After doing partial fraction decomposition if necessary and using the standard Laplace transform pairs, we can find the inverse Laplace transform of Y(s). The step response y(t) for this system is y(t) = 44 * (1 - e-t/3), where e is the base of the natural logarithm and t is time in seconds.
This exponential term represents how the response will gradually reach the final value of 44 as time goes to infinity, depicting the characteristic response of a first-order system when subjected to a step input.