# Step response to feedback loop with disturbance

When using step response to a feedback loop with disturbance. Why do we analyze the step response of the disturbance D and the step response of the input R separately. Instead of considering them together like with $$Y = \frac{GR}{1+HG} + \frac{GD}{1+HG}$$ given that $Y$ is the output.

I'm assuming we can't take the step response with both together in the function as we want the transfer function to be in terms of $\cfrac{Y}{R}$ or $\cfrac{Y}{D}$, but I just wanted to confirm that this was the case.

• I think it came directly from mathematics. Where solution to a non-homogenous differential equation is calculated as complementary solution + particular solution. – nidhin May 29 '14 at 19:32