# Transfer function of two inputs?

Suppose I have a system with feedback. Consider the input $$\d\$$ that represents disturbances to the plant; also, consider the input $$\V\$$ that represents sensor noise on the feedback loop. I can calculate the closed-loop transfer function $$\\dfrac{Y(s)}{d(s)}\$$ and $$\\dfrac{Y(s)}{V(s)}\$$. Then, my question is: does it even make sense to talk about the transfer function $$\\dfrac{D(s)}{V(s)}\$$, if so, could it be calculated as $$\\dfrac{d(s)}{V(s)}=\dfrac{d(s)}{Y(s)}\dfrac{Y(s)}{V(s)}\$$?

Thanks!

• For two different inputs (e.g. reference and disturbance) we have, of course, two different transfer functions. It makes no sense to combine both.
– LvW
Jan 28 at 8:25

There may be some sensible reason to calculate $$\D(s)/V(s)\$$, but I wouldn't call it a "transfer function", under pretty much any circumstances.