Suppose i have the system equation
$Y(s) = G(s)X(s)+ 3T(s)$
Then what is the transfer function of the system?
I know that the transfer function is $Y(s)/X(s)$, but i can't get that expression.
Suppose i have the system equation
$Y(s) = G(s)X(s)+ 3T(s)$
Then what is the transfer function of the system?
I know that the transfer function is $Y(s)/X(s)$, but i can't get that expression.
If you consider $X(s)$ as the only input of the system then the transfer function only exists for $T(s)=0$, and it is given by $G(s)$. Strictly speaking, with $T(s)\neq 0$, the system cannot be characterized by a transfer function because it is no longer linear. Note that a linear system must produce an output $Y(s)=0$ for $X(s)=0$. However, this is not the case for $T(s)\neq 0$.
You could also treat that system as a (linear) multiple input single output (MISO) system with two inputs $X(s)$ and $T(s)$. In that case there are two transfer functions: $$H_X(s)=\frac{Y(s)}{X(s)}\Big|_{T(s)=0}=G(s)$$
and $$H_T(s)=\frac{Y(s)}{T(s)}\Big|_{X(s)=0}=3$$