How to implement a modified transfer function?

Question

my field is not that much related to, but I need to build a model-based simulation in simulink. The model has a transfer modified function as follows:

r(s)/q(s)=t/(t*s+1)

I know the basics, however, to implement this, I got into question, whether I have to use a Gain block with value of t before and after a transfer function like this 1/(s+1), or it should be implemented in another fashion? As t is not a constant. Thanks.

Answer 1

Firstly note that t/(t*s + 1) is equivalent to 1/(s+(1/t)). In both cases t > 0 or the system is unstable or ill-defined.

If t was constant then you could use a Transfer Function block, which is the equivalent of the first of the following implementations. Since t is not constant, you cannot use a Transfer Function block, but you can use the second implementation shown below.