How to implement a transfer function with variable coefficients?

I want to implement two filters using transfer functions with variable coefficients and passing a gaussian noise. The two filters are:

F1: F(s) = ((5d)^(1/2))/(b+s);
F2: F1(s) = (((5d)^(1/2))*((b/sqrt(3))+s)) / (b+s)^2;

Where d and b vary every time step.

The implementations for the two filters in simulink are as follow:

For the first filter:

For the second one:

The obtained results have values of 10^-12, while the expected results should be between 10^-3 - 10.

Since it's the first time when I try t implement a tf with variable coefficients I am not sure the implementations are correct.

Answer 1

[Bora Eryilmaz]

The top part of your first diagram does not implement 1/(b+s).

To confirm this, label the output of the top sum block as e. Then you have

e = noise - b/s

Also, label the output that gets multiplied by sqrt(5d) as y. Then you have

y = e/s

Solving from noise to y gives

y = (noise - b/s) / s

which is obviously not

y = noise / (b+s)