Conflicting Simulink mdoels - transfer function

I have a simulink model where the model on the right which is simplified does not give the same output as the expanded version on the right, I cannot figure out way as the equatiosn are the same, you may check page 5 of 9 of the pdf attached. I have attached the two simulink models as combined_control_model (left hand block diagram) and control_model (the right hand one).

Any assitance will be highly appreciated.

The constants are the same for both models, i.e:

Dm = 0.2;
L = 1.69e-2;
Km = 2.83e-2;
Kb = 2.82e-2;
Kf=5.8e-2;
J = 1.7767;
R = 0.5;

The block diagrams.

Final output velocity

Answer 1

[Paul]

The block diagrams don't represent the same system. The easiest way to see this is that the loop transfer functions are different between the two diagrams. The manipulation of the middle transfer function in the diagram on the left into the middle portion of the diagram on the right is incorrect.

[Tinotenda Kurimwi]

Thank you for the respone, much appreaited.

This is how I have formulated the two ("middle sections"), is this incorect mathematically or is it incorrect when transfered to simulink? I am not sure I understand.

[Paul]

It is true that

(Km*Dm*s - 10*Dm)/s == Km*Dm - 10*Dm/s

However, we are dealing with a transfer function here that relates an input to an output. Let Y(s) be the Laplace transform of the output and U(s) of the input. U(s) is the input to the scope at top of the digram and Y(s) is the input to the rightmost tramsfer function in the block diagram. In these terms, it is true that:

Y(s) = ( (Km*Dm*s - 10*Dm)/s) * U(S) == (Km*Dm - 10*Dm/s) * U(s)

But it's not true that

Y(s) = Km*Dm*U(s) - 10*Dm/s * D(s)

where D(s) is an additional input into the system unrelated to U(s) that you introduced in the diagram on the right, with d(t) = 1.

[Tinotenda Kurimwi]

Thank you, Paul. I understand makes. I really apreciate the help.

I might be stretching my luck but I will try anyway as I have been at this thing for 2 days now. With the following block diagrams, are they all different as you exaplined or are they the same(in simulink)? They are presenting an input voltage (left hand side) to an output velocity (right hand side).

[Paul]

They are all different. Figure 3 becuase of reason already explained. Figure 4 and Figure 5 differ because there is a term missing in the coefficent of s^3 in G2(s) in Figure 5.

[Tinotenda Kurimwi]

understood. Again, THANK YOU.