# Finding transfer function from diagram

I'm trying to find transfer function of this block diagram.

So far I've started with the smallest loop, but it's nonsense because don't know how to deal with Tf(s)(Friction torque) to Motor angular speed.

Here's my calculation attempt. Any kick to the right direction is appreciated.

Seemingly there's no overwhelming interest to kick anybody. So, here's a kick.

See the next simple (much simpler than your system) block diagram and the equations which show the same math as the drawn blocks:

The boxes have linear transfer functions A,B, C and D. They contain numbers and some of them may also have the Laplace variable s.

x, v, y and z are the signal variables, actually signal Laplace transforms.

The transfer functions affect by multiplying the variables. The summing junction generates the sum v.

Your job is to reduce the equation set to one by eliminating intermediate variables v and y. The remaining equation contains the transfer functions, the input x and the output z. It will be z=Hx where H is the wanted transfer function between x and z. H can be simple or complex depending on the block transfer functions and the circuit. It can well contain s and its powers as well in the nominator and in the denominator.

In this case A,B,C and D are not defined with finer details, so you'll end to z=Hx where the final transfer function H=AC/(1+ACD+AB)

End of the kick.

Not asked: Your system has more intermediate variables so it will be much more complex to derive the final transfer function.

Simulating the system does not need the final transfer function. If you really have only one parameter (the Kp) which needs tuning a good value may be found in a simulation even by trial and error. I'm afraid simulation will reveal some unexpected things. At lest if the intermediate variables are monitored, too.

You can run a system simulator program or even a circuit analysis program which has the needed blocks. This needs a circuit analyzer which has ideal voltage controlled voltage sources (=amplifiers), summing junctions and ideal integrators. A Laplace domain transfer function block would be useful, but it's not a must.