I plan to determine the open/close loop transfer function of the attached motor. I have been able to combine K(s) to 1/s in series but am not too sure of how to add up 12/pi outside the summing junction and what to use as the gain(either tetha 0/teta 1 or teta 0/V1(s).
1.) Together with the first block (12/Pi) and Andy aka`s answer you will be able to find the closed-loop transfer function.
2.) The open-loop function is the product of all forward blocks (without the feedback path). This expression should not be confused with the "loop gain" which is simply the product A*B (using Andy aka`s notation)-
3.) The full closed-loop gain is defined as the ratio of two angles (tetha,0/teta,i).
The relation between open loop F(s) and closed loop H(s) is H(s)=F(s)/1+F(s) if and only if the feedback is 1. In your case the feedbak is 12/pi, but also the setpoint is multiplied with same, so the solution of your homework is: - find how to move the feedback into the loop and make feedback =1, then some coeficient will cancell out and use the formula openv vs. closed loop with fbck=1