# Finding Open/closed loop transfer function

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).

Also how to use this to determine the closed loop of the system

Start by putting some equations on it: -

simulate this circuit – Schematic created using CircuitLab

The output of A is called Vout, but clearly ....

$V_{out} = A(V_{in} - B\cdot V_{out})$

This boils down to $\dfrac{V_{out}}{V_{in}} = \dfrac{A}{1+AB}$

• Thanks Andy, In finding the forward path for the open loop I have added 12/pi that is not in the feedback path. does that look ok. – Shittu Olalekan Dec 23 '15 at 21:36

1.) Together with the first block (12/Pi) and Andy akas 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 akas notation)-

3.) The full closed-loop gain is defined as the ratio of two angles (tetha,0/teta,i).

• LvW, Going by your second comment, for the open loop transfer function, all the forward function including 12/pi with input(teta i) & output(Vi(s)). Thats what I've done before posting the diagram. – Shittu Olalekan Dec 23 '15 at 21:31
• Whats a unity negative feedback? – Shittu Olalekan Dec 23 '15 at 21:51

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

• Quote: "....find how to move the feedback into the loop and make feedback =1"...My comment: For which purpose such an unnecessary procedure? – LvW Dec 24 '15 at 8:36
• @LvW Because this is a classic exercise at univeristy, and two same gains 12/pi are pointing that professor wants exactly that thing. – Marko Buršič Dec 24 '15 at 17:14
• Ahhh - yes, this could be the case. – LvW Dec 25 '15 at 8:25