How Does Unity Position Feedback Affect System Dynamics in Control Theory?

[donpacino]

G(s): https://app.box.com/s/s7szsp7rztjndh58oolc
H(s): https://app.box.com/s/8hn2fryguhnis8mr0469
F(s) open loop tf when K1=K2: https://app.box.com/s/arwnrxwopi6y2cjls42q
Root Locus of F(s): https://app.box.com/s/wzaupxumo3j96lvjwobo
2nd Order Approx K1=K2: https://app.box.com/s/p2vyncwxhil3252g07d8

I'm hoping that F(s) above is correct as this is what I've based everything afterwards on...

While you did not answer Milesyoung's question, your F(s) open loop is correct.

 

[toolpusher123]

In response to 'milesyoung' post #87;

• Closed Loop Tf: https://app.box.com/s/twk1h23blxebgawzaw7d

• Characteristic Equation for post #87: https://app.box.com/s/qivkcx0b0csz6xx8oe8e

Miles I have submitted my report. I must thank you for all your help & suggestions. Now that the project is complete, I have a much better understanding of the processes/concepts involved. At the beginning I really did not have a clue. So thanks again for your patience & commitment...

Edit: Thanks to anyone else on the site who added any input.

 

[milesyoung]

While you did not answer Milesyoung's question, your F(s) open loop is correct.

That's the equivalent system for the forward path of the outer feedback loop, but that's not the function you should use in place of $F(s)$, since it depends on $K_1,K_2$.

Miles I have submitted my report. I must thank you for all your help & suggestions. Now that the project is complete, I have a much better understanding of the processes/concepts involved. At the beginning I really did not have a clue. So thanks again for your patience & commitment...

You're very welcome. Since you've submitted it, I can show you what I was getting at:

The characteristic equation for your system with velocity feedback is (using your definitions):
$$
1 - \frac{K_1 H(s) G(s)}{1 - K_1 s H(s) G(s)} = 0 \Leftrightarrow 1 - K_1 s H(s) G(s) - K_1 H(s) G(s) = 0\\
\Leftrightarrow 1 + K_1\left[-s H(s) G(s) - H(s) G(s)\right] = 0 \Leftrightarrow 1 + K_1 F(s) = 0, F(s) = -s H(s) G(s) - H(s) G(s)
$$
If you plot the root locus for $F(s)$, you should notice some significant differences from the system without velocity feedback, e.g. it's stable for any $K_1$, and the dominant branch lies much further into the LHP.

 

[toolpusher123]

No my post was in response to your post (post # 87).
My solution regarding my system i.e. K1 = K2 was to find the open-loop tf. The equation I used to do this was: https://app.box.com/s/arwnrxwopi6y2cjls42q

• Did I enter an incorrect tf in order to plot 'root locus' of system when K1 = K2 ?
• Is this the correct root locus i.e. with 'velocity feedback': https://app.box.com/s/wzaupxumo3j96lvjwobo

Edit: From post #87 ( "your F(s) open loop is correct").

 

[milesyoung]

Did I enter an incorrect tf in order to plot 'root locus' of system when K1 = K2 ?

Yes, it should be $F(s) = -s H(s) G(s) - H(s) G(s)$, as per my post #93.

Is this the correct root locus i.e. with 'velocity feedback': https://app.box.com/s/wzaupxumo3j96lvjwobo

No, it should look like this: