root locus plot from rlocus command

[Susan]

I'm confused a little on the MATLAB rlocus plot. When I plot my open loop TF with controller using the rlocus, what am I changing when I use my cursor and move the black square around? I thought I was changing the location of the poles of the closed loop TF?
The yellow box shows gain is changing?

If it's gain that I'm changing, is that the Kp value in my PID controller?

[Arkadiy Turevskiy]

You are changing the overall open loop system gain. If your controller is C and plant is P, open loop transfer function is sys=C*P.

When you do root locus you assume a gain k applied to open loop transfer function, so that your open loop transfer function is effectively k*CP. You vary k from 0 to Inf and see how that affects your close loop system poles.

So, in effecft you apply the same gain to Kp,Ki, and Kd.

If you want to design your controller using root locus then do not use rlocus function. Instead launch a SISO Design Tool

Post by Susan

sisotool(sys)

Root locus plot and bode plot will open up. Use that root locus plot to design. You will see red squares that show where closed loop poles are. Move the red squares to change system gain. You can also add poles and zeros to your controller in that tool.

Arkadiy

Post by Susan
I'm confused a little on the MATLAB rlocus plot. When I plot my open loop TF with controller using the rlocus, what am I changing when I use my cursor and move the black square around? I thought I was changing the location of the poles of the closed loop TF?
The yellow box shows gain is changing?
If it's gain that I'm changing, is that the Kp value in my PID controller?

[Susan]

Thank you, Arkadiy. I'm trying to finish up some research and my advisor suggested the following steps.

1- Use Z-N method to find values for kp, Td, and Ti.
** I did this no problem, but there's a zero at the origin so I added an additional integral.

2- use the Td and Ti from the Z-N method, keep Kp as variable and do a root locus of the closed loop system, based on varying the Kp. Then use the root locus to select the value of Kp that would give an optimal damping (0.7).

**is there a good way to vary Kp using the siso tool? I used the sgrid command and moved the gain until I reached a damping of .7, but like you said this is not just Kp. It's the system gain.

Do you have any suggestions for how to vary just Kp in the root locus?

[Arkadiy Turevskiy]

If your PID controller is Kp(1+Td*s +1/(Ti*s)) , then root-locus will let you vary Kp.
This is because the whole controller gets mutiplied by Kp.

If your PID is Kp+Ki/s+Kds, then it is a different story.

Post by Susan
Thank you, Arkadiy. I'm trying to finish up some research and my advisor suggested the following steps.
1- Use Z-N method to find values for kp, Td, and Ti.
** I did this no problem, but there's a zero at the origin so I added an additional integral.
2- use the Td and Ti from the Z-N method, keep Kp as variable and do a root locus of the closed loop system, based on varying the Kp. Then use the root locus to select the value of Kp that would give an optimal damping (0.7).
**is there a good way to vary Kp using the siso tool? I used the sgrid command and moved the gain until I reached a damping of .7, but like you said this is not just Kp. It's the system gain.
Do you have any suggestions for how to vary just Kp in the root locus?

[Susan]

I changed my PID to
s=tf('s')
Contr_Kp_Ti_Td = Kp*(1+Td*s +1/(Ti*s))

I plotted the CL loop TF with unity feedback where the OL = Contr_Kp_Ti_Td*Plant*Ki (where Ki is an additional integrator to cancel the zero at the origin).

I found that a gain of zero results in the damping value of .785 which is as close as I can get to 0 .707, the value we want. A gain of zero means a PID=0. This is bad news b/c my system won't reach the desired set points without a controller.

My advisor said to find the gain plotting the CL...but I also tried the OL which is what I thought was correct for RL. Anyway, I was able to get a damping value of .707 this way.

Am I using the sisotool incorrectly or should I have been plotting the OL the whole time? The gain I found in the sisotool would be my new Kp, right?

[Arkadiy Turevskiy]

You always work with open loop in root locus.
so just do

Post by Susan

C=(1+Td*s +1/(Ti*s); assume Kp=1
OL=C*P; %P is your plant
sisotool(OL)

use root locus plot in SISO Tool to find the gain that gives you good design. This is your Kp.

Post by Susan
I changed my PID to
s=tf('s')
Contr_Kp_Ti_Td = Kp
I plotted the CL loop TF with unity feedback where the OL = Contr_Kp_Ti_Td*Plant*Ki (where Ki is an additional integrator to cancel the zero at the origin).
I found that a gain of zero results in the damping value of .785 which is as close as I can get to 0 .707, the value we want. A gain of zero means a PID=0. This is bad news b/c my system won't reach the desired set points without a controller.
My advisor said to find the gain plotting the CL...but I also tried the OL which is what I thought was correct for RL. Anyway, I was able to get a damping value of .707 this way.
Am I using the sisotool incorrectly or should I have been plotting the OL the whole time? The gain I found in the sisotool would be my new Kp, right?