Ploting root locus, when the gain is in the path and not the loop

How do I go by ploting the root locus of a system when the K is located in the path and not the loop.

Matlab uses the rlocus function expecting a control system that looks like the one below.

                      +-----+
          ---->O----->| SYS |----+---->
              -|      +-----+    |
               |                 |
               |       +---+     |
               +-------| K |<----+
                       +---+

I however am looking for the root locus for a system with the gain K is in the open loop transfer function

                    +---+   +-----+
          ---->O--->| K |-->| SYS |----+---->
              -|    +---+   +-----+    |
               |                       |
               |                       |
               +-----------------------+

[FATIH GUNDOGAN]

It had been a while, but might be useful for similar questions.

Keep K=1 (dont use second argument of the rlocus function, it automatically makes K=1)

Just multiply your SYS with a constant gain

and rlocus(SYS)

Answer 1

[Fangjun Jiang]

Combine your SYS with K into a new system.

Do the root locus for the open-loop system.

If you want to do the root locus for the closed-loop system, K would be 1.

[Alan]

I'm not sure exactly what your trying to explain. I did a some research on the root locus. I found out that the root locus is dependent only on the characteristic equation. The Characteristic equation for both of the transfer function above are the same. Therefore if you use the the rlocus function as rlocus(sys,k) you should get the same plot for both either configuration.

[Fangjun Jiang]

You may be right. It has been a long time since I finished the control theory course or used root locus. All I am trying to say is that you can convert between your two diagrams.

Note that in terms of transfer function between output and input, they are different between your two diagrams.