# Help with root locus

1. Mar 7, 2006

### formulajoe

I had to use state-variable feedback to design a position control system for a motor. I have to design the controller using root locus methods.
The gain that is varied is located in the feedback loop as shown in the picture.
I am completely lost as to how to generate a root locus with the gain in the feedback loop.
Can anybody give me a general form to get into so I can draw the root locus?

File size:
58.8 KB
Views:
117
2. Mar 7, 2006

### Corneo

Let the output of the summer going into G(s) be called E(s). Y(s) is then E(s)G(s). But E(s) = V(s)-K(s+1)Y(s). So

$$Y(s) = E(s)G(s) = [V(s) - K(s+1)Y(s)] G(s)$$
$$Y(s) = \frac {E(s)G(s)}{1 + K(s+1)G(s)}$$

Then you draw the root locus plot of G(s) (s+1).