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# Designing with Root Locus

Asked by Jorge_Luis Quintero on 1 Jul 2012

Hi all. Im very confused right now trying to find the answers for the problem below:

```R-----(sum block)-------(s+a/s+20)----(20/s*3+8s*2-18s+20)------>C
```
`                                                                                                |-----------------------(K/s+b)---------------|`
`        The feedback  block is (K/s+b) and is negative feedback`
```Plot the root locus for a = 1, b = 20 Determine the range of K for the system is stable. Graph as the settling time varies and the rate of overshoot for the set of K values ​​that make the system stable. Plot the response to a step input and then to a unit ramp function of time. Plot the error function versus time and determine the steady-state error for both inputs.
```

So when im trying to solve this problems, Im doing as matlab says in http://www.mathworks.com/help/toolbox/control/ref/rlocus.html so My system becomes sys=(s+a/s+20)(20/s*3+8s*2-18s+20)(1/s+b).

I dont know for sure if this is correct, so i hope someone could help me here in this problem, and besides of this, how could i get the error function versus time and the steady-state error for both inputs ( step and ramp).

## 1 Comment

Arkadiy Turevskiy on 3 Jul 2012

What are you confused about? You need to be more specific.