Plot step response w/ smallest rise time, dependant on Kp & Kd constraints, assuming lowest natural freq.

Hi all,

So I am designing a PD controller and need to plot the following system taking into account the following constraints.

Transfer function -> -1 / -s^2 + 1*s + 2

Damping ratio -> 0.4-0.6

Kp & Kd constraints ->

My question involves the required code to plot the step response with the smallest rise time when Kp & Kd are selected from the area shown on the graph, whilst assuming the lowest natural frequency.

Following are two sections of code I have attempted and the results I produced:

This graph suggests that I need pole placement as described here:

How would I apply this proper pole placement within my code to allow for the correct step response to be plotted?

Thanks all!

Answer 1

[Sebastian Castro]

To get the rise time for your system, you can always use the stepinfo function. The output of this function will, among other things, return your rise time. So, for different systems, you can record that rise time:

>> s = stepinfo(sys)
>> tr = s.RiseTime;

Also, you can do pole placement with the place function.

- Sebastian