"Stability analysis" in PID controller design

Thread Starter


Joined Feb 5, 2010
Hello everyone, I am new on here. New to be on this forum.

I have to do mini-project for Control and Robotic System class. I have to design PID controller, from one problem, and then simulate it in simulink.

On part where it ask to do PID controller design, it states "stability analysis". What exactly I have to do on that part? State when, under what conditions, the system is be stable?


Joined Feb 4, 2008
For, example state the values of Kp, Kd and Ki which make the system stable at a step input change.

Thread Starter


Joined Feb 5, 2010
Thanks... I have another question..

So, I need to have ts equal 3 seconds or less. I set it equal to 2.95 sec.
then I find wn (4/(zts)) and later C1=2zwn and C2=wn^2
(While z = 0.9)

For Kp I get something like 0.689
Kd is 0.2259
Ki I set to 0 (for PD controller)

However.. when I simulate it in Simulink.. it seems like that a limit is applies on vertical axis, not horizontal one. Horizontal being ts.

I tried different values for z and ts and all doing the same.

Can someone help me? Why I am getting such results?


Joined Mar 6, 2009
It would be useful if you re-phrased the problem in a more systematic manner and gave a diagram of the system you are trying to control or stabilise. Your design goal is not clear.