# Step response of feedback system

We have a feedback system F(s) as in this figure: and this is the step response of G(s): and H=10.

F(s): We got the root locus of the system F(s) as this: then we determined the gain at marginal stability: which is equal to 2.5.

Then, we made H = 2.57 (slightly larger than 2.5) and we obtained the step response of the new system Fh(s). Here is it with the step response of the original system F(s): Then, we made H = 2.43 (slightly lower than 2.5) and we obtained the step response of the new system Fl(s). Here is it with the step response of the original system F(s): My questions:

• What can we know from the step response plot of G(s)?
• What can we know from the step response plot of F(s)?
• When we changed the gain to 2.57, how did the system F(s) change? What can we conclude by comparing the step responses of F(s) and Fh(s)?
• When we changed the gain to 2.43, how did the system F(s) change? What can we conclude by comparing the step responses of F(s) and Fl(s)?
• What are your answers? – Chu Nov 3 '15 at 8:50
• This question and MATLAB outputs are awfully homeworky looking – Daniel Nov 3 '15 at 8:55
• 1. G(s) unstable. 2. It's overdamped and F(s) is stable. 3. Fh(s) becomes underdamped. 4. Fl(s) becomes unstable. I don't know if my answers are correct. Even if they are, I need some details and explanations. – ammar Nov 3 '15 at 8:55
• Give me a link where I can read about step responses and stability because I've searched but found no good results. – ammar Nov 3 '15 at 9:52
• Over 20 seconds to respond to a step change (graph 1)? – Andy aka Nov 3 '15 at 10:29