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We have a feedback system F(s) as in this figure:

G(s)

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)?
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  • \$\begingroup\$ What are your answers? \$\endgroup\$ – Chu Nov 3 '15 at 8:50
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    \$\begingroup\$ This question and MATLAB outputs are awfully homeworky looking \$\endgroup\$ – Daniel Nov 3 '15 at 8:55
  • \$\begingroup\$ 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. \$\endgroup\$ – ammar Nov 3 '15 at 8:55
  • \$\begingroup\$ Give me a link where I can read about step responses and stability because I've searched but found no good results. \$\endgroup\$ – ammar Nov 3 '15 at 9:52
  • \$\begingroup\$ Over 20 seconds to respond to a step change (graph 1)? \$\endgroup\$ – Andy aka Nov 3 '15 at 10:29
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  • G(s) is unstable because the step-response doesn't have a steady-state value. It goes to infinity.
  • F(s) is stable since its step response has a steady-state value near 0.1. It's underdamped response.
  • Fh(s) is stable since its step response has a steady-state value near 0.2. It's underdamped response with more oscillations than F(s).
  • Fl(s) is unstable because it doesn't have a steady-state value. It has a very large oscillations that start after some time.
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