The following transfer function is out of control:

$\backslash [$

$\backslash$frac$\{10\}\{$s$^\{2\}+11\}$

$\backslash ]$

Explain why the system is out of control, and describe what the shape of the step response would be$.$

Write out the transfer function $\backslash (\backslash$mathrm$\{$Q$\}(\backslash$mathrm$\{$s$\})\backslash )$ of a system with one negative feedback loop with a feedback transfer function of $\backslash (\backslash$mathrm$\{$G$\}(\backslash$mathrm$\{$s$\})\backslash ).$

Design the simplest feedback transfer function $\backslash ($ G$($s$)\backslash )$ to make $\backslash ($ Q$($s$)\backslash )$ stable.

What are the conditions on the constants of $\backslash (\backslash$mathrm$\{$G$\}(\backslash$mathrm$\{$s$\})\backslash )$ that will ensure that the system is in control?

Show all your work in the PDF$.$ There is nothing to enter into MOM. If your work is not shown, you will not get credit even if the answers are correct.

You will be graded on the following:

$1.$ Your explanation must include the value of the pole$/$poles that are causing the issue. You must describe what the time domain response is like to justify that the system is out of control. Hint: Use quadratic equation.

$2.\backslash (\backslash$mathrm$\{$G$\}(\backslash$mathrm$\{$s$\})\backslash )$ must be correct.

$3.$ Conditions on $\backslash (\backslash$mathrm$\{$G$\}(\backslash$mathrm$\{$s$\})\backslash )$ must be correct. $\backslash (\backslash$mathrm$\{$G$\}(\backslash$mathrm$\{$s$\})\backslash )$ must be correct for this part to be graded.