Note: You may only use Matlab to work on or solve this problem $($Simulink is not allowed$).$ Neither you, nor your selected method, can add any additional feedback elements or loops.

Part A $(75$ points$)$ Given the following plant and feedback element blocks, connected in a standard, negative feedback loop configuration, design a controller that will cause the system to meet as many of the performance goals listed in table $1$ as possible. Solutions that meet all performance goals are possible.

Plant:

$\{$: $1/($s$+4)($s$+5)$

Feedback Element:

$\{\begin{array}{c}\text{:}\frac{5}{s+10}\end{array}$

Table $1$: Performance goals for project A design.

$\backslash$table$[[$Parameter$,$Performance Target or Criterion$],[$Steady State Gain,$1],[$Steady State Error,$\mathrm{.}005][10\%-90\%$ Rise time, seconds$][2\%$ Settling Time, seconds$][$Maximum Overshoot Value, $1\mathrm{.}18]$

Part B $(25$ points$)$ stabilize the following unstable plant transfer function using a controller with non$-$negative coefficients in the numerator and deniminator. Use same feedback element as in Part A$.$ You only have to demonstrate a stable system; no other performance criteria apply, however up to $5$ points of extra credit will be applied for solutions that meet additional performance goals as listed below.

Plant: $(1/($s$-5)($s$+2)$

performance goals for project B design.

$[$Steady State Gain, $5][$Steady State Error, Rise Time, Seconds$][2\%$ Settling Time, Seconds$][$Maximum Overshoot Percentage,