represented by the dynamic equation:

$m{l}^2{}^{}=-$mglsin$-b{}^{}+u$

Into a linear parameter$-$varying system given by:

$m{l}^2{}^{}=-mgl{f}_{sin}()-b{}^{}+u$

where $f_{sin}()\frac{sin()}{}$ with $f_{sin}()in[-1,1].$ Using this LPV system description, design a gain$-$scheduled control system $($for a grid of $in[\frac{-}{2},\frac{}{2}])$ to place the poles of all your LTI systems at $s_{1,2}=-4+-4j.$ Implement your solution in the Simulink model provided using the $1$D$-$Table lookups provided. In that model the parameters are defined as $m=2kg,b=\mathrm{.}1,l=1m,g=9\mathrm{.}81\frac{m}{s^2}.$ Note: The Simulink model compares two responses: one is a large angle initial condition, the other is $\frac{1}{100}$ of that. The gain scheduled control system should show a consistent response between the two initial conditions.