By using a function cost, Design a Model Predictive Controller $($MPC$)$ for a simple $2$nd$-$order system with the transfer function

$G(s)=\frac{7}{(S+3)(S+9)}$

Use MATLAB to simulate the closed$-$loop response of the system with the MPC controller $($don$\text{'}$t use mpc command in matlab$).$ Your design should include the selection of sampling time and tuning parameters for the MPC$.$ Write reflection on the response obtained in the graph

$(20$ Marks$)$