$9\mathrm{.}9$ Show a step by step simulink model build of a buck$-$boost voltage regulator. The buck$-$boost converter of Fig. $9\mathrm{.}46$ operates in the continu$-$

ous conduction mode, with the element values shown. The nominal input voltage is V$\_($s$)=48$V$,$ and it is desired to regulate the output voltage at $-15$ V $.$ Des ign the best compensator that you can, wh ich has

high crossover frequency $($but no greater than $10\%$ of the switching frequency$),$ large loop g ain over the bandwidth of the feedback loop, and phase margin of at least $52^($@$).$

Fig. $9\mathrm{.}46$ Buck$-$boost

voltage regulator system.

Problem $9\mathrm{.}9.$

show the model responses for the following problems:

$($a$)$ Specify the required value of H$.$ Sketch Bode plots of the uncompensated loop gain magnitude and phase, as well as the magnitude and phase of your proposed compensator transfer function

G$\_($c$)($s$).$ Label the important features of your plots.

$($b$)$ Construct Bode diagrams of the magnitude and phase of your compensated loop gain T$($s$),$ and also of the magn itude of the quant ities T$//(1+$T$)$ and $1//(1+$T$).$

$($c$)$ Discuss your design. What prevents y ou from further increasing the crossover frequency? How large is the loop gain at $120$ Hz $?$ Can you obtain more loop gain at $120$ Hz $?$