Please demonstrate how to use the PLECS simulation software to design a PD controller for the following buck$-$boost converter.

Use PLECS simulation software to create the bode plot of the G$\_$vd $($control$-$to$-$output transfer function$)$for the Buck$-$Boost converter described below.

Use the following parameters:

$($a$)$Input Voltage $=12$V

$($b$)$Output Voltage $=5$V

$($c$)$Switching Frequency $=300$kHz

$($d$)$Inductance $=50$H

$($e$)$Resistance in series with inductance $=1$m$$

$($f$)$Input Capacitance $=100$F

$($g$)$Output Capacitance $=100$F

$($h$)$Resistance in series with input capacitance $=1$m$$

$($i$)$Resistance in series with output capacitance $=1$m$$

$($j$)$MOSFET with body diode drain to source on resistance $=5$m$$

$($k$)$Load current: i$)10$A ii$)30$A

Change Output Voltage $=15$V$.$Use PLECS to create the bode plot of the G$\_$vd $($control$-$to$-$output transfer function$)$for the Buck$-$Boost converter.

Design a Proportional Derivative compensator transfer function for the Buck$-$Boost converter described by the bode plots of the G$\_$vd $($control$-$to$-$output transfer functions$)$above$.$

Meet the following requirements:

$($a$)$Crossover frequency at $30$kHz

$($b$)$Phase margin at $50$

The construction of the base buck$-$boost converter circuit in the software should look as follows: