Design a controller for a temperature control lab arduino model, the input must be voltage and the output temperature, the set room is $23$C and the Temperature that must reach is $40$C$,$ must raise quickly without overshoot and considers constants such as the gain of the transistor and it$$s emissivity in reference to this model script in Matlab:

close all; clear all; clc

$\%$ include tclab.m for initialization

tclab;

disp$(\text{'}$Test Heater $1\text{'})$

disp$(\text{'}$LED Indicates Temperature'$)$

figure$(1)$

t$1$s $=[]$;

t$2$s $=[]$;

h$1$s $=[]$;

h$2$s $=[]$;

$\%$ initial heater values

ht$1=0$;

ht$2=0$;

h$1($ht$1)$;

h$2($ht$2)$;

for i $=1$:$399$

tic;

if i$==5$

disp$(\text{'}$Turn on heater $1$ to $60\%\text{'})$

ht$1=60$;

h$1($ht$1)$;

end

if i$==105$

disp$(\text{'}$Turn off heater $1\text{'})$

ht$1=0$;

h$1($ht$1)$;

end

if i$==150$

disp$(\text{'}$Turn on heater $2$ to $80\%\text{'})$

ht$2=80$;

h$2($ht$2)$;

end

if i$==205$

disp$(\text{'}$Turn off heaters'$)$

ht$1=0$;

ht$2=0$;

h$1($ht$1)$;

h$2($ht$2)$;

end

$\%$ read temperatures

t$1=$ T$1$C$()$;

t$2=$ T$2$C$()$;

$\%$ LED brightness

brightness$1=($t$1-30)/50\mathrm{.}0$; $\%<30$degC off, $>100$degC full brightness

brightness$2=($t$2-30)/50\mathrm{.}0$; $\%<30$degC off, $>100$degC full brightness

brightness $=$ max$($brightness$1,$brightness$2)$;

brightness $=$ max$(0,$min$(1,$brightness$))$; $\%$ limit $0-1$

led$($brightness$)$;

$\%$ plot heater and temperature data

h$1$s $=[$h$1$s$,$ht$1]$;

h$2$s $=[$h$2$s$,$ht$2]$;

t$1$s $=[$t$1$s$,$t$1]$;

t$2$s $=[$t$2$s$,$t$2]$;

n $=$ length$($t$1$s$)$;

time $=$ linspace$(0,$n$+1,$n$)$;

clf

subplot$(2,1,1)$

plot$($time$,$t$1$s$,\text{'}$r$.\text{'},$'MarkerSize',$10)$;

hold on

plot$($time$,$t$2$s$,\text{'}$b$.\text{'},$'MarkerSize',$10)$;

ylabel$(\text{'}$Temperature $($degC$)\text{'})$

legend$(\text{'}$Temperature $1\text{'},$'Temperature $2\text{'},$'Location','NorthWest'$)$

and also this matlab script:

function dTdt $=$ arduino$\_$ode$($time$,$T$,$heater$)$

$\%$ mass

m $=0\mathrm{.}001$; $\%$ kg $(2$ gm$)$

$\%$ heat transfer coefficient

h $=200$; $\%$ W$/$m$^2-$K

$\%$ surface area

A $=2/100^2$; $\%$ m$^2$

$\%$ heater input

alpha $=0\mathrm{.}022$; $\%$ W$/($heater input$)$

$\%$ heat capacity

Cp $=4900\mathrm{.}0$; $\%$ J$/$kg$-$K

$\%$ approximate time constant

$\%$tau $=$ m$*$Cp$/($h$*$A$)$;

$\%$disp$([\text{'}$Time constant: $\text{'}$ num$2$str$($tau$)])$

$\%$ ambient temperature

Ta $=23+273\mathrm{.}15$; $\%$ K

heater $=100$;

dTdt $=($h$*$A $*($Ta $-$ T$)+$ alpha $*$ heater$)/($m$*$Cp$)$;

end

subplot$(2,1,2)$

plot$($time$,$h$1$s$,\text{'}$r$-\text{'},$'LineWidth',$2)$;

hold on

plot$($time$,$h$2$s$,\text{'}$b$--\text{'},$'LineWidth',$2)$;

ylabel$(\text{'}$Heater $(0-5\mathrm{.}5$ V$)\text{'})$

xlabel$(\text{'}$Time $($sec$)\text{'})$

legend$(\text{'}$Heater $1\text{'},$'Heater $2\text{'},$'Location','NorthWest'$)$

drawnow;

t $=$ toc;

pause$($max$(0\mathrm{.}01,1\mathrm{.}0-$t$))$

end

disp$(\text{'}$Turn off heaters'$)$

h$1(0)$;

h$2(0)$;

disp$(\text{'}$Heater Test Complete'$)$