Explain to me in pseudo-code what needs to be done, and how it needs to be done in detail. Do that, and the algorithm can be written in Perl.

First, we need to give the script the name of the file with the minimal EDR. Then, we can code this before the foreach loop

# get minimal EDR filename from commandline
my $minEDRfile = shift;
my $MinEDRstr = `grep -A37 "EDR alpha" $f | tail -n35|awk "{print \\\$
+4+\\\$5}"`;
        my @MinEDRvars = split(/\n/,$MinEDRstr);
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Then, inside the loop, at the print, we add an extra column to the sprintf statement:

# Print the outputs 
foreach my $i(0..$NU-1){
  print F sprintf("%8.3E %12.6E %12.6E %12.6E\n",
    $R,$Uvars[$i],$EDRvars[$i], 
    $EDRvars[$i] - $MinEDRvars[$i]
  );
}
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And so, we call it:

./process.pl min_EDR_filename.log