これを置く方法:
WWW_ROOT."images".DS."uploaded_files".DS."research".DS. $pdfname;
この中に
exec("convert -scale 1500x1000 " . escapeshellarg(BASE_URL."app/webroot/images/uploaded_files/research/${dirname}/img%d_".$pdfname.".png"));
BASE_URLを置き換えます。"app/webroot/images/uploaded_files/research/${dirname}/