With this script you may see, why your Dyson Pure Hot and Cool will not connect with MQTT. My is not 3.1.1 compatible

Mqtt311Client.php

<?php
$errNo = 0;
$errMsg = '';

// throws WARNING if hostname is invalid. Add @.
if ($res = @fsockopen($ipAddress, 1883, $errNo, $errMsg, 10)) {
    //var_dump(chr(63>>8));
    //var_dump(bin2hex('11110000'));

    $packetType = '1';
    $flag = '0';
    $remainingChars = '00';
    $fixedHeader = $packetType . $flag . $remainingChars;

    // variable header 10 bytes
    $msb = '00';
    $lsb = '04';
    $mByte = dechex(ord('M'));
    $qByte = dechex(ord('Q'));
    $tByte = dechex(ord('T')); // twice
    $protocollLevel = '04'; // Always 4

    $useUsername = '0';
    $usePassword = '0';
    $willRetain = '0';
    $willQos = '00'; // 0, 1, 2, but never 3
    $willFlag = '0'; // if 0 QoS and Retain must be 0, too
    $cleanSession = '1'; // 0 = store session for reconnect; 1 = always create new connection
    $keepAliveMsb = '00'; // 0 = deactivate
    $keepAliveLsb = '00'; // 0 = deactivate

    $connectFlag = dechex(bindec(
        $useUsername . $usePassword . $willRetain . $willQos . $willFlag . $cleanSession . '0'
    ));

    $variableHeader = $msb . $lsb . $mByte . $qByte . $tByte . $tByte . $protocollLevel . $connectFlag . $keepAliveMsb . $keepAliveLsb;

    $client = [];
    $client[] = dechex(ord('s'));
    $client[] = dechex(ord('f'));
    $client[] = dechex(ord('1'));
    $client[] = dechex(ord('7'));
    $client[] = dechex(ord('0'));
    $client[] = dechex(ord('1'));
    $client[] = dechex(ord('7'));
    $client[] = dechex(ord('9'));
    $clientId = implode('', $client);

    $payLoad = dechex(count($client)) . $clientId;

    fwrite($res, hex2bin($fixedHeader . $variableHeader . $payLoad));
    //$disconnect = hex2bin('F0');
    //fwrite($res, $disconnect);

    while (!feof($res)) {
        $result = fgets($res, 1024);
        $splitResult = str_split(bin2hex($result));
        if (
            $splitResult[0] === dechex(2)
            && $splitResult[1] === dechex(0)
            && $splitResult[2] . $splitResult[3] === '02'
        ) {
            var_dump('CONNACK received');
        } else {
            var_dump('Disconnected');
        }

        if ($splitResult[4] . $splitResult[5] === '00') {
            var_dump('No Session');
        } else {
            var_dump('Session created');
        }

        switch ($splitResult[6] . $splitResult[7]) {
            case '00':
                var_dump('Connection accepted');
                break;
            case '01':
                var_dump('The Server does not support the level of the MQTT protocol requested by the Client');
                break;
            case '02':
                var_dump('The Client identifier is correct UTF-8 but not allowed by the Server');
                break;
            case '03':
                var_dump('The Network Connection has been made but the MQTT service is unavailable');
                break;
            case '04':
                var_dump('The data in the user name or password is malformed');
                break;
            case '05':
                var_dump('The Client is not authorized to connect');
                break;
        }

        printf('%b', $result);
    }
    fclose($res);
} else {
    var_dump($errNo);
    var_dump($errMsg);
}
die();