{"id":1517,"date":"2025-12-08T08:02:45","date_gmt":"2025-12-08T07:02:45","guid":{"rendered":"https:\/\/control-advent.com\/?p=1517"},"modified":"2025-12-08T08:02:46","modified_gmt":"2025-12-08T07:02:46","slug":"08-will-the-elf-by-elf-sweetness-regulation-work-as-planned","status":"publish","type":"post","link":"https:\/\/control-advent.com\/?p=1517","title":{"rendered":"08 &#8211; Will  the Elf-by-Elf sweetness regulation work as planned?"},"content":{"rendered":"\n<p>Santa wants to upgrade his legendary Christmas Hot Cocoa Boiler so it can keep up when he changes his mind \u2014 which he often does \u2014 about how sweet the cocoa should be.<\/p>\n\n\n\n<p>To help him, the elves designed a clever new system where sweetness no longer changes in a poof of magic, but slowly drifts up or down thanks to:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A set of <strong>chocolate-brown<\/strong> levers &#8211; pulling one will make sweetness creep upward by 1 unit per minute;<br><\/li>\n\n\n\n<li>A set of <strong>snow-white<\/strong> levers &#8211; pulling one will make sweetness drift downward by 1 unit per minute.<\/li>\n<\/ul>\n\n\n\n<p>In the proposed system, pulling two identical levers will make sweetness change twice as fast (i.e., 2 units per minute). If instead at any moment a brown-lever elf and a white-lever elf are both pulling, their actions <strong>cancel<\/strong>, and both elves step aside to go drinking a ginger ale.<\/p>\n\n\n\n<p>And when &amp; how shall an elf decide to do something? The proposal is that every minute, a new elf arrives and decides what to do based on the average sweetness of the previous minute:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If the cocoa was <strong>too bland<\/strong>, the elf pulls one chocolate-brown lever.<\/li>\n\n\n\n<li>If it was <strong>too sweet<\/strong>, the elf pulls one snow-white lever.<\/li>\n<\/ul>\n\n\n\n<p>Santa is happy, but you are worried that this strategy may hide a serious problem, especially when Santa suddenly asks for a sweeter cocoa. <strong>Which one?<\/strong><\/p>\n\n\n\n<p>a. \ud83c\udf6b\ud83d\ude80\ud83e\uddca <em>Watch out!<\/em><em><br><\/em>If Santa asks for a sweeter cocoa, the system could run away and push sweetness all the way to its maximum \u2014 and get stuck there forever!<\/p>\n\n\n\n<p>b. \u2615\ud83c\udfa2\ud83d\udcc8 <em>Watch out!<\/em><em><br><\/em>If Santa asks for a sweeter cocoa, the sweetness may shoot too high at first and overshoot the new level before settling.<\/p>\n\n\n\n<p>c. \ud83e\udddd\u200d\u2642\ufe0f\ud83d\udd25\u2699\ufe0f <em>Watch out!<\/em><em><br><\/em>If Santa asks for a sweeter cocoa right when a new elf arrives, the poor machine might panic, overheat, and jingle itself to pieces!<\/p>\n\n\n\n<p>d. \u2744\ufe0f\u23f3\u2615 <em>Watch out!<\/em><em><br><\/em>If Santa asks for a sweeter cocoa, sweetness might briefly drift downward first \u2014 because a white-lever elf might react before any brown-lever elf jumps in.<\/p>\n\n\n\n<p>e. \ud83e\udddd\ud83c\udfa7\u2744\ufe0f Watch out!<strong><br><\/strong>Tiny random fluctuations in sweetness levels when the elf arrives might confuse the arriving elves, making them pull the wrong lever again and again.<\/p>\n\n\n\n<p>f. \ud83c\udf85\ud83c\udf6a\ud83e\udd2a Watch out!<\/p>\n\n\n\n<p>If Santa tastes too many test samples, he might lose his sense of sweetness entirely and give the elves completely contradictory commands!<\/p>\n\n\n<div class='bootstrap-yop yop-poll-mc'>\n\t\t\t\t\t\t\t<div class=\"basic-yop-poll-container\" style=\"background-color:#b70004; border:0px; border-style:solid; border-color:#b70004; border-radius:0px; padding:10px 10px;\" data-id=\"45\" data-temp=\"basic\" data-skin=\"minimal\" data-cscheme=\"black\" data-cap=\"0\" data-access=\"wordpress\" data-tid=\"\" data-uid=\"e68ba4a8fee1b00b3ab89adc3c30fcce\" data-pid=\"1517\" data-resdet=\"percentages\" data-show-results-to=\"\" data-show-results-moment=\"never\" data-show-results-only=\"false\" data-show-message=\"true\" data-show-results-as=\"bar\" data-sort-results-by=\"as-defined\" data-sort-results-rule=\"asc\"data-is-ended=\"0\" data-gdpr=\"no\" data-gdpr-sol=\"consent\" data-css=\".basic-yop-poll-container[data-uid] .basic-vote { text-align: center; }\" data-counter=\"0\" data-load-with=\"1\" data-notification-section=\"top\"><div class=\"row\"><div class=\"col-md-12\"><div class=\"basic-inner\"><div class=\"basic-message hide\" style=\"border-left: 10px solid #008000; padding: 0px 10px;\" data-error=\"#ff0000\" data-success=\"#008000\"><p class=\"basic-message-text\" style=\"color:#000000; 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font-size:14px; font-weight:normal; text-align:center;\">Choose an option:<\/div><ul class=\"basic-answers basic-h-answers\"><li class=\"basic-answer col-xs-6 col-sm-6 col-md-2\" style=\"padding:0px 0px;\" data-id=\"381\" data-type=\"text\" data-vn=\"5\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[381]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[381]\" name=\"answer[45]\" value=\"381\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">a<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 col-md-2\" style=\"padding:0px 0px;\" data-id=\"382\" data-type=\"text\" data-vn=\"29\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[382]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[382]\" name=\"answer[45]\" value=\"382\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">b<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 col-md-2\" style=\"padding:0px 0px;\" data-id=\"383\" data-type=\"text\" data-vn=\"0\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[383]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[383]\" name=\"answer[45]\" value=\"383\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">c<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 col-md-2\" style=\"padding:0px 0px;\" data-id=\"387\" data-type=\"text\" data-vn=\"3\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[387]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[387]\" name=\"answer[45]\" value=\"387\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">d<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 col-md-2\" style=\"padding:0px 0px;\" data-id=\"388\" data-type=\"text\" data-vn=\"1\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[388]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[388]\" name=\"answer[45]\" value=\"388\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; font-size: 14px; font-weight: normal;\" tabindex=\"0\">e<\/span><\/label><\/div><\/li><li class=\"basic-answer col-xs-6 col-sm-6 col-md-2\" style=\"padding:0px 0px;\" data-id=\"390\" data-type=\"text\" data-vn=\"3\" data-color=\"#000000\" data-make-link=\"no\" data-link=\"\"><div class=\"basic-answer-content basic-text-horizontal\"><label for=\"answer[390]\" class=\"basic-answer-label\"><input type=\"radio\" id=\"answer[390]\" name=\"answer[45]\" value=\"390\" autocomplete=\"off\"><span class=\"basic-text\" style=\"color: #ffffff; 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Register here<\/a><\/p><p><a href=\"https:\/\/control-advent.com\/wp-login.php?action=lostpassword\" target=\"_blank\">Forgot password<\/a><\/p><\/div><\/div><\/div><\/div><\/div><\/div><\/div><\/div>\n\t\t\t\t\t\t<\/div>\n\n\n\n<p><strong>Related control topic: integral control<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Santa wants to upgrade his legendary Christmas Hot Cocoa Boiler so it can keep up when he changes his mind \u2014 which he often does \u2014 about how sweet the cocoa should be. To help him, the elves designed a &hellip; <span class=\"more-link\"><a href=\"https:\/\/control-advent.com\/?p=1517\" class=\"readmore\">Continue reading<span class=\"screen-reader-text\">08 &#8211; Will  the Elf-by-Elf sweetness regulation work as planned?<\/span><\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":1519,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[111],"class_list":["post-1517","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-english","tag-2025-en"],"_links":{"self":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts\/1517","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1517"}],"version-history":[{"count":1,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts\/1517\/revisions"}],"predecessor-version":[{"id":1518,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/posts\/1517\/revisions\/1518"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=\/wp\/v2\/media\/1519"}],"wp:attachment":[{"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1517"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1517"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/control-advent.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1517"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}