Control Advent Calendar

a. 🤷‍♂️🎄🗺️ What do I know?! I thought this advent calendar is about control and not geography? b. 📐🧠🧭 Of course, NP = Not stable Pole and SP = Stable Pole c. 🌍🔥🧊 Due to global warming, the ice at the north pole is melting (unstable), whereas Antarctica is a continent and cannot melt away (stable). d. 📉📈⚙️ Of…

In Santa’s workshop, the gingerbread conveyor belt chugged along with the serenity of a sleigh ride on fresh snow, carrying neat rows of biscuits to the decorating station. This smooth operation was the merit of a Pinecone–Icicle (PI) controller (very similar to the Pinecone–Icicle–Dancing (PID) controller used for controlling the vapour pressure, see 16 December,…

In the Christmas bakery, the elves are busy preparing different goods including yummy Christmas cookies. The production is sectioned into different work areas and in the baking and oven area the elves are tasked with baking the cookies being delivered from the dough preparation and cookie cutting area. The arrival of the trays is random…

Only 4 days left, and a digital Christmas countdown clock was designed very thoroughly by an elf. Starting from today, it digitally generates the sequence x1x2 = 11  →  10  →  01  →  00 with a sampling time of 24 hours. Knowing discrete-time state-space models from control theory, she implemented the clock as x1(k+1) = f1(x1(k),x2(k)), x2(k+1)= f2(x1(k),x2(k)). With some AI, the clock…

Santa is testing the sweetness-control dynamics of his magical Hot Cocoa Machine. To observe its behaviour, the elves run a long enchanted Sweetness Testing Strip: the machine will push out a strip of paper at a constant speed, and plot on it the sweetness level that the machine produces, so that the sweetness dynamics get…

Christmas is coming soon, which puts everyone into high gear. Santa and his elves are preparing everything for their big gift-giving night. They tinker, refine and plan so that everything can run smoothly. They remember last year and how chaotic it got at the end of the night when Santa was completely exhausted and tired.…

This year, Santa’s castle is abuzz with excitement as the elves enthusiastically participate in the inaugural Christmas Contest for Gingerbread House Baking. Each elf is putting forth their unique recipe for crafting this beloved sweet decoration. These recipes include specific guidelines on adjusting the amount of grain flour in the dough [in kilograms] and the…

Remember the network at Candy-Workshop 3 of who follows whom: Keep in mind that if one elf follows another, the reverse does not necessarily apply. Also, if an elf follows another elf, it means that they take over the opinion of the elf they follow. Elf Kristian from Candy-Workshop 5 finds himself in a tricky…

In the gift factory of the North Pole, many processes use vapor pressure to work.The vapor pressure is controlled by opening and closing a valve. In the past, this valve was controlled using a simple analog on/off controller. Unfortunately, this caused sustained oscillations: the vapor pressure kept going up and down instead of settling at…

In Santa’s workshop, preparations are in full swing: gifts from all the different workshops arrive on a conveyor belt at the gift wrapping station, where the elves wrap them up. But there is a problem. When large, heavy gifts coe onto the conveyor belt, it kepps stopping. With small, light gifts, it sometimes runs too…

Santa is known for many traits such as his love of red clothing and his long white beard. A well-kept secret is that Santa’s beard grows exactly 1 cm per week. What is charming for some, however, causes extra work for others. Santa himself does not worry much about his beard – he prefers spending his…

The elves play different games during the weekends. The main aspect for them is that every rule is followed, the games are fair and everybody is having fun. Today, they agreed to play a round of “elf chess” where one steps/jumps on a tile on the giant chess board and then, one every five minutes,…

Santa’s sleigh must be taken to one of four special sleigh workshops for inspections.One of these workshops is specially designed to keep the sleigh stable – but Santa has a small problem: he has completely forgotten which one is the right one. This is not insignificant, because his sleigh must be perfectly level during inspection.…

Santa continues refining the temperature-control system of his Christmas Hot Cocoa Machine. To train the elves, he asks them to explain what feedback really means. Five enthusiastic elves step forward… with five very different answers. Which elf is actually describing correctly what feedback control is? a.❄️⚡️⏱️ Elf Frostflash – “Speed is everything.”“Feedback means reacting super fast. If…

Influencer is a new and trendy profession and for sure even elves are on social media and spread the news among themselves. At Candy-Workshop 3 there is an interesting network of who follows whom: Keep in mind that if one elf follows another, the reverse does not necessarily apply. Also, if an elf follows another…

For the annual Grand Elf Light Show, five elves are tasked with walking around the courtyard (see the map) while each holding the end of a light chain, with which they dramatically wave around in time to the music. The other end of each light chain is plugged into a socket placed at the center…

Santa wants to upgrade his legendary Christmas Hot Cocoa Boiler so it can keep up when he changes his mind — which he often does — about how sweet the cocoa should be. To help him, the elves designed a clever new system where sweetness no longer changes in a poof of magic, but slowly…

Elf Elfis is in charge of keeping a pot of warm punch cozy for the elves’ winter party. The punch is heated by placing candles under the pot. He knows that when the room temperature is 22 °C and he places one candle under the pot, the punch reaches 32 °C. Elf Merry-Linn explained that the punch…

Santa is determined to keep the temperature inside his Christmas Workshop perfectly stable. But every now and then, when someone opens the giant wooden workshop door, a cold North-Pole draft blows in and chills the room. From previous experiments, the elves now know that: The elves propose a number of different control strategies: Strategy 0…

The elves are out for a fun skating adventure! The ice rink is partly a frozen lake on the right side and partly an over-frozen meadow on the left side of the plot. (The border between the two areas is marked with a black line.) You can see the trails they skate along, with each…

Santa is building a huge gingerbread house at the North Pole, but he’s worried it might not stay standing once it’s covered in holiday decorations and delightful treats. The stability of this sweet creation depends on how many candy canes are used to support the gingerbread roof. The clever elves have discovered that they can…

It is a frosty Christmas Eve, and Santa is getting ready for his big night of delivering gifts. The sleigh is loaded, the stars are twinkling, but there is one problem – his reindeer have picked up a strange habit. Whenever he tells them to reach a specific desired speed, the reindeer would only reach…

Santa has parked his red sleigh – due to lack of time in forward direction – in a parking lot perpendicular to the road and left from the yellow Ferrari of the Easter rabbit. (It will be a mess getting old Red Nose to the other side when he’s back). After delivery of electronic devices…

This year, the North Pole has been buried under record-breaking snowfall — so much, in fact, that entire workshops briefly vanished under snowdrifts taller than Santa’s sleigh. The elves are exhausted from nonstop shovelling, the reindeer keep losing track of the landing strip, and Santa has finally admitted that things can’t continue like this. To…

The holidays are upon us, and it’s time to embrace the magic of the season! From baking warm gingerbread cookies to spreading kindness through good deeds, fetching logs for the fire, and choosing just the right holiday cards – Christmas brings cozy, joyful traditions for everyone to share. But this year, there’s a new way…