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 a steady value.
To fix this problem, the elves decided to try a more sophisticated and magical solution: the Pinecone–Icicle–Dancing (PID) controller. It contains three parts:
- Pinecone (P): The magical pinecone reacts to the difference between the desired pressure and the current pressure. It amplifies or attenuates this difference by a factor K.
- Icicle (I): The icicle grows or melts depending on the same pressure difference.
The time constant Ti determines how fast this happens: a larger Ti means the icicle grows more slowly. - Dancing elves (D): The dancing elves react to how fast the pressure is changing.
The time constant Td determines how strongly they react to quick changes: a larger Td means the elves try harder to anticipate where the pressure is heading.
The controller output is the sum of the effects of the pinecone, the icicle, and the dancing elves.
The elves enthusiastically replace the old on/off controller with this new PID controller and switch the system back to automatic mode. To their great disappointment, the vapor pressure is still oscillating!
Assume that:
- the pressure sensor is clean (not noisy), and
- the oscillations are caused by the controller reacting too aggressively.
The elves now wonder whether adjusting the pinecone gain K, the icicle growing time Ti, and the dancing time Td could calm things down.
How should these parameters be modified to decrease the oscillations?
a. 📈🌲⏱️ Increase K, increase Ti, and increase Td.
b. 📈🌲⬇️ Increase K, increase Ti, and decrease Td.
c. 📈❄️⏱️ Increase K, decrease Ti, and increase Td.
d. 📈❄️⬇️ Increase K, decrease Ti, and decrease Td.
e. 📉🌲⏱️ Decrease K, increase Ti, and increase Td.
f. 📉🌲⬇️ Decrease K, increase Ti, and decrease Td.
g. 📉❄️⏱️ Decrease K, decrease Ti, and increase Td.
h. 📉❄️⬇️ Decrease K, decrease Ti, and decrease Td.
i. 🤷♂️🔄❌ None of the above: if a system oscillates, there is no way to stop it.
Related control theory topic: PID controller