Understanding PID controllers

Xiao Ming was given such a task: there is a water tank that is leaking, and the rate of leakage is variable; however, it is necessary to keep the water level at a certain height. Whenever the water level drops below this required level, water must be added to the tank. At first, Xiao Ming used a ladle to add water; the faucet was about ten meters away from the tank, so he had to make several trips to fill it up. So he switched to using a bucket – one bucket at a time – which reduced the number of trips needed and increased the speed at which water was added. However, the tank overflowed several times, causing his shoes to get wet accidentally. Xiao Ming then thought of another solution: instead of using a ladle or a bucket, he would use a basin. After trying this method a few times, he found that it worked perfectly – he didn’t have to make many trips, and the water wouldn’t overflow either. This inspection time is called the sampling period. At first, Xiao Ming used a ladle to add water; the faucet was about ten meters away from the tank, so he had to make several trips to fill it up. So he switched to using a bucket – one bucket at a time – which reduced the number of trips needed and increased the speed at which water was added. However, the tank overflowed several times, causing his shoes to get wet accidentally. Xiao Ming then thought of another solution: instead of using a ladle or a bucket, he would use a basin. After trying this method a few times, he found that it worked perfectly – he didn’t have to make many trips, and the water wouldn’t overflow either. The size of this water addition tool is called the proportionality coefficient. Xiaoming noticed that although the water didn’t overflow when added in excess, it sometimes rose to a level significantly higher than the desired height, still posing a risk of wetting the shoes. He came up with another idea: he installed a funnel on the water tank, so that instead of pouring water directly into the tank, it was poured into the funnel and added slowly. This solves the problem of overflow, but the water addition rate slows down again, and sometimes it can’t keep up with the rate of leakage. So he tried using funnels of different sizes to control the water addition rate, and finally found a funnel that satisfied him. The time of the funnel is called the integration time. Xiao Ming was finally able to catch his breath, but the requirements for the task suddenly became stricter. The timeliness of water level control had to be improved; once the water level dropped too low, water had to be added immediately to the required level, and it couldn’t be increased by too much, otherwise no payment would be given. Xiao Ming is in trouble again! So he racked his brains again and finally came up with a solution: keep a basin of spare water nearby. Once the water level dropped, water could be poured in directly from the basin, without going through a funnel. This ensured timely refilling, but the water level might sometimes become too high. He is asking to drill a hole a little above the water level, and then connect a pipe to the spare bucket below, so that the excess water can flow out through the hole above. The rate at which this water leaks is called the differential time. In the story, Xiaoming’s experiments are carried out step by step independently, but in reality, the tool used for adding water, the diameter of the funnel, and the size of the overflow hole all affect the speed at which water is added as well as the amount of overshoot in water level. After conducting subsequent experiments, it is often necessary to adjust the results of previous experiments. A person uses PID control to pour water from a kettle into a cup that has a scale marked at half full, then stops; set value: the half-full mark on the cup ； Actual value: The actual amount of water in the cup ； Output value: Water volume poured out by the kettle and water volume scooped out by the cup ； Measurement: Human eye (equivalent to a sensor)
Subject: Human
Action being performed: Pouring water
Reverse action: Scooping water

Let’s go take a look at the PID control equations. Continuous, discrete. . . There are probably 1 million papers; if you can understand 2 of them, that’s good. If not, don’t ask – asking is pointless and wastes effort. . . If you know how to use it, then great. . . If you know how to use it, just gather 3 numbers; make them up however you can. . . Now I understand it; I can write the PID algorithm myself, so why go and use someone else’s pre-written PID program? :lol