PID refinement

What is? PID？
PID, Namely “ The proportion （proportional）、 integral （integral）、 differential （derivative）”, Is a very common control algorithm .
PID There has been a 107 It's about 20 years old .
It's not something very sacred , Everyone must have seen it PID Practical application of
Like a four-axis aircraft , Another example is the balance car ...... And the constant speed cruise of the car 、3D The temperature controller on the printer ....
It's something like this ： A physical quantity needs to be “ Stay stable ” The occasion of （ Like maintaining balance , Stable temperature 、 Speed, etc ）,PID It's going to come in handy .
So here comes the question ：
such as , I want to control one “ The heat is fast ”, Keep the temperature of a pot of water at 50℃, Such a simple task , Why use the theory of calculus .
You must be thinking ：
This is not so easy Well ~ Less than 50 Just let it heat up , Greater than 50 Power off at 90 degrees , Not to go ？ A few lines of code use Arduino Write it in minutes .
you 're right ~ In the case of low demands , It can be done ~ But！ If you put it another way , You know what the problem is ：
What if my control object is a car ？
If you want to keep the speed of the car at 50km/h Immobility , Dare you do that again .
imagine , If the car's constant speed cruise computer at a certain time to measure the speed is 45km/h. It immediately commands the engine ： Speed up ！
result , Suddenly there's a 100% Full throttle , Buzz , The car sped up to 60km/h.
At this time, the computer issued a command ： brake ！
result , Squeak ............... wow ............( Passenger vomiting )
therefore , On most occasions , use “ Switching quantity ” To control a physical quantity , It seems relatively simple and rough . occasionally , It can't be stable . Because of MCU 、 Sensors are not infinitely fast , collection 、 Control takes time .
and , The control object has inertia . For example, you unplug a heater , its “ Waste heat ”（ Thermal inertia ） It may also raise the water temperature for a little longer .
At this time , We need a kind of 『 Algorithm 』：
It can bring the physical quantity that needs to be controlled near the target
It can “ foresee ” The change trend of this quantity
It can also eliminate heat dissipation 、 Static error caused by resistance and other factors
....
therefore , Mathematicians at that time invented this enduring algorithm —— This is it. PID.
You should already know ,P,I,D There are three different regulatory effects , It can be used alone （P,I,D）, You can also use two （PI,PD）, You can also use three together （PID）.
What is the difference between these three functions ？ My guest, don 't worry , Listen to me slowly
Let's just say PID The three most basic parameters of the controller ：kP,kI,kD.
kP
P It means proportion . Its effect is most obvious , The principle is also the simplest . Let's start with this ：
The amount that needs to be controlled , For example, water temperature , There's it now 『 Current value 』, There's also what we expect 『 The target 』.
When the gap is small , Just let the heater “ airily ” Heat it up .
If for some reason , The temperature has dropped a lot , Just let the heater “ A little bit of force ” Heat it up .
If the current temperature is much lower than the target temperature , Just let the heater “ At full power ” heating , Get the water temperature near the target as soon as possible .
This is it. P The role of , Compared with the switch control method , Is it right? “ gentle ” A lot .
When you actually write a program , Let the deviation （ The goal subtracts the current ） With the regulating device “ The intensity of adjustment ”, Establish a relationship of first degree function , You can achieve the most basic “ The proportion ” Controlled ~
kP The bigger it is , The more radical the regulation is ,kP Turning down makes the regulation more conservative .
If you're making a balance car , With P The role of , You'll find that , The balance car goes back and forth near the balance angle “ Shaking ”, It's hard to hold on .
If you've reached this point —— congratulations ！ Success is only a small step away ~
kD
D Better understand the role of , So let's start with D, The final say I.
We had just now P The role of . It's not hard for you to find out , Only P It doesn't seem to get the balance station up , The temperature of the water is also controlled dangerously , It seems that the whole system is not particularly stable , Always in “ shake ”.
Imagine a spring in your heart ： Now in equilibrium position . Give it a pull , And let go . And then it will vibrate . Because the resistance is very small , It can oscillate for a long time , It's going to stop at equilibrium again .
Please imagine ： If you immerse the system in the water shown above , Pull it again ： In this case , It takes much less time to return to equilibrium .
We need a control function , Let the controlled physical quantity “ The rate of change ” Tend to 0, Which is similar to “ damping ” The role of .
because , When you're closer to the goal ,P The control effect is less . The closer to the goal ,P The softer the effect of . There are many internal and external factors , Make the control variable swing in a small range .
D The purpose of this paper is to make the speed of physical quantity tend to 0, Just when , This quantity has speed ,D Just push in the opposite direction , Try to stop the change .
kD The greater the parameters , The stronger the braking force is in the opposite direction of speed .
If it's a balance car , add P and D Two kinds of control functions , If the parameters are adjusted properly , It should be able to stand up ~ Cheers .
wait ,PID The three brothers seem to have another . look PD You can keep the physical quantity stable , That's more I why ？
Because we ignore an important situation ：
kI
Take hot water as an example . If someone takes our heating device to a very cold place , It's boiling water . It needs to be burned to 50℃.
stay P Under the influence of , The water temperature rises slowly . Until it goes up to 45℃ when , He found a bad thing ： It's too cold , The speed at which water dissipates heat , and P The controlled heating rate is equal to .
This is how to do ？
P Brother thinks so ： I'm close to the goal , Just heat it gently .
D Brother thinks so ： Heating is equal to heat dissipation , The temperature didn't fluctuate , I don't seem to have to adjust anything .
therefore , The temperature of the water stays at forever 45℃, Never to 50℃.
As a person , According to common sense , We know , The heating power should be further increased . But how to calculate the increase ？
The method that the predecessors thought of was really ingenious .
Set an integral . As long as the deviation exists , And I'm going to integrate the deviation over and over again （ Add up ）, And respond to the intensity of regulation .
thus , Even if 45℃ and 50℃ The difference is not too big , But over time , As long as the target temperature is not reached , This integral is increasing . The system will gradually realize that ： We haven't reached the target temperature yet , It's time to increase the power ！
After reaching the target temperature , Suppose the temperature doesn't fluctuate , The integral value will not change again . At this time , The heating power is still equal to the cooling power . however , The temperature is stable 50℃.
kI The greater the value of , The greater the coefficient of the integral , The more obvious the integral effect .
therefore ,I Is that , Reduce the static error , Make the controlled physical quantity as close as possible to the target value .
I There's a problem with using it ： You need to set an integral limit . Prevent from heating at the beginning , I'll just multiply the integral too much , It's hard to control .