Adding PID controller Chapter. #346

Gathros · 2018-08-08T16:57:32Z

No description provided.

jiegillet · 2018-08-09T00:05:39Z

contents/pid_controller/pid_controller.md

+#Proportional-Integral-Derivative Controller
+
+You are a helmsmen keeping a vessel on course in various conditions, how do you do that.
+A common way is to steer based on current course error, past error and the current rate of change.


If you're going for an analogy, I would love to see this sentence expanded to a paragraph. Something like: you are aiming towards the lighthouse, but you are 4 degrees to the left, that is your current error and you need to correct that. You're been zig zagging left and right for the past 10 minutes, you should fix that too. You also notice that steering has become hard and harder, maybe you've hit a new current? Taking all this information into account, you can correct your course to have a smooth trip, just like you father taught you, just like his father taught him.

jiegillet

These are just my thoughts (and typos), not a real review. I would love to see graphs of the corrections with coefficients too big, too small and just right. I think that could help.

jiegillet · 2018-08-09T00:10:20Z

contents/pid_controller/pid_controller.md

+
+Where $K_{p}$ is a constant and $e(t)$ is the current error.
+The performance of the controller improves with larger $K_{p}$;
+if $K_{p}$ is too high then when the error is too high, the system becomes unstable, i.e. the rc car drives in a circle.


Wouldn't it zig zag out of control?

Yeah, this is also not clear to me. I would be expecting an instability like what we see with euler methods. Also: what if K is a function of the error? Is this common practice?

jiegillet · 2018-08-09T00:10:25Z

contents/pid_controller/pid_controller.md

+
+## The Algorithm
+
+Luckily the algorithm is very simple, You just need to make the PID equation decrete.


decrete => discrete

jiegillet · 2018-08-09T00:13:02Z

contents/pid_controller/pid_controller.md

+$$ U = K_{p} e(t) + K_{i} \int_{0}^{t} e(x) dx + K_{d} \frac{de(t)}{dt} $$
+
+To use a PID controller, you need to tune it, by setting the constants, $K_{p}$, $K_{i}$, and $K_{d}$.
+There are multiple methods of tuning like, manual tuning, Ziegler–Nichols, Tyreus Luyben, and more.


I'd love to see one of those method expanded later, I've tried to make a PID controlled segway-type device using an arduino once, but I could never quite get the constants right manually.

jiegillet · 2018-08-09T00:13:18Z

contents/pid_controller/pid_controller.md

+To use a PID controller, you need to tune it, by setting the constants, $K_{p}$, $K_{i}$, and $K_{d}$.
+There are multiple methods of tuning like, manual tuning, Ziegler–Nichols, Tyreus Luyben, and more.
+
+The uses of PID controllers are thoreticaly any process which has mesurable output and a known ideal output,


thoreticaly => theoretically

zsparal

I don't think I caught all the grammatical errors, but I listed a few. I'm also a little unsure about the text itself: it sounds pretty foreign in places.

I mentioned it in a few cases but there are a bunch more where I didn't have the time to come up with a better sounding alternative.

zsparal · 2018-08-09T10:48:13Z

contents/pid_controller/pid_controller.md

+The PID controller is in three parts proportional controller, integral controller, and derivative controller.
+
+Before we get into how a PID controller works, we need a good example to use to explain how it work.
+Imagine you are making a self driving rc car that drives on a line, how wuld make it work given that the car moves with a constent speed.


self driving -> self-driving
rc -> RC
wuld -> would
constent -> constant

zsparal · 2018-08-09T10:49:56Z

contents/pid_controller/pid_controller.md

+The proportional-integral-derivative controller (PID controller) is a control loop feedback mechanism, used for continuously modulated control.
+The PID controller is in three parts proportional controller, integral controller, and derivative controller.
+
+Before we get into how a PID controller works, we need a good example to use to explain how it work.


This sentence sounds pretty strange. The repetition (how a PID controller works ... explain how it works) could use a little work.

zsparal · 2018-08-09T10:51:32Z

contents/pid_controller/pid_controller.md

+#Proportional-Integral-Derivative Controller
+
+The proportional-integral-derivative controller (PID controller) is a control loop feedback mechanism, used for continuously modulated control.
+The PID controller is in three parts proportional controller, integral controller, and derivative controller.


I think this would sounds better as: The PID controller is comprised of three parts: proportional controller, integral controller, and derivative controller

zsparal · 2018-08-09T10:52:57Z

contents/pid_controller/pid_controller.md

+
+### Proportional Controller
+
+If the car is too far to the right then you would turn left and visa versa.


visa versa -> vice versa

zsparal · 2018-08-09T10:59:00Z

contents/pid_controller/pid_controller.md

+### Proportional Controller
+
+If the car is too far to the right then you would turn left and visa versa.
+Since there is a range of angles you can turn the wheel, you can turn with proportion to how far you are from the line.


I'm not the biggest fan of this sentence either. The Since there is a range of angles... part sets up an explanation that's pretty much never expanded on.

Something like You can turn the wheel proportional to how far you are from the line. In fact, this is exactly what the proportional controller does. The formula describing its behavior is given by: would sound better I think.

Even if you leave the current version:
with proportion to -> proportional to

zsparal · 2018-08-09T11:08:45Z

contents/pid_controller/pid_controller.md

+
+$$ U = K_{p} e(t) + K_{i} \int_{0}^{t} e(x) dx + K_{d} \frac{de(t)}{dt} $$
+
+To use a PID controller, you need to tune it, by setting the constants, $K_{p}$, $K_{i}$, and $K_{d}$.


tune it, -> tune it (it doesn't need the comma)

zsparal · 2018-08-09T11:09:12Z

contents/pid_controller/pid_controller.md

+To use a PID controller, you need to tune it, by setting the constants, $K_{p}$, $K_{i}$, and $K_{d}$.
+There are multiple methods of tuning like, manual tuning, Ziegler–Nichols, Tyreus Luyben, and more.
+
+The uses of PID controllers are theoretically any process which has mesurable output and a known ideal output,


mesurable -> measurable

zsparal · 2018-08-09T11:10:09Z

contents/pid_controller/pid_controller.md

+There are multiple methods of tuning like, manual tuning, Ziegler–Nichols, Tyreus Luyben, and more.
+
+The uses of PID controllers are theoretically any process which has mesurable output and a known ideal output,
+but controllers are used mainly for regulating temperature, pressure, force, flow rate, feed rate, speed, and more.


speed, and more -> speed and more

zsparal · 2018-08-09T11:10:25Z

contents/pid_controller/pid_controller.md

+
+## The Algorithm
+
+Luckily the algorithm is very simple, You just need to make the PID equation discrete.


zsparal · 2018-08-09T11:10:36Z

contents/pid_controller/pid_controller.md

+## The Algorithm
+
+Luckily the algorithm is very simple, You just need to make the PID equation discrete.
+Thus, the equation looks like this,


this, -> this:

leios

I have noted everything I thought was odd about the text, but haven't yet gotten to the code. Overall, I am happy with its addition to the AAA.

After these revisions are done, there will be at least one more review. The car analogy works, well, but it's a bit there's a sentence missing somewhere that I cannot quite figure out to make it flow with the rest of the text.

leios · 2018-08-12T22:45:49Z

contents/pid_controller/pid_controller.md

@@ -0,0 +1,84 @@
+#Proportional-Integral-Derivative Controller


Does there need to be a space here?

# Proportional-Integral-Derivative Controller

leios · 2018-08-12T22:46:40Z

contents/pid_controller/pid_controller.md

@@ -0,0 +1,84 @@
+#Proportional-Integral-Derivative Controller
+
+The proportional-integral-derivative controller (PID controller) is a control loop feedback mechanism, used for continuously modulated control.


The Proportional-Integral-Derivative controller (PID controller)

capitalize PID because the acronym follows

leios · 2018-08-12T23:05:19Z

contents/pid_controller/pid_controller.md

+
+### Proportional Controller
+
+If the car is too far to the right then you would turn left and vice versa.


would -> should

leios · 2018-08-12T23:50:18Z

contents/pid_controller/pid_controller.md

+### Proportional Controller
+
+If the car is too far to the right then you would turn left and vice versa.
+But there are a range of angles you can turn the wheel, so you can turn proportional to how far you are from the line.


This sentence is a bit unclear to me and I don't like starting sentences with But. I think it might be clearer to say:

In this case, the amount of turning should be proportional to your distance from the line

leios · 2018-08-12T23:50:39Z

contents/pid_controller/pid_controller.md

+
+$$ P = K_{p} e(t), $$
+
+Where $K_{p}$ is a constant and $e(t)$ is the current error.


How is the error defined? Is it the distance from the line?

$$e(t)$$ is canonically defined as $$setpoint(t) − measured_value(t)$$

leios · 2018-08-13T00:01:23Z

contents/pid_controller/pid_controller.md

+### Integral Controller
+
+I looks like we are done, we start driving but if some wind starts pushing the car then we get a constant error.
+We need to know if we are spending too long on one side and account for that.


To correct this error, we need...

leios · 2018-08-13T00:02:53Z

contents/pid_controller/pid_controller.md

+The way to do that is to sum up all the errors and multiply it by a constant.
+This is what the integral controller (I controller) does, which is given by,
+
+$$ I = K_{i} \int_{0}^{t} e(x) dx, $$


is this a different e? Its dependent on position instead of time. Maybe it would be nice to create three separate errors e_P, e_D and e_I so we can differentiate?

Also, is the integral going from 0 -> t but in terms of dx?

leios · 2018-08-13T00:04:22Z

contents/pid_controller/pid_controller.md

+
+### Proportional-Integral-Derivative Controller
+
+The PID controller is just a sum of all there three constrollers, of the form,


The PID controller is just a sum of all three controllers and is of the form,

leios · 2018-08-13T00:05:12Z

contents/pid_controller/pid_controller.md

+
+To use a PID controller, you need to tune it by setting the constants, $K_{p}$, $K_{i}$, and $K_{d}$.
+If you choose the parameters for your PID controller incorrectly, the output will be unstable, i.e., the output diverges.
+There are multiple methods of tuning like, manual tuning, Ziegler–Nichols, Tyreus Luyben, Cohen–Coon, and Åström-Hägglund.


Will these be covered? If so, leave a note.

They aren't algorithms it's just done by hand so I don't imagine there being a chapter on it.

Hmm, then for completeness we might want to differentiate these.

If these are mentioned, they should be described. You can add a simple list with all of them and how they are differentiated from each other.

It might be worth adding a separate heading for tuning and discussing these in-turn.

Why not link to the wiki page https://en.wikipedia.org/wiki/PID_controller#Overview_of_tuning_methods

If possible, it would be nice to have citations for all of these with bibtex-cite

How do you cite?

Put the appropriate bibtex citation in the literature.bib file at the start of the directory, then put {{ "ct1965" | cite } where you want to cite it and add a

### Bibliography {% references %} {% endreferences %}

at the bottom

Cool, Thanks.

leios · 2018-08-13T00:05:52Z

contents/pid_controller/pid_controller.md

+If you choose the parameters for your PID controller incorrectly, the output will be unstable, i.e., the output diverges.
+There are multiple methods of tuning like, manual tuning, Ziegler–Nichols, Tyreus Luyben, Cohen–Coon, and Åström-Hägglund.
+
+The uses of PID controllers are theoretically any process which has measurable output and a known ideal output,


theoretically, PID controllers can be used for any process with a measurable output and a known ideal output,

leios · 2018-08-21T10:49:34Z

I am sorry it's taking me so long to get to this. It's mostly there. I'll look over the text once more and check out the code next.

leios

Overall positive changes. There is still some work to do, though. The code is readable and there are only a few minor corrections to the text, mainly a differentiation between Ziegler–Nichols, Tyreus Luyben, Cohen–Coon, and Åström-Hägglund tuning methods.

leios · 2018-09-10T23:12:05Z

contents/pid_controller/pid_controller.md

+The PID controller is comprised of three parts: proportional controller, integral controller, and derivative controller.
+
+Before we get into how a PID controller works, we need a good example to explain things.
+Imagine you are making a self-driving RC car that drives on a line, how would make it work given that the car moves with a constant speed.


What do you mean "how would make it work"? Do you mean: "how would we keep the car on the line"?

Yeah, that's what I mean.

I meant this as a fix. The sentence doesn't currently make sense.

leios · 2018-09-10T23:12:49Z

contents/pid_controller/pid_controller.md

+### Proportional Controller
+
+If the car is too far to the right then you should turn left and vice versa.
+Since there are a range of angles you can turn the wheel, so you should turn proportional to the distance from the line.


Since there are a range of angles you can turn the wheel, so you should turn proportional to the distance from the line.

contents/pid_controller/pid_controller.md

leios · 2018-09-10T23:17:29Z

contents/pid_controller/pid_controller.md

+Where $K_{p}$ is a constant and $e(t)$ is the current distance from the line, which is called the error.
+The performance of the controller improves with larger $K_{p}$;
+if $K_{p}$ is too high then when the error is too high, the system becomes unstable.
+In this case, the car would turn in circles, since there is a maximum angle the wheel can turn, else it would zig zag around the line.


This sentence feels weird. Maybe:

In this case, the car would turn in circles because there is a maximum angle the wheel can turn, otherwise it would zig zag around the line.

leios · 2018-09-10T23:18:45Z

contents/pid_controller/pid_controller.md

+Where $K_{d}$ is a constant.
+If $K_{d}$ is too high then the system is overdamped, i.e. the car takes too long to get back on track.
+If it's too low the system is underdamped, i.e. the car oscillates around the line.
+When the car is getting back on track quickly with little to no oscillations then the system is called critically damped.


When the car returns to the track quickly...

leios · 2018-09-10T23:20:27Z

contents/pid_controller/pid_controller.md

+### Integral Controller
+
+The Proportional and Derivative controllers are robust enough to get the on course.
+We start driving, but then some wind starts pushing the car which introduces a constant error.


Maybe combine these two sentences?

The Proportional and Derivative controllers are robust enough to get the on course, but what if some wind starts pushing the car and introduces a constant error?

leios · 2018-09-10T23:23:12Z

contents/pid_controller/pid_controller.md

+The Proportional and Derivative controllers are robust enough to get the on course.
+We start driving, but then some wind starts pushing the car which introduces a constant error.
+We need to know if we are spending too long on one side and account for that.
+The way to do that is to sum up all the errors and multiply it by a constant.


Maybe

Well, we would need to know if we are spending too long on one side and account for that, and we can figure that out by summing up all the errors and multiply it by a constant.

leios · 2018-09-10T23:28:36Z

contents/pid_controller/pid_controller.md

+
+## Example Code
+
+This example is not calculating the time elapsed, instead it is setting a value called dt.


It is not clear from the code what this example is supposed to output or do, in general.

I just need a clear description of what this example code is trying to do. I am having a little trouble figuring out what the code is supposed to be doing, but I think it's a 1D analog to the car example, right? We are trying to keep the car on setpoint?

contents/pid_controller/code/c/pid_controller.c

leios

A few more suggestions

leios · 2018-09-11T23:59:03Z

contents/pid_controller/pid_controller.md

+The PID controller is comprised of three parts: proportional controller, integral controller, and derivative controller.
+
+Before we get into how a PID controller works, we need a good example to explain things.
+Imagine you are making a self-driving RC car that drives on a line, how would make the car stay on track given that it moves with a constant speed.


This sentence still doesn't make sense. Maybe:

Imagine you are making a self-driving RC car that drives on a line, how could we keep the car on track if it moves with a constant speed?

leios · 2018-09-12T00:01:38Z

contents/pid_controller/pid_controller.md

+
+Before we get into how a PID controller works, we need a good example to explain things.
+Imagine you are making a self-driving RC car that drives on a line, how would make the car stay on track given that it moves with a constant speed.
+


Maybe add a sentence here like:

This could be done with a PID controller, which is a combination of Proportional, Integral, and Derivative (PID) controllers.

I prefer introducing it over time, to make it easier to follow.

My argument was that it was not followable without a transitional sentence.

leios · 2018-09-12T00:03:30Z

contents/pid_controller/pid_controller.md

+
+### Proportional Controller
+
+If the car is too far to the right then you should turn left and vice versa.


I think sticking to "we" instead of "you" makes sense, but that's personal preference. Maybe something like:

Imagine our RC car is moving too far to the right, in this case it makes sense to turn left.

leios · 2018-09-12T00:05:10Z

contents/pid_controller/pid_controller.md

+
+### Derivative Controller
+
+The P controller works well but it has the added problem of overshooting a lot, we need to dampen these oscillations.


Does the P controller really provide an oscillation? It seems like just an overshooting, right? If that's the case, it makes more sense to say "dampen this motion" then "dampen these oscillations"

P controllers may over shoot then it will start to oscillate around the track. So you're dampening this oscillation not the motion of the car.

It's not clear to me how we can model the error in the P controller as an oscillation. Again, an animation or some depiction could help here.

leios · 2018-09-12T00:07:49Z

contents/pid_controller/pid_controller.md

+### Integral Controller
+
+The Proportional and Derivative controllers are robust enough to keep on course, but what if some wind starts pushing the car and introducing a constant error?
+Well, we would need to know if we are spending too long on one side and account for it, we can figure it out by summing up all the errors and multiply it by a constant.


Well, we would need to know if we are spending too long on one side to account for it, and we can figure it out by summing up all the errors and multiply it by a constant.

leios · 2018-09-12T00:08:41Z

contents/pid_controller/pid_controller.md

+
+To use a PID controller, you need to tune it by setting the constants, $K_{p}$, $K_{i}$, and $K_{d}$.
+If you choose the parameters for your PID controller incorrectly, the output will be unstable, i.e., the output diverges.
+There are multiple methods of tuning like, manual tuning, Ziegler–Nichols, Tyreus Luyben, Cohen–Coon, and Åström-Hägglund.


If these are mentioned, they should be described. You can add a simple list with all of them and how they are differentiated from each other.

It might be worth adding a separate heading for tuning and discussing these in-turn.

leios · 2018-09-12T00:11:22Z

contents/pid_controller/pid_controller.md

+## Example Code
+
+The example code is of a 1-dimensional RC car that is trying to change from the first lane to the second lane, where the numbers represent the center of the lane.
+This example is we can't calculate the time elapsed, instead we are setting a value called dt for time elapsed.


This sentence is unclear. Did you mean:

In this example, we can't calculate the time elapsed, so we are instead setting a value called dt for time elapsed.

In this case, why are we using dt instead of time or some other parameter? dt always describes the size of a timestep, not the time, itself.

If the normal case is to calculate time, as indicated in line 10 of the code, why do we provide an example that doesn't do this? What is the point in the time parameter to begin with? Is it for dynamic timestepping?

The I and D controllers use the time parameter for calculating integration and differentiation.

leios · 2018-09-12T00:13:59Z

contents/pid_controller/pid_controller.md

+
+## Example Code
+
+The example code is of a 1-dimensional RC car that is trying to change from the first lane to the second lane, where the numbers represent the center of the lane.


I need some more information here or in the code because it's unclear. What does setpoint mean? "where the numbers represent the center of the lane" is really vague. What does that mean?

I don't know what you want me to write there, I can't make it more clear.

leios

We need to add in the license at the bottom of the chapter:

## License
The text of this of this chapter is licensed under the [Creative Commons Attribution-ShareAlike 4.0 International License](https://creativecommons.org/licenses/by-sa/4.0/legalcode) with attribution to Gathros.
The code examples are licensed under the MIT license (found in LICENSE.md).

[<p><img  class="center" src="../cc/CC-BY-SA_icon.svg" /></p>](https://creativecommons.org/licenses/by-sa/4.0/)

I cannot approve this fully until until #560 is merged

For each of the 3 controllers, it makes sense to have a quick animation of a car moving on a dotted line to show what the controllers are actually doing. I can make these, if you want.

Ultimately, it's pretty close to being completed, just a few graphics and citations.

leios · 2018-12-25T20:48:08Z

contents/pid_controller/pid_controller.md

@@ -0,0 +1,86 @@
+# Proportional-Integral-Derivative Controller
+Written by Gathros


I think we might want to remove this now that we have the license at the bottom? I 'm actually not sure about this, though, so I'm happy leaving a note on authorship at the top too.

leios · 2018-12-25T20:51:18Z

contents/pid_controller/pid_controller.md

+Written by Gathros
+
+The Proportional-Integral-Derivative controller (PID controller) is a control loop feedback mechanism, used for continuously modulated control.
+The PID controller is comprised of three parts: proportional controller, integral controller, and derivative controller.


I think I might do something like this:

The PID controller has three components:

proportional controller: quick description

integral controler: quick description

derivative controller: quick description

leios · 2018-12-25T21:09:31Z

contents/pid_controller/pid_controller.md

+The PID controller is comprised of three parts: proportional controller, integral controller, and derivative controller.
+
+Before we get into how a PID controller works, we need a good example to explain things.
+Imagine you are making a self-driving RC car that drives on a line, how could we keep the car on track if it moves with a constant speed?


Maybe add

For the following sections, imagine you are designing a self-driving RC car that tries to remain on a line...

(or something similar)

leios · 2018-12-25T21:23:25Z

contents/pid_controller/pid_controller.md

+
+### Proportional Controller
+
+Imagine our RC car is moving too far to the right, in this case it makes sense to turn left.


Imagine our RC car is moving too far to the right of the line, in this case it makes sense to turn left.

leios · 2018-12-25T21:32:39Z

contents/pid_controller/pid_controller.md

+Where $K_{p}$ is a constant and $e(t)$ is the current distance from the line, which is called the error.
+The performance of the controller improves with larger $K_{p}$;
+if $K_{p}$ is too high then when the error is too high, the system becomes unstable.
+In this example, the car would turn in circles, since there is a maximum angle the wheel can turn, else it would zig zag around the line.


It would be nice to have an animation to show these.

leios · 2018-12-25T21:53:24Z

contents/pid_controller/pid_controller.md

+$$ I = K_{i} \int_{0}^{t} e(\uptau) d\uptau, $$
+
+Where $K_{i}$ is a constant.
+The peformance of the controller is better with higher $K_{i}$; but with higher $K_{i}$ it can introduce oscillations.


Again, a side-by-side animation would do well here

leios · 2018-12-25T21:53:43Z

contents/pid_controller/pid_controller.md

+
+The Proportional and Derivative controllers are robust enough to keep on course, but what if some wind starts pushing the car and introducing a constant error?
+Well, we would need to know if we are spending too long on one side to account for it, and we can figure it out by summing up all the errors and multiply it by a constant.
+This is what the integral controller (I controller) does, which is described by,


Again, no comma (I think)

leios · 2018-12-25T21:53:59Z

contents/pid_controller/pid_controller.md

+
+### Proportional-Integral-Derivative Controller
+
+The PID controller is just a sum of all three controllers and is of the form,


Again no comma (I think)

leios · 2018-12-25T21:54:48Z

contents/pid_controller/pid_controller.md

+
+To use a PID controller, you need to tune it by setting the constants, $K_{p}$, $K_{i}$, and $K_{d}$.
+If you choose the parameters for your PID controller incorrectly, the output will be unstable, i.e., the output diverges.
+There are multiple methods of tuning like, manual tuning, Ziegler–Nichols, Tyreus Luyben, Cohen–Coon, and Åström-Hägglund.


If possible, it would be nice to have citations for all of these with bibtex-cite

contents/pid_controller/pid_controller.md

Gathros · 2018-12-30T18:18:54Z

I, Gathros, the copyright holder of this work, irrevocably grant anyone the right to use this work, including derivatives created during the review process, under the Creative Commons Attribution ShareAlike 4.0 license (legal code).

(Anyone may use, share or remix this work, as long as they credit me and share any derivative work under this license.)

leios

Overall, good. Some of the suggestions were nitpicks, but others still need to be addressed from before.

leios · 2020-07-14T22:17:46Z

contents/pid_controller/pid_controller.md

+The PID controller has three components: proportional controller, integral controller, and derivative controller.
+
+Before we get into how a PID controller works, we need a good example to explain things.
+For the following sections, imagine you are designing a self driving RC car that tries to remain on a line as it is moving with a constant speed. How would you keep it on course.


Suggested change

For the following sections, imagine you are designing a self driving RC car that tries to remain on a line as it is moving with a constant speed. How would you keep it on course.

For the following sections, imagine you are designing a self-driving RC car that tries to remain on a line as it is moving with a constant speed. How would you keep it on course?

leios · 2020-07-14T22:30:23Z

contents/pid_controller/pid_controller.md

+### Proportional Controller
+
+Imagine our RC car is too far to the right of the line, in this case it makes sense to turn left.
+Since there are a range of angles you can turn the wheel, you should turn proportional to the distance from the line.


Suggested change

Since there are a range of angles you can turn the wheel, you should turn proportional to the distance from the line.

Since there are a range of angles you could turn the wheel by, it is unclear what strategy would work best to return the RC car to the line; however, it is clear that if the angle chosen is proportional to the distance from the line, the car will always be moving towards it.

leios · 2020-07-14T22:31:06Z

contents/pid_controller/pid_controller.md

+
+$$ P = K_{p} e(t), $$
+
+Where $K_{p}$ is a constant and $e(t)$ is the current distance from the line, which is called the error.


Suggested change

Where $K_{p}$ is a constant and $e(t)$ is the current distance from the line, which is called the error.

Where $$K_{p}$$ is an arbitrary constant and $$e(t)$$ is the current distance from the line, which is called the error.

leios · 2020-07-14T22:32:28Z

contents/pid_controller/pid_controller.md

+$$ P = K_{p} e(t), $$
+
+Where $K_{p}$ is a constant and $e(t)$ is the current distance from the line, which is called the error.
+The performance of the controller improves with larger $K_{p}$;


Suggested change

The performance of the controller improves with larger $K_{p}$;

The performance of the controller improves with larger $$K_{p}$$;

leios · 2020-07-14T22:33:35Z

contents/pid_controller/pid_controller.md

+
+Where $K_{p}$ is a constant and $e(t)$ is the current distance from the line, which is called the error.
+The performance of the controller improves with larger $K_{p}$;
+if $K_{p}$ is too high then when the error is too high, the system becomes unstable.


Suggested change

if $K_{p}$ is too high then when the error is too high, the system becomes unstable.

however, if $$K_{p}$$ and $$e(t)$$ are too high then the system becomes unstable.

leios · 2020-08-05T22:13:57Z

contents/pid_controller/pid_controller.md

+Well, we would need to know if we are spending too long on one side to account for it, and we can figure it out by summing up all the displacements, usually refered to as errors, and multiply it by a constant.
+This is what the integral controller (I controller) does, which is described by
+
+$$ I = K_{i} \int_{0}^{t} e(\uptau) d\uptau, $$


\uptau doesn't seem to exist in mathjax, can we use tau?

leios · 2020-08-05T22:14:39Z

contents/pid_controller/pid_controller.md

+
+$$ U = K_{p} e(t) + K_{i} \int_{0}^{t} e(x) dx + K_{d} \frac{de(t)}{dt} $$
+
+To use a PID controller, you need to tune it by setting the constants, $K_{p}$, $K_{i}$, and $K_{d}$.


Suggested change

To use a PID controller, you need to tune it by setting the constants, $K_{p}$, $K_{i}$, and $K_{d}$.

To use a PID controller, you need to tune it by setting the constants, $$K_{p}$$, $$K_{i}$$, and $$K_{d}$$.

leios · 2020-08-05T22:15:13Z

contents/pid_controller/pid_controller.md

+
+To use a PID controller, you need to tune it by setting the constants, $K_{p}$, $K_{i}$, and $K_{d}$.
+If you choose the parameters for your PID controller incorrectly, the output will be unstable, i.e., the output diverges.
+There are multiple methods of tuning like, manual tuning, Ziegler–Nichols, Tyreus Luyben, Cohen–Coon, and Åström-Hägglund.{{ "wikipid" | cite }}


Suggested change

There are multiple methods of tuning like, manual tuning, Ziegler–Nichols, Tyreus Luyben, Cohen–Coon, and Åström-Hägglund.{{ "wikipid" | cite }}

There are multiple methods of tuning like manual tuning, Ziegler–Nichols, Tyreus Luyben, Cohen–Coon, and Åström-Hägglund.{{ "wikipid" | cite }}

``

leios · 2020-08-05T22:18:56Z

contents/pid_controller/pid_controller.md

+### Bibliography
+
+{% references %} {% endreferences %}


Move this to after the example code

leios · 2020-08-05T22:19:21Z

contents/pid_controller/pid_controller.md

+
+{% references %} {% endreferences %}
+
+## The Algorithm


Suggested change

## The Algorithm

## Putting it all together

ntindle · 2021-08-28T05:15:23Z

[lang: c]

leios · 2021-11-07T17:20:49Z

@Gathros It's been years. I really dropped the ball on chapter reviews, but I am making it a priority now and I promised you that your chapter would be the first one in, so would you mind either:

Continuing with the PR
Allowing me to either push to this branch or create a separate PR from this one with my own changes. Obviously, if I need to create a second PR, you will still be in the git history.

If I don't get a response, I will go ahead and start with 2

Improving the discriptions of a PID controller.

37b0068

Gathros added Implementation This provides an implementation for an algorithm. (Code and maybe md files are edited.) Chapter This provides a new chapter. (md files are edited) labels Aug 8, 2018

Gathros assigned leios Aug 8, 2018

jiegillet reviewed Aug 9, 2018

View reviewed changes

fixing spelling and chaning the intro.

874abf5

zsparal suggested changes Aug 9, 2018

View reviewed changes

Gathros added 2 commits August 9, 2018 12:43

updaing text of pid_controller.md

17b7226

Adding information unstable controllers

aaa8c40

leios requested changes Aug 13, 2018

View reviewed changes

pid_controller.md update

7a1ad44

leios reviewed Sep 10, 2018

View reviewed changes

Gathros added 2 commits September 11, 2018 11:21

some changes to pid_controller.md

4c0aa45

more changes to pid_controller.md

6bdd7ad

leios reviewed Sep 12, 2018

View reviewed changes

more updates to pid_controller.md

28c3f5c

leios mentioned this pull request Sep 21, 2018

Chapter submissions and planned revision #388

Closed

leios reviewed Dec 25, 2018

View reviewed changes

Small chapter changes to pid_controller.md

182f4bf

Gathros changed the title ~~Adding PID controller Chapter.~~ Adding PID controller Chapter. WIP Dec 26, 2018

Gathros added 3 commits December 30, 2018 10:54

Adding wikipedia to bib file

6a8b5e1

Adding animations

a0608f3

Adding animations and citations

45e66ef

Gathros changed the title ~~Adding PID controller Chapter. WIP~~ Adding PID controller Chapter. Dec 30, 2018

Merge branch 'master' into PID

570b7b1

leios reviewed Aug 5, 2020

View reviewed changes

Adding small fixes and another video

2d2be13

Merge branch 'PID' of github.com:Gathros/algorithm-archive into PID

aadf198

github-actions bot added the lang: c C programming language label Aug 28, 2021

Merge branch 'master' into PID

9a7849e

leios mentioned this pull request Nov 7, 2021

Add a Cryptography Chapter #278

Closed

leios mentioned this pull request Dec 5, 2021

Adding bang-bang control algorithm #968

Open


		## The Algorithm

		Luckily the algorithm is very simple, You just need to make the PID equation decrete.


		### Proportional Controller

		If the car is too far to the right then you would turn left and visa versa.


		$$ U = K_{p} e(t) + K_{i} \int_{0}^{t} e(x) dx + K_{d} \frac{de(t)}{dt} $$

		To use a PID controller, you need to tune it, by setting the constants, $K_{p}$, $K_{i}$, and $K_{d}$.

		@@ -0,0 +1,84 @@
		#Proportional-Integral-Derivative Controller


		$$ P = K_{p} e(t), $$

		Where $K_{p}$ is a constant and $e(t)$ is the current error.


		### Proportional-Integral-Derivative Controller

		The PID controller is just a sum of all there three constrollers, of the form,


		## Example Code

		This example is not calculating the time elapsed, instead it is setting a value called dt.


		Before we get into how a PID controller works, we need a good example to explain things.
		Imagine you are making a self-driving RC car that drives on a line, how would make the car stay on track given that it moves with a constant speed.


		### Derivative Controller

		The P controller works well but it has the added problem of overshooting a lot, we need to dampen these oscillations.


		## Example Code

		The example code is of a 1-dimensional RC car that is trying to change from the first lane to the second lane, where the numbers represent the center of the lane.

		@@ -0,0 +1,86 @@
		# Proportional-Integral-Derivative Controller
		Written by Gathros

	For the following sections, imagine you are designing a self driving RC car that tries to remain on a line as it is moving with a constant speed. How would you keep it on course.
	For the following sections, imagine you are designing a self-driving RC car that tries to remain on a line as it is moving with a constant speed. How would you keep it on course?

	Since there are a range of angles you can turn the wheel, you should turn proportional to the distance from the line.
	Since there are a range of angles you could turn the wheel by, it is unclear what strategy would work best to return the RC car to the line; however, it is clear that if the angle chosen is proportional to the distance from the line, the car will always be moving towards it.

	Where $K_{p}$ is a constant and $e(t)$ is the current distance from the line, which is called the error.
	Where $$K_{p}$$ is an arbitrary constant and $$e(t)$$ is the current distance from the line, which is called the error.

	The performance of the controller improves with larger $K_{p}$;
	The performance of the controller improves with larger $$K_{p}$$;

	if $K_{p}$ is too high then when the error is too high, the system becomes unstable.
	however, if $$K_{p}$$ and $$e(t)$$ are too high then the system becomes unstable.

	There are multiple methods of tuning like, manual tuning, Ziegler–Nichols, Tyreus Luyben, Cohen–Coon, and Åström-Hägglund.{{ "wikipid" \| cite }}
	There are multiple methods of tuning like manual tuning, Ziegler–Nichols, Tyreus Luyben, Cohen–Coon, and Åström-Hägglund.{{ "wikipid" \| cite }}
	``

Adding PID controller Chapter. #346

Are you sure you want to change the base?

Adding PID controller Chapter. #346

Conversation

Gathros commented Aug 8, 2018

Choose a reason for hiding this comment

jiegillet left a comment • edited Loading

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

zsparal left a comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

leios left a comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

leios Dec 26, 2018 • edited Loading

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

leios commented Aug 21, 2018

leios left a comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

leios left a comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

leios left a comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

Choose a reason for hiding this comment

jiegillet left a comment •

edited

Loading

leios Dec 26, 2018 •

edited

Loading