Saturday, October 25, 2008

Using a DC motor as a servo with PID control (part 1)

PID motor control with an Arduino from Josh Kopel on Vimeo.



I found that the newer ink jet printers often use a combination of a DC motor and an optical encoder to take the place of stepper motors for print head positioning (linear motion) and paper feed (rotary positioning). The pieces often come out (after some effort) as a whole, and they seemed like a natural to experiment with.

The motors themselves are pretty nice if you just want to make something move and control its speed, and in combination with the encoder, I thought I could use them as a free alternative to a hobby servo. I knew there had to be some information out there about using a feedback loop to position a motor, and of course there was. It turns out that the classic way of doing this is through a PID servo controller (Proportional, Integral, Derivative). At its simplest this method can be thought of as a way to use the difference between where the motor should be and where it is (error), plus the speed at which the error is changing, plus the sum of past errors to manage the speed and direction that the motor is turning.

Ok, so I have to say at this point, that I am not an engineer. I did take an engineering calc. class or two, but that was more then 25 years ago, and I never much understood it even then. So all I really have to go on is my intuition about how this is working, a few good explanations, and some example code. As always , Google is your friend. If you do have a good understanding I would welcome your comments!

The first resource I found was this exchange on the Arduino forums and then followed through to an article that really explained what was going on here at

After reading the article a few times I put together some simple code, and was amazed to find that the thing worked almost perfectly the first time.
The key elements of the code look like this
int val = analogRead(potPin); // read the potentiometer value (0 - 1023)
int target = map(val, 0, 1023, 0, 3600);// set the seek to target by mapping the potentiometer range to the encoder max count
int error = encoder0Pos - target; // find the error term = current position - target
// generalized PID formula
//correction = Kp * error + Kd * (error - prevError) + kI * (sum of errors)

// calculate a motor speed for the current conditions
int motorSpeed = KP * error;
motorSpeed += KD * (error - lastError);
motorSpeed += KI * (sumError);
// set the last and sumerrors for next loop iteration
lastError = error;
sumError += error;
What is going on here is:
1. read a value from the potentiometer through an analog to digital input (0-1023)

2. map that value so that it lives in the range from 0-3600 (the count from one full rotation of the motor). We need to scale like this so we can make an apples to apples comparison with the current position reported by the optical encoder. The current position is being calculated in another function (an ISR) whenever an interrupt is generated by the optical encoder (more on what this is all about here).

3. create an error term by subtracting the value we want to go to (target) from where we are (encoder0Pos)

4. multiply the error by a constant (proportional gain) to make it large enough to effect the speed. This is the Proportional term, and gives us a simple linear speed value. Basically it says that the further we are from where we want to be, the faster we need to go to get there. The converse is true, so that we will slow down as we approach our destination. Of course, if we are going to fast to begin with, we may overshoot. Then the Proportional will switch signs (from - to + or visa versa) and we will back up towards our target. If the speed is really off then we end up zooming past many times and oscillating until we (hopefully) get to the target.

5. add the difference between the error NOW and the error from the last time around. This is a way to figure out how fast the error is changing, and is the Derivative term of the equation, and you can think of it a bit like looking into the future. If the error rate is changing fast then we are getting close to where we want to be FAST and we should think about slowing down. This helps dampen the oscillation from the position term by trying to slow us down faster if we are approaching the target too quickly. Again, we multiply the value by a constant to amplify it enough to matter.

6. lastly add in the sum of all past errors multiplied by a constant gain. This is the Integral term, and is like looking at our past performance and learning from our mistakes. The further off we were before, the bigger this value will be. If we were going too fast then it will try to slow us, if to slowly, then it speeds us up.

7. set the lastError to the current error, and add the current error to our sum.

The resulting motorSpeed value will be a signed integer. Since the Adafruit controller takes an unsigned int as its speed value I do a little more manipulation to figure out the direction and get a abs() value for the speed, but that part is all pretty easy.

As I said, it seems really simple for such a complicated process. It turns out that the geared motor from the ink jets is much easier to control that some other mechanical systems. The physics of its gears, and the performance curve of the simple DC motor mean that you can be pretty far off on your tuning and it will still end up in the right place (eventually). If we were trying to do extremely precise positioning, or make it all work really fast, or handle huge inertial loads, then it would need to be a lot more robust. I am still working on "tuning " the configuration (i.e. slowly changing the 3 constant parameters one-by-one until it works best) and I will write more about that later.

In the mean time here is the code [SORRY! It looks like the code has vanished, and I cannot find a copy. DO NOT DISPAIR! Instead go here]. Bear in mind that it is designed for use with the Adafruit controller and library. You will also most likely find that it does not work well with the constants I have chosen*. In that case you will need to do some tuning yourself. Stay tuned (hah) and I will show you how I did it.

*discerning readers of code will notice that the Kd constant is 0 meaning that this is actually a PI controller. I found that while the Derivative made the motor settle into position faster, it also injected an enormous amount of noise and jitter. This is due in part to the cheap, noisy, and non-linear potentiometer I am using. I need to do some more experimenting before I can really call it a complete PID.

Oh yeah, if you are taking apart an ink jet you may find these Optical Encoder datasheets to be valuable. These are specific to Agilent parts, but I have found they all share pretty much the same pin-outs.


Dan Thompson said...

Hi Josh, Just came across this video and your blog. Very cool stuff. It's all a bit advanced for me at the moment, but interesting none the less.

Keep on Hacking! ;)

Dave said...

Cool project, thanks for posting. I've got several inkjets and a couple of big laser printers I'm tearing down for parts. Great sources for mechanical bits!

I noticed the nice encoders on those motors and have been thinking about doing a similar project, just as soon as I decide what to do with them. Nice to have your work as a reference!

Unknown said...

Thank, I can get some idea to solve the problems. :D

mircho said...

Hi Josh,
This post and video are inspiring.
I came across your blog, after searching for info how to use a geared dc brush motor with an encoder from an old CDROM. The motor is working, the shaft encoder seems to be linear, but I don't have any sophisticated tools (oscilloscope) or any electronics knowledge to decode the small pcb of the encoder.
From my limited knowledge of electronics and while reading the HP datasheets you provided (thanks!) I may tell that the encoder PCB looks a lot like the described in the sheets possible implementations. But that's all. I cannot come up with any idea how to wire it to the Arduino.
Five flat cables go into the PCB. Two of them are clearly the +9V and GND for powering the motor. But the other 3 I cannot decode. Do you have any practical advise how to proceed? (I have a multimeter tool and can measure things with it :))
Thanks in advance, even only for the effort to read this!

I am being elaborate here, because I found few practical ideas in Google how to reuse salvaged DC motors from CDROMS, so maybe this will help other Googlers.

Josh Kopel said...

@mircho CD-ROM motors are usually "brushless" which means you need some fairly complex signals to drive them. They basically require three sine waves in a specific phase relationship. Not to easy to do unfortunately (that is why they use custom control chips. The boards they are on most often have a magnetic encoder with alternating north south zones, and some tiny hall effect chips to pick up the magnetic field changes and generate feedback for the controller. I have messed with them a bit, but never gotten anywhere to speak of.

Unknown said...

Hi Josh, this is very very nice stuff. I've been looking for a good encoder for my robot's wheels for a while and now (thanks to you) I've found them :-)

I'm only worried about the maximum frequency Arduino can handle interrupts from the encoders. 18k lines per revolution is a lot. My robot will do ~2 wheel rotations per second max, i.e. 36k interrupts per second or 72k for two wheels. How is your experience with this? Do you think Arduino can handle it?

Josh Kopel said...

@bjoern I think it can. My own admittedly unscientific experiments had the wheel spinning pretty fast. I am not sure if it was it 2rev/second but it was worth a try. You will want to experiment with the interrupt settings though. For instance, you can cut the triggering in half by only attaching the interrupt to one transition (i.e. HIGH, or LOW).

Check out oskay's comment here. They know what they are talking about.

Have fun and let me know what you end up with!

Yasaman said...

Hey , I have a question , I'm using optical encoder and I'm not using a potentiometer ??? which parts of your code should I change ???

Paulo Martins said...

Hi, fantastic work.

I'm trying to do position control with a Pololu 29:1 gear motor and after several hours or days i cant seem to tune it. I've also use the graphical pid tuning here: to no avail. No matter how i change Kp Ki or Kd i cant control it smoothly.
Do you think it's because it is a geared motor?

best Regards,
Paulo Martins

Josh Kopel said...

@Paulo Martins thanks, it has been a few years since I worked with this code (or pid in any way) so I am not sure how much help I can offer. I do remember reading about how geared motors were difficult to work with since the latency introduced by the gear lash is a problem. Tuning seemed to be a black art, that gui looks pretty cool if it works!

@Yasaman I am not quite sure what you are asking. The code does not care which kind of encoder it is attached to as long as it gets the quadrature signal. You should REALLY be using the official PID library, not my stuff.

Paulo Martins said...

Thanks for the quick reply, i'll try to dig some more into this subject.

insert said...

Hi Josh,

By and chance do you still have the code, the link is dead.


Josh Kopel said...

Sorry, it looks like that code has vanished into the bottomless chasm of server relocation.
It is really not much of a loss though, as my code was not very good!
Instead I highly recommend using one of the real PID libraries, like this one

Richard said...

Hi Josh. firstable congratulations!! I am working on a project like this. I would like to know if you can post the schematics and the value of the potentiometer. Thank you

Richard said...

i'm not sure how to connect the elements. Sorry about my english

Unknown said...

Great explanation, but how did u find the constanst values? I mean Kp,Ki, Kd?

Unknown said...

any link for the code used in this project? thanks

Josh Kopel said...

Jai (and everyone else who has commented),
Thanks for your interest, it always amazes me that people are still discovering this site!
This project is now about 6 years old, and I long ago lost the code.
In any case, it was all out of date.
There are many much better examples of using PID control on the site.
Check here first:

Good luck and have fun!


Unknown said...

yes 6 years ago and yet everyone keep doing what you did, talk about their luck or skills share half and leaves the rest to the same ppl who dont fully understand (i mean everyone who "shares" keeps sharing half of the exp how can the rest keep up) so yes 6 years and people keep looking for someone who actually share and teaches the right way "not that you did" tho its obvs that thru this comments you can see theirs still others with unanswered questions and pointing to "The key elements of the code" does not help ppl who dont understand reach this level that you had luck with at the end of the day your left with defeating the reason of the tutorial, i mean you did wrote " Stay tuned (hah) and I will show you how I did it.
" turns out 6 years later we are all still waiting

Unknown said...
This comment has been removed by a blog administrator.
maninblack said...

Hi,where is your sample time?

Unknown said...

Hi, John
Thanks your project and I like it. I want to DIY fry cam for my photograph passionate. I can use a multimeter, but I 'm newbie about the writing code for PID. Do you know where I can find to buy drive motor and controller online?