Petter Reinholdtsen

While working on a CNC with servo motors controlled by the LinuxCNC PID controller, I recently had to learn how to tune the collection of values that control such mathematical machinery that a PID controller is. It proved to be a lot harder than I hoped, and I still have not succeeded in getting the Z PID controller to successfully defy gravity, nor X and Y to move accurately and reliably. But while climbing up this rather steep learning curve, I discovered that some motor control systems are able to tune their PID controllers. I got the impression from the documentation that LinuxCNC were not. This proved to be not true.

The LinuxCNC pid component is the recommended PID controller to use. It uses eight constants Pgain, Igain, Dgain, bias, FF0, FF1, FF2 and FF3 to calculate the output value based on current and wanted state, and all of these need to have a sensible value for the controller to behave properly. Note, there are even more values involved, theser are just the most important ones. In my case I need the X, Y and Z axes to follow the requested path with little error. This has proved quite a challenge for someone who have never tuned a PID controller before, but there is at least some help to be found.

I discovered that included in LinuxCNC was this old PID component at_pid claiming to have auto tuning capabilities. Sadly it had been neglected since 2011, and could not be used as a plug in replacement for the default pid component. One would have to rewriting the LinuxCNC HAL setup to test at_pid. This was rather sad, when I wanted to quickly test auto tuning to see if it did a better job than me at figuring out good P, I and D values to use.

I decided to have a look if the situation could be improved. This involved trying to understand the code and history of the pid and at_pid components. Apparently they had a common ancestor, as code structure, comments and variable names were quite close to each other. Sadly this was not reflected in the git history, making it hard to figure out what really happened. My guess is that the author of at_pid.c took a version of pid.c, rewrote it to follow the structure he wished pid.c to have, then added support for auto tuning and finally got it included into the LinuxCNC repository. The restructuring and lack of early history made it harder to figure out which part of the code were relevant to the auto tuning, and which part of the code needed to be updated to work the same way as the current pid.c implementation. I started by trying to isolate relevant changes in pid.c, and applying them to at_pid.c. My aim was to make sure the at_pid component could replace the pid component with a simple change in the HAL setup loadrt line, without having to "rewire" the rest of the HAL configuration. After a few hours following this approach, I had learned quite a lot about the code structure of both components, while concluding I was heading down the wrong rabbit hole, and should get back to the surface and find a different path.

For the second attempt, I decided to throw away all the PID control related part of the original at_pid.c, and instead isolate and lift the auto tuning part of the code and inject it into a copy of pid.c. This ensured compatibility with the current pid component, while adding auto tuning as a run time option. To make it easier to identify the relevant parts in the future, I wrapped all the auto tuning code with '#ifdef AUTO_TUNER'. The end result behave just like the current pid component by default, as that part of the code is identical. The end result entered the LinuxCNC master branch a few days ago.

To enable auto tuning, one need to set a few HAL pins in the PID component. The most important ones are tune-effort, tune-mode and tune-start. But lets take a step back, and see what the auto tuning code will do. I do not know the mathematical foundation of the at_pid algorithm, but from observation I can tell that the algorithm will, when enabled, produce a square wave pattern centered around the bias value on the output pin of the PID controller. This can be seen using the HAL Scope provided by LinuxCNC. In my case, this is translated into voltage (+-10V) sent to the motor controller, which in turn is translated into motor speed. So at_pid will ask the motor to move the axis back and forth. The number of cycles in the pattern is controlled by the tune-cycles pin, and the extremes of the wave pattern is controlled by the tune-effort pin. Of course, trying to change the direction of a physical object instantly (as in going directly from a positive voltage to the equivalent negative voltage) do not change velocity instantly, and it take some time for the object to slow down and move in the opposite direction. This result in a more smooth movement wave form, as the axis in question were vibrating back and forth. When the axis reached the target speed in the opposing direction, the auto tuner change direction again. After several of these changes, the average time delay between the 'peaks' and 'valleys' of this movement graph is then used to calculate proposed values for Pgain, Igain and Dgain, and insert them into the HAL model to use by the pid controller. The auto tuned settings are not great, but htye work a lot better than the values I had been able to cook up on my own, at least for the horizontal X and Y axis. But I had to use very small tune-effort values, as my motor controllers error out if the voltage change too quickly. I've been less lucky with the Z axis, which is moving a heavy object up and down, and seem to confuse the algorithm. The Z axis movement became a lot better when I introduced a bias value to counter the gravitational drag, but I will have to work a lot more on the Z axis PID values.