In conjunction with the release of the new Arduino PID Library I’ve decided to release this series of posts. The last library, while solid, didn’t really come with any code explanation. This time around the plan is to explain in great detail why the code is the way it is. I’m hoping this will be of use to two groups of people:

People directly interested in what’s going on inside the Arduino PID library will get a detailed explanation.

Anyone writing their own PID algorithm can take a look at how I did things and borrow whatever they like.

It’s going to be a tough slog, but I think I found a not-too-painful way to explain my code. I’m going to start with what I call “The Beginner’s PID.” I’ll then improve it step-by-step until we’re left with an efficient, robust pid algorithm.

The Beginner’s PID

Here’s the PID equation as everyone first learns it:

This leads pretty much everyone to write the following PID controller:

/*working variables*/ unsigned long lastTime; double Input, Output, Setpoint; double errSum, lastErr; double kp, ki, kd; void Compute() { /*How long since we last calculated*/ unsigned long now = millis(); double timeChange = (double)(now - lastTime); /*Compute all the working error variables*/ double error = Setpoint - Input; errSum += (error * timeChange); double dErr = (error - lastErr) / timeChange; /*Compute PID Output*/ Output = kp * error + ki * errSum + kd * dErr; /*Remember some variables for next time*/ lastErr = error; lastTime = now; } void SetTunings(double Kp, double Ki, double Kd) { kp = Kp; ki = Ki; kd = Kd; }

Compute() is called either regularly or irregularly, and it works pretty well. This series isn’t about “works pretty well” though. If we’re going to turn this code into something on par with industrial PID controllers, we’ll have to address a few things:

Once we’ve addressed all these issues, we’ll have a solid PID algorithm. We’ll also, not coincidentally, have the code that’s being used in the lastest version of the Arduino PID Library. So whether you’re trying to write your own algorithm, or trying to understand what’s going on inside the PID library, I hope this helps you out. Let’s get started.

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UPDATE: In all the code examples I’m using doubles. On the Arduino, a double is the same as a float (single precision.) True double precision is WAY overkill for PID. If the language you’re using does true double precision, I’d recommend changing all doubles to floats.





Tags: Arduino, Beginner's PID, PID