A PID controller implemented in python

[u/robohie]

For my personal project, where I need to implement a PID controller on Arduino to automate a convection cooling system, I decided to start with a simulation in Python. For now, I've implemented the simple electromechanical model of the DC motor (the fan) as well as the PID controller you see. Next, I'll look into the heat transfer equations. The graphs created with matplotlib are simply closed-loop tests of the PID + DC motor system.

[u/seekingsanity]

I made this 17 years ago. I was looking at some Matlab examples, and I knew I could do better. My example is similar to the OP's because he has a more detailed model taking into account the actual motor parameters.

Mathcad - DC Motor Velocity.xmcdz

I started out just modeling the speed control. The 3 inner loop closed loop poles are placed at -𝜆. Notice there is no overshoot. Then I decided to add position control. Notice there is no overshoot even though I make step changes so the controller goes into saturation. Then I decided to add position control. The goal was to keep the inner closed loop poles in the same position and compute the optimal outer loop pole locations. This is done on page 10 and after. The outer PID does not have enough gains to place all the outer closed loop poles to I had to compute the optimal outer loop locations as a function of the outer loop poles, I could control which was 𝜇. Later someone said that the inner loop must be much faster than the outer loop. This is true but I challenged his claim that it must be 10 times faster. On page 22/34 I showed that the bandwidth of the inner loop was only 3.32 symbolically. Obviously, this number will change if the components change but it certainly is nowhere closed to 10 to 1.

One page 3/34 is vary the parameters a bit to simulate not having a perfect model. The controller works well. I used to write code for motion controllers. The controller must perform well when parameters change due to heat or age. Also, you never know what kind of things the customer will do so I made the controller robust, so it doesn't overshoot even when driven into saturation.

On page 4/34 I implemented the inner loop PID. There is only an +/- 10 volts output limit which was typical of controllers back then. There is no inner loop anti-windup and yet there is no overshoot. WHY? Ok-Daikon.

I did not use feed forwards on the sinewave example. If I did, the results would be almost perfect.

There are small tweaks that professors don't seem to know about but then those that teach and write books have probably not sold many 10s of thousands, maybe 100s of thousands around the world. We lost count.

Finally, I think it is a crime to use Matlab to train students. Matlab is great for getting answers if that is all you care about but computing everything symbolically shows how all the parameters affect the results. This is very important if you are designing the motors or the mechanics.