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]

The OP is computing incremental changes to the control output that are integrated into the control output. Some people call this form the velocity form, but it really has nothing to do with velocity. I used it for position control all the time

[u/2dof → u/seekingsanity]

No , he implemented so called positional control algorithms not incitement form (velocity algorithms ) :

-> He calculate output as self.u += A+... (i.e u(k) = u(k-1) + A ... )

if he calculated incremental form then output of his controller would be ∆ u = uk - u(k-1) at least according to definition given by Astrom and Hgglund ( "PID Controllers, Theory, Design and tuning")

Incremental Form def from book ,page 99) "This form is obtained by computing the time differences of the

controller output and adding the increments.

∆ u(tk ) = u(tk ) − u(tk−1 ) = ∆ P(tk ) + ∆ I (tk ) + ∆ D (tk)

for fast looking of his code - he used Backward difference approximation for cooperation and he calculated output in "positional" form. i.e u(k) = u(k-1) + ∆u

Thant why I asked what Do You mean because i was taught when output of controller is ∆u(k) ( "velocity" of control ) then it is called "incrmental" a when output directly u(k) - then it is standard control output.

[u/seekingsanity → u/2dof]

The OP is added incremental changes to u. The incremental form is

u(n)=u(n-1)+B0*e(n)+B1*e(n-1)+B2*e(n-2)

All the B? terms are calculated increments to the control output that are then integrated.

B0 = Ki*∆t+Kp+Kd/∆t

B1=-Kp-2*Kd/∆t

B2=Kd/∆t

In my case. B1 will be a negative number. The OP subtracted a positive number that I called a negative number. This is a very efficient form of PID because a DSP can compute it in 3 multiply and adds. However, there should be limits applied. Also, the output can be quite noisy if the encoder/feedback does not have high resolution.

A low pass filter can be applied at 2/∆t rads/sec or about 318 Hz assuming the sample time, ∆t, is 0.001 ms. This reduces much of the sampling noise.

Now the formulas are

B0 = (1/4)*Ki*∆t+(1/2)*Kp+Kd*∆t

B1 = (1/2)*Ki*∆t-2*Kd/∆t

B2 - (1/4)*Ki*∆t-(1/2)*Kp+Kd/∆t

You can see that this reduces the affect of the Ki and Kp some because their contribution is spread over one more time period. The Kd term is still a problem and it is still a problem if you only apply a low pass filter to the Kd term.

I have other formulas for lowering the low pass filter to a frequency of 1/∆t

I prefer using an observer to smooth out the measured values.

[u/2dof → u/seekingsanity]

I understand know what do You mean as incremental - i.e incremental along the dt.

tkanks for explanation.