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License: MIT License
PID controller implementation written in C.
License: MIT License
#include <stdio.h>
#define KP 2.0
#define KI 0.5
#define KD 0.1
float setpoint = 25.0;
float error, last_error, integral, derivative;
float temperature[3], pwm_output[3];
void read_temperature()
{
// read temperature from sensors and store in temperature array
}
void update_pid()
{
// calculate error value
error = setpoint - temperature[0];
// calculate integral term
integral += error;
// calculate derivative term
derivative = error - last_error;
// calculate PID output
pwm_output[0] = KP * error + KI * integral + KD * derivative;
// limit PWM output to a safe range
if (pwm_output[0] > 255) pwm_output[0] = 255;
if (pwm_output[0] < 0) pwm_output[0] = 0;
// update last_error
last_error = error;
// set PWM output to thermoelectric cooler
}
int main()
{
// initialize integral and last_error
integral = 0.0;
last_error = 0.0;
while (1)
{
read_temperature();
update_pid();
}
return 0;
}
Code now (bi-linear transform):
pid->differentiator = -(2.0f * pid->Kd * (measurement - pid->prevMeasurement)
+ (2.0f * pid->tau - pid->T) * pid->differentiator)
/ (2.0f * pid->tau + pid->T);
if you assume tau = 0, e[n] - e[n-1] = 0
, then you'll get: D[n] = D[n-1]
, so it keeps always the previous value (and doesn't go to 0).
if you assume tau >>T, e[n] - e[n-1] = 0
, then you'll get: D[n] = -1*D[n-1]
, so it keeps oscillating (and doesn't go to zero).
After reviewing other sources, I suggest using Backward-Euler transform s→(z-1)/z
, then you'll get:
D[n] = K[d]/(tau + T)*(e[n] - e[n-1]) + tau/(tau + T)*D[n-1] // classical form
D[n] = K[d]/(tau + T)*(measurement[n-1] - measurement[n]) + tau/(tau + T)*D[n-1] // derivative on measurement
in this case it works as expected, for both "test cases" from above, if e[n] - e[n-1] = 0
then D[n] = 0
Hello, I would like to ask how the finally function 'TestSystem_Update' in the file 'PID_Test.c' comes from and what is the specific significance. Thank you~
Basically the integration can be stopped when a PID(timestep+1) would be limited by the all 3 parts. This is resulting into calculating all 3 parts and throwing away the part for the integration when a limit would occur.
Hello Mr Phil,
I think you should add the link to your video in the README. There is some useful information in the video https://www.youtube.com/watch?v=zOByx3Izf5U.
Best,
Vincent
Can you clarify which license applies to this code, please?
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