Calculating Kp,Ki & kd values with Astrom-Hagglund(Relay) Method

[Vindhyachal.takniki]

Hi,

I was reading your blog post here: http://brettbeauregard.com/blog/2012/01/arduino-pid-autotune-library/ and trying to implement autotune library to maintain temperature in industrial ovens.

1. We bought a Delta Electronics PID and oven and see how it Delta Electronics PID controller do autotune. Below is the graph we obtained
2. Since it looks like Astrom-Hagglund(Relay) Method, sowe tried to get Kc & Tu values from it.
3. For our reading we took readings from second cycle only.
4. a) Tu is calculated in seconds
b) Kc = (4*D)/(pi*A)
D=100 taken since relay is 100% on or off only
A=Difference between +peak and -peak value.

5. One important thing we note that its not symmetrical oscillation, (zero to +peak) is higher than (zero to -peak) value.

6. But when we put it in formula as in link above menetioned code, outout is always saturated high. I think we have to normailize outut formula before using, but dont know how to do it or anything we are doing in our code.

Code: [Select]

const float32_t c_output_max = 100.0f;
const float32_t c_output_min = 0.0f;

float32_t input_temperature;
float32_t setpoint_temperature;
float32_t output_duty_cycle;

float32_t i_term;
float32_t last_input;

//ku = 12.60633212609071966486208026713f;   units: per degree celsius
//tu = 820  seconds
float32_t kp = 7.563799f;   //kp = 0.6*Ku
float32_t ki = 0.018448f;  // ki = 1.2*Ku/Tu
float32_t kd = 775.289425f;    // ki = 0.075*Ku*Tu


float32_t sample_time = 1.0f;  // 1 second


//sample_time + derivative_kick + On-The-Fly Tuning Changes + integral windup +
void compute_pid_duty_cycle(void)
{ 
    float32_t error;
    float32_t d_input;

    /* get error */   
    error = setpoint_temperature - input_temperature;

    /* integral error */
    i_term = i_term + (error * ki);
    if(i_term > c_output_max)
    {
        i_term = c_output_max;
    }   
    else if(i_term < c_output_min)
    {
        i_term = c_output_min;
    }   
    else
    {
    }   
       

/* differential error */   
    d_input = input_temperature - last_input;

/*Compute PID Output*/
    output_duty_cycle = (kp * error) + (i_term) - (kd * d_input);
    if(output_duty_cycle > c_output_max)
    {
        output_duty_cycle = c_output_max;
    }   
    else if(output_duty_cycle < c_output_min)
    {
        output_duty_cycle = c_output_min;
    }   
    else
    {
    }       

    /*Remember some variables for next time*/
    last_input = input_temperature;
   
} /* function ends here */


[Vindhyachal.takniki]

Have written below code, but outout is very fluctating and then clamped to either zero or highest.

This is general three gains Kp, Ki and Kd.
I think one reason might be: dimensions dont match on both sides . Though i am not sure of this.

1. kp has unit : (change in output)/celsius.
since Kp is proportional to D/A  , where D= change in output which we take 0 to 100, since its relay method.
A= change in temperature.

2. ki = 1.2*Ku/Tu  so its units: (change in output)/(celsius * second).

3. ki = 0.075*Ku*Tu  so its units: (change in output * second)/(celsius).

4.While on left of equation , which is outout it is dimension less or percentage

I have checked another PID controller from another company they also used porportional band, ; https://web-material3.yokogawa.com/IM05P01C31-01EN.pdf


But i dont get how to caculate it.
Defination sats: " It is amount of change in input (or deviation), as a percent of span, required to cause the control output to change from 0% to 100% "
For example in our test, with set point 70C, max goes to 78.6, minimum goes to 69.0,

sensor span is -200C to  + 600C

How to calculate it?

is it : (78.6-69.0)*100/(600+200C)  ??

Code: [Select]

void compute_pid_duty_cycle(void)
{ 
    float32_t error;
    float32_t temp_integral;
    float32_t derivative;

/* get error */   
    error = setpoint_temperature - input_temperature;
   
    if(first_time)
    {
        first_time = 0U;
        previous_err = error;
    }   

/* integral error */
    integral = integral + error;   //dt = 1sec
    temp_integral = integral * ki; 
   
    if(temp_integral > c_output_max)  //integral windup up
    {
        temp_integral = c_output_max;
    }   
    else if(temp_integral < c_output_min)
    {
        temp_integral = c_output_min;
    }   
    else
    {
    } 

/* differential error */ 
    derivative = error - previous_err;     //dt = 1seconds

/* Compute PID Output */
    output_duty_cycle = (kp * error) + (temp_integral) + (kd * derivative);
    if(output_duty_cycle > c_output_max)
    {
        output_duty_cycle = c_output_max;
    }   
    else if(output_duty_cycle < c_output_min)
    {
        output_duty_cycle = c_output_min;
    }   
    else
    {
    }       

/* Remember some variables for next time */
    previous_err = error;
   
} /* function ends here */