sampling time in PID computing

[Carlos_Eguti]

Hi everybody !

I'm working with a PID algorithm to control a servomotor with PWM driver conected to a 1 channel encoder. Always the same question, but..

I decided to use this PID form:

Pk = Kp * (ek – ek1)
Ik = Ki * T * ek
Dk = (Kd/T) * (ek - 2*ek1 + ek2)

CVk = CVk1 + Pk + Ik + Dk

where ek = setpoint – encoder frequency

I will put the intire code but, first, I need one tecnical informatiom:

How can I find or determine the sampling time "T" to do the calculations?

Someone could give me some light, please?

Thanks
Carlos

[SherpaDoug]

That is the time between data samples. If 10 times a second you read the A/D, do the math, and produce an output, then your T is 1sec/10=100ms. You want to make this value stable with some sort of paced loop in your software.
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[Carlos_Eguti]

Hi Mr. SherpaDoug or/ and Everybody

My complete code is that: is not working very well. Lie, don't work nothing ...

// PCM Version 3.168

#include <16f877A.h>
#device ADC=10

#include <STDLIB.H>
#include <MATH.H>

#fuses HS, NOWDT, NOLVP, PUT, NOPROTECT, NOBROWNOUT

// Cristal with 20MHZ OK
#use delay(clock=20000000)


// GLOBAL VARIABLES


int16 frequency=0;
int16 frequency_k=0;


// -------------------------------------------------------------
// CCP1 interruption
// -------------------------------------------------------------

#int_ccp1
void ccp1_isr(void)
{

static int16 old_ccp = 0;
int16 current_ccp=0;
int16 isr_ccp_delta=0;

// read register 16-bit on CCP1
current_ccp = CCP_1;

isr_ccp_delta = current_ccp - old_ccp;

old_ccp = current_ccp;

// Frequency calculation for 16mhz
frequency = (int16)(625000 / isr_ccp_delta);


}


// -------------------------------------------------------------
// MAIN PROGRAM
// -------------------------------------------------------------


void main(void)
{


// Variable Declarations
// -------------------------------------------------------------

//Set Point
long SP=700;
//Encoder output
long PV=0;

//Control Variable
long CVk=0;
//Control Variable previous value
long CVk1=0;

//previous error 2
signed long ek2=0;
//previous error 1
signed long ek1=0;
//current error
signed long ek=0;

//setpoint direction mark
int fg=1;

//proportional term
float Pk = 0.0;
//integral term
float Ik = 0.0;
//derivative term
float Dk = 0.0;

//sampling time (test with 100ms)
float T=0.1;


// Init PIC
// -------------------------------------------------------------

// ADC Setup
setup_adc_ports(NO_ANALOGS);
setup_adc(ADC_OFF);



// Setup of Timer1 and port CCP1
set_timer1(0);
setup_timer_1(T1_INTERNAL | T1_DIV_BY_8); // 20MHz count
setup_ccp1(CCP_CAPTURE_RE);



// Setup of CCP2 as PWM signal
setup_timer_2(T2_DIV_BY_4, 250, 1);
setup_ccp2(CCP_PWM);



// Enable Interrupsts
enable_interrupts(INT_CCP1);
enable_interrupts(GLOBAL);




// Main LOOP
// ------------------------------------------------------------------------
while(1)
{



// --------------------------------------------------------
// Set the setpoint speed through push-button on E0 pull-up.
// SP increasing 5 by 5 until reach a maximum value, then return decreasing.
if (! input(PIN_E0))
{

delay_ms(100);

if (fg == 1)
SP = SP + 5;

else
SP = SP - 5;

if (SP >= 1024)
{
fg = 0;
SP = 1000;
}

}
// -------------------------------------------------------



// -------------------------------------------------------
// PID CYCLE

// change invalid frequency value with last value
if (frequency > 200)
frequency = frequency_k;


// Converter the frequency data from encoder -------------
PV = (10 * ( 212 - frequency )) / 6;


// error calculation --------------------------------------
ek = (signed long)(SP - PV);



// Proportional Gain calculation --------------------------
// Kp = 2 (proportional coeficient)
Pk = 2.0 * (float)(ek - ek1);


// integral Gain calculation ------------------------------
// Ki = 1.5 (integral coeficient)
Ik = 1.5 * T * (float)ek;



// derivative Gain calculation ----------------------------
// Kd = 2 (derivative coeficient)
Dk = (2.0 / T) * (float)(ek - 2 * ek1 + ek2);



// Control Variable (Output) ------------------------------
CVk = CVk1 + (long)(Pk + Ik + Dk);



// anti wind-up test --------------------------------------
// range between 700 and 1000 for duty cycle
if (CVk > 1000)
CVk = 1000;

if (CVk < 700)
CVk = 700;


// Variables up-date --------------------------------------
frequency_k = frequency;
CVk1 = CVk;
ek1 = ek;
ek2 = ek1;


// Set duty cycle on CCP2 ----------------------------------
set_pwm2_duty(CVk);


// Main LOOP end
// ------------------------------------------------------------------------
}



// Main program end
// ------------------------------------------------------------------------
}


Unfortunately, I'm working with an old compiler version, but here in this lab, we have, at this momment, only this version. I'm trying to buy a new version, but it is difficult.

I'm using a interrupt to read the frequency from an optical encoder, connect on the wheel of the servo, and electrical connected at CCP1 port. The servo running at low speeds and I have 70 pulses per wheel turn. This part of the code I caught from this Forum.

As you see, the problem is to find the sampling interval.

Any suggestions or comments?


Carlos

[SherpaDoug]

From this line
delay_ms(100);
I would guess you are going through your main loop somewhat less than every 100ms, as the rest of your code takes some time to run. I would set a pin to 1 when you are doing your computation like this:

[Carlos_Eguti]

Good idea !!!
I'll try it.

But, another question. Is possible to transform an interrupt in fuction? I mean, is there a way to fix an interruption procedure calling?

anyway,
Thanks