Performing abc-dq/ dq-abc transformation for PI controller

I wanted to do a control system using PI control and for PI control to get zero-steady state error, the input has to be constant which is the purpose of doing the abc-dq transformation. I've did this for matlab simulink and is now translating the model to code. My inputs are three-phase sine waves. There is a "wt"/"theta" in the formula which I use Phase locked loop in matlab to obtain that variable. How do I do that in code without using any hardware? and able to code the transformation?

abc-dq transformation.PNG

what do you mean by How do I do that in code without using any hardware?
are you looking for a system with hardware DSP support?
what development systems have you considered? what programming language?

you can use the math.h library (see more here: https://www.arduino.cc/en/Math/H)

from the transformation you provided you get (hope my math is not too rusty!):
Capture.PNG

I would code (not tested!) that as below:

#include <math.h>

const int F 50; //assuming that is your frequency in ω
const double w = 2*PI*F;
const double x=2/3;

void abc_dq_transformation{
int t=0;
double ua[F],ub[F],uc[F]; //I’ll let you initialise those input arrays. Can be static or you may create a routine to initialise them
double ud[F],uq[F],u0[F];

     for(t=0; t<F;++t){ //using sample interval of one unit. You can change that if you need to
         ud[t] = x*((ua[t]*cos(w*t))+ (ub[t]*cos((w*t)-(x*PI))+ (uc[t]*cos((w*t)+(x*PI)));
         uq[t] = -1*x*((ua[t]*sin(w*t))+ (ub[t]*sin((w*t)-(x*PI))+ (uc[t]*sin((w*t)+(x*PI)));
         u0[t] = 0.5*x*(ua[t]+ub[t]+uc[t]);
     }

}

hope that helps

Capture.PNG

sherzaad:
you can use the math.h library (see more here: https://www.arduino.cc/en/Math/H)

from the transformation you provided you get (hope my math is not too rusty!):
Capture.PNG

I would code (not tested!) that as below:

#include <math.h>

const int F 50; //assuming that is your frequency in ω
const double w = 2PIF;
const double x=2/3;

void abc_dq_transformation{
int t=0;
double ua[F],ub[F],uc[F]; //I’ll let you initialise those input arrays. Can be static or you may create a routine to initialise them
double ud[F],uq[F],u0[F];

for(t=0; t<F;++t){ //using sample interval of one unit. You can change that if you need to
        ud[t] = x*((ua[t]cos(wt))+ (ub[t]cos((wt)-(xPI))+ (uc[t]cos((wt)+(xPI)));
        uq[t] = -1x((ua[t]sin(wt))+ (ub[t]sin((wt)-(xPI))+ (uc[t]sin((wt)+(xPI)));
        u0[t] = 0.5x(ua[t]+ub[t]+uc[t]);
    }

}




hope that helps

Thanks a lot.