Discrete PID controller simulation

Hello,

I have implemented a discrete PID controller in C language via the Simulink

S-function. Here is my C code which I have inserted into the text field in the

Outputs tab in the S-function Builder

double        tmp; // temporary control value
double        satU;
double        dup; // increment of proportional part
double        dui; // increment of integral part
double        dud; // increment of derivative part
double        du;  // increment of control value

dup = Kp[0]*(xD[0] - xD[1]);                        // dup(k) = Kp*[e(k) - e(k-1)]
dui = (Kp[0]*T[0])/(2*Ti[0])*(xD[0] + xD[1]);       // dui(k) = (Kp*T)/(2*Ti)*[e(k) + e(k-1)]
dud = (Kp[0]*Td[0])/T[0]*(xD[0] - 2*xD[1] + xD[2]); // dud(k) = (Kp*Td)/T*[e(k) - 2*e(k-1) + e(k-2)]
du  = dup + dui + dud;                              // du(k)
tmp = xD[3] + du;                                   // u(k) = u(k-1) + du(k)
 
// antiwind-up
if(tmp > Umax[0]){
    satU = Umax[0];
}else if(tmp < Umin[0]){
    satU = Umin[0];
}else{
    satU = tmp;
}
y0[0] = satU;

Here is the C code which I have inserted into the text field in the

Discret Update tab in the S-function Builder

xD[0] = u0[0] - u1[0]; // e(k) = sp - cv 
xD[2] = xD[1];         // e(k-2) = e(k-1)
xD[1] = xD[0];         // e(k-1) = e(k)
xD[3] = u2[0];         // bumpless transition: u(k-1) = tr

I have prepared following simulation for the testing purposes

i.e. controller controls FOPDT system with transfer function

and transport delay . Parameters of the

PID controller are set in following manner: .

It is worthwile to say that the control value of the PID controller

is saturated in range . I have chosen sampling period

in respect to the system time constant (the sampling period

is used by the PID algorithm and also by the ZOH blocks).

Simulation output (without switching between controller output and manually set

control value) is given below

The controlled variable oscillates and I don't understand why. The same setting of

the controller behaves correctly in analog case with PID controller block from Simulink library.

I have tried smaler sampling period values but results are same. Can anybody give me an advice

what I am doing wrong?

[mustafa sgaban]

where you put the values of Kp, Ti,Td?

deosnt include in the code