I have a problem regarding putting a PID controller in my simulink file.
In my simulink file, i used pid controller to control my process. I used s-function as my process block diagram.
According Ziegler-Nichols method, for the first step we set k equal to the smallest value (0.5) so I put 0.5 in my proportional value . but there is no different between the result with controller and without controller.Even i increase or decrease proportional value.
Why this problem occur? hope someone can help me.Thank you.
my block diagram is look like below picture.refer to this picture
http://s1009.photobucket.com/albums/af218/syarinazulkifeli/?action=view¤t=Untitled-1.png
Here is my s-function file:
function [sys,x0,str,ts]= reactor_sfcn(t,x,u,flag)
switch flag
case 0
[sys,x0,str,ts]=mdlInitializeSizes;
case 1,
sys = mdlDerivatives(t,x,u);
case 3,
sys = mdlOutputs(t,x,u);
case 9
sys =[];
end
function [sys,x0,str,ts] = mdlInitializeSizes()
s = simsizes;
s.NumContStates = 11;
s.NumDiscStates = 0;
s.NumOutputs = 11;
s.NumInputs = 1;
s.DirFeedthrough = 0;
s.NumSampleTimes = 1;
sys = simsizes(s) ;
x0 = [0.0258,0,0,0,0,0,0,0,8.83,303.15,303.15];
str=[] ;
ts = [0 0];
function sys = mdlDerivatives (t,x,u)
Tjo = u;
sys = reactor(t,x,Tjo);
function sys = mdlOutputs(t,x,u)
% sys(1)=x(1);
% sys(2)=x(2);
% sys(3)=x(3);
% sys(4)=x(4);
% sys(5)=x(5);
% sys(6)=x(6);
% sys(7)=x(7);
% sys(8)=x(8);
% sys(9)=x(9);
% sys(10)=x(10);
% sys(11)=x(11);
sys = x;
Link of s-function file
function DXDT = reactor(t,x,Tjo)
% -------------------------------------------- %
% Parameters definition
% -------------------------------------------- %
I = x(1); X = x(2); P0 = x(3);
P1 = x(4); P2 = x(5); Q0 = x(6);
Q1 = x(7); Q2 = x(8); M = x(9);
Tjo = x(10); T = x(11);
% ---------------------------------------
% Constants
% =======================================
%constant
M0 = 8.83;
I0 = 0.0258;
Qh = 60.44;
MMWm = 100.3;
U0 = 55.1;
% Densities
dp = 1200;
dm = 968-1.225*(T-273.15);
Rhoc = 998;
% volume expansion factor
Fev = (dm - dp)./dp ;
% volume fraction
Fvm = (1 - X)./(1 + Fev*X);
Fvp = X*(1-Fev)./(1+Fev*X);
% Total reactant mixture density
Rho = dm*Fvm + dp*Fvp;
% Reactor and jacket volume
Vc = 2;
V = 2;
% Reactor dimension
At =3.1416*0.15*0.113;
% coolant flow rate
Mc = 0.41/18;
%
Cpc = 77.22;
Cp = 199.13;
% Average coolant temperature
Tji = 303.15;
Tj =(Tji+Tjo)/2;
% Overall heat transfer coeff
alpha = 0.4;
U = U0-alpha*X;
delHp = 57800;
% ---------------------------------------
% Rates of reaction
% =======================================
% Fujita-Doolittle equation
Tgp = 114 +273.25 ;
A = 0.168-8.21e-6*(T-Tgp)^2;
B = 0.03;
g = exp(2.303*Fvm/(A + B*Fvm));
% Dissociation rate
F = 0.58;
Kd = (6.32e16*exp(-15.43e3/T));
% Propagation rate
Tep = 5.4814e-16*exp(13982/T);
Kp0 = 2.952e7*exp(-4353/(1.987*T));
Kp = (Kp0*g)./(g + (Tep*P0.*Kp0));
% Termination rate
Tet = (1.1353e-22*exp(17420/T))./I0;
Kt0 = 5.88e9*exp(-701/(1.987*T));
Kt = (Kt0*g)./(g + (Tet*P0.*Kt0));
Ktc = 0;
Ktd = Kt ;
% -------------------------------------------- %
% ODE's
% -------------------------------------------- %
dIdt = -Kd*I - ((Fev*I.*P0.*(1 - X)*Kp)./(1 + Fev*X));
dXdt = Kp*(1 - X).*P0;
dP0dt = (-Fev*P0.*P0.*(1 - X)./(1 + Fev*X)).*Kp + 2*F*Kd*I - Kt*P0.*P0;
dP1dt = (-Fev*P0.*P1.*(1 - X)./(1 + Fev*X)).*Kp + 2*F*Kd*I - Kt*P0.*P1 + (Kp*M0*(1 - X)./(1 + Fev*X)).*P0;
dP2dt = (-Fev*P0.*P2.*(1 - X)./(1 + Fev*X)).*Kp + 2*F*Kd*I - Kt*P0.*P2 + (Kp*M0*(1 - X)./(1 + Fev*X)).*(2*P1 + P0);
dQ0dt = (-Fev*P0.*Q0.*(1 - X)./(1 + Fev*X)).*Kp + Ktd*P0.*P0 + 0.5*Ktc*P0.*P0;
dQ1dt = (-Fev*P0.*Q1.*(1 - X)./(1 + Fev*X)).*Kp + Ktd*P0.*P1 + Ktc*P0.*P1;
dQ2dt = (-Fev*P0.*Q2.*(1 - X)./(1 + Fev*X)).*Kp + Ktd*P0.*P2 + Ktc*(P1.*P0 + P1.^2);
dMdt = (-Kp*P0*M0*(1 - X)./(1 + Fev*X)).*((Fev*(1 - X)./(1 + Fev*X)) + 1);
Rm = (-delHp)*dMdt;
dTjodt = (Mc*Cpc*(Tji-Tjo)+ U*At*(T-Tj))/(Vc*Rhoc*Cpc/18);
dTdt = (Qh+(Rm*V*MMWm)-(U*At*(T-Tj)))/(V*Rho*Cp);
DXDT =[dIdt;dXdt;dP0dt;dP1dt;dP2dt;dQ0dt;dQ1dt;dQ2dt;dMdt;dTjodt;dTdt];
First I woult check if the s-function for the process is working as expected. Disconnect the PID controller and connect a step, ramp or a sin block. This could give you a hint if the block for the process is OK and how large the static coefficient is.
A second hint: the Ziegler-Nichols method says one should increase the Kp until the system gets marginaly stable. Have you tested only one value for the proportional gain? Depending on the plant 0.5 can be really small value and way under the levels you need to control the system.