Question

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&current=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];

Answer 1

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.