% function [Ki,K] = area2PI_dist (A0,A1,A2,A3,Kmax);
%
% Function araa2PI calculates parameters of the PI controller:
%
% u = (Ki/s + K) * e
%
% from the measured areas of the process A0 to A3 (A0 is the process steady-state gain)
% for "optimal" disturbance rejection.
% The parameter Kmax represents the highest allowed open-loop gain K*A0 


function [Ki,K] = area2PI_dist (A0,A1,A2,A3,Kmax);

Ceta1 = A0*A0*A3 - 2*A0*A1*A2 + A1*A1*A1;
Ceta2 = A1*A2 - A0*A3;

if (Ceta1 == 0)
   Num = A3;							% Numerator
   Den = 2*(A1*A2-A0*A3);			% Denominator
   
   if (Num == 0)
      K = 0;
   elseif (Den == 0)
      if (A0 ~= 0)
         K = Kmax/A0;
      else
         K = Kmax;
      end;
   else
      K = Num/Den;
   end;
   
   Tmp = K*A0;							% Nominal gain
   
   if (Tmp > Kmax) | (Tmp < 0)
      K = Kmax/A0;
   end;
   
else
   
   K = (Ceta2 - sign(Ceta2)*A1*sqrt(A2*A2-A1*A3))/Ceta1;
   
   Tmp = K*A0;							% Nominal gain
   
   if (Tmp > Kmax) | (Tmp < 0)
      K = Kmax/A0;
   end;
   
end;

Ki = 0.5*(K*A0 + 1)*(K*A0 + 1)/A1;