pcomp.m

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function [numopen, denopen, denclsd] = pcomp(num, den, zeta)

% Hadi Saadat,  1998

discr=[
'                                                                         '
'  The function pcomp(num, den, zeta) is used for the design of gain      '
'  factor compensation.  num and den are row vectors of polynomial        '
'  coefficients of the uncompensated open-loop plant transfer function.   '
'  zeta is the desired damping factor.  K0 for the required damping ratio '
'  is found.  The function returns the open-loop and the closed-loop      '
'  numerator and denominator of the compensated system transfer function. '
'                                                                         '];
%disp(discr);

c1=0:.1:10; c2=11:1:100; c3=110:10:1000;
k=[c1 c2 c3]; kk=k';
j=0;
r=rlocus(num,den,k);
 ri=imag(r);  risum=sum(ri);
costhta=cos([pi-angle(r)]);
j= find (risum > .5);
if isempty(j)==1;
        disp('Warning: zeta line does not cross root-locus')
        return,else, end
 l=length(costhta);
 for i=1:l for c=1:j
     if costhta(i,c) ==-1 costhta(i,c)=1; end,end,end
cost=(costhta(:,j));
l=length(cost);
if cost(1) > zeta
        i = find(cost < zeta);
else
        i = find(cost > zeta);
end
if length(i) == 0
        disp('Warning: zeta line does not cross root-locus'),return
else
while i(1)>l i(1)=i(1)-l; end

        i2 = i(1);
        i1 = i2 - 1;
        k1 = min(kk(i1,:));
        k2 = min(kk(i2,:)) ;
        m1 = min(cost(i1,:));
        m2 = min(cost(i2,:));
        K0 = k1 + (m1-zeta)*(k2-k1)/(m1-m2);
end
K0=round(100*K0)/100;
clc
fprintf('Controller gain:    K0 = %g',K0),
fprintf('\n\n')
% the following statements will form the characteristic Equation
% of the compensated system.
m=length(num); n=length(den);
if n > m
o=zeros(1,n-m); mk=[o,1]; num1=conv(num,mk);
else, num1=num, end
numgc=K0; numopen=conv(numgc,num1);
denopen= den;
denclsd=denopen+numopen;
numopen=numopen(n-m+1:length(numopen));
%fprintf('Row vectors of polynomial coefficients of the compensated system:\n\n')
%fprintf('Open-loop num. '),disp(numopen)
%fprintf('Open-loop den. '),disp(denopen)
%fprintf('Closed-loop den'),disp(denclsd)
fprintf('Compensated open-loop ')
GH = tf(numopen, denopen)
fprintf('Compensated closed-loop ')
T = tf(numopen, denclsd)

discr2=[
'Roots of the compensated characteristic equation:       '
'                                                        '];
disp(discr2)
R=roots(denclsd);
disp(R)
rreal=real(R);
  for l=1:n-1
  if rreal(l) >=0
  fprintf('   Root on the RHP, system is unstable. \n\n')
  else,end
  end