fpseudo.m

控制系统计算机辅助设计——MATLAB语言与应用(源代码）

function [kpc,comden,lamda,cdomi]=fpseudo(w,f,ci,kform,weight)
%FPSEUDO        Calculate pseudo-decoupling controller.
%       [KPC,Comden]=fpseudo(w,f,ci) returns the ci-th column, KPC, of
%       a constant pre-compensator numerator transfer function matrix and
%       a common denominator polynomial, Comden. The coefficients of KPC
%       are calculated such that F*(KPC(s)/Comden(s)) is approximately a
%       multiple of the ci-th unit vector over the frequency range W. F is
%       an MVFR matrix of the plant and W is the associated frequency vector.
%
%       [KPC,Comden,lamda]=FPSEUDO(W,F,ci) also returns lamda, the min. cost.
%       [KPC,Comden,lamda]=FPSEUDO(W,F,ci) also returns the resulting column
%       dominance for the ci-th column of the pre-compensated system.
%
%       [KPC,Comden,lamda]=FPSEUDO(W,F,ci,KFORM) returns KPC whose elements
%       have the orders specified in KFORM.
%        E.g. for a system with 3 inputs KFORM of
%         [ 1 -2 -2    =>     row 1   k*s^-2
%           3 -1  0    =>     row 3   k*s^-1 + k*s^0
%                             row 2        0
%
%       [KPC,Comden,lamda]=FPSEUDO(W,F,ci,KFORM,Weight) applies the weighting,
%       Weight(i), at each frequency W(i).
%       See also  FADJ,FCDOM

%       Dr M.P. Ford 2nd September 1987
% Copyright (c) 1987 by GEC Engineering Research Centre & Cambridge Control Ltd
%       MRN0019

nargs=nargin;
error(nargchk(3,5,nargs));
[fm,fn]=fsize(w,f);
lw=length(w);
if nargs<4     % form default kform = constants
   kform=[(1:fn)',zeros(fn,1)];
end
if nargs<5     % default weight = 1
   weight=ones(lw,1);
end
weight=weight(:);
if length(weight)~=lw
   error('Number of Weightings must equal the number of frequency points.')
end

% find maximum and minimum power of K

[km,kn]=size(kform);
if kn<2
   error('Must have at least 2 columns in kform')
end
if any(kform(:,1)<1)|any(kform(:,1)>fn)
   error('Kform row index outside the range of the column indices of F')
end

kmax=max(max(kform(:,2:kn)));
kmin=min(min(kform(:,2:kn)));
kmnvec=kmax:-1:kmin;
kmn=length(kmnvec);
% form K vector of 0's and 1's
kvec=zeros(fn*kmn,1);
for i=1:km
      ki=kform(i,1);   %   row of pre-compensator
      for j=2:kn       %   for each power specified in that row
	  kj=find(kmnvec==kform(i,j));  %  find index of power
	  kvec((kj-1)*fn+ki)=1;
      end % for j
end % for i
disp(' Accumulating the frequency responses.')
[nli,mwi]=pseudint(w,f,kmax,kmin,ci,weight);
% reduce nli and mwi to eliminate the missing terms in kform
nli=nli(kvec,kvec);
mwi=mwi(kvec,kvec);

j=find(kvec==1);
comden=zeros(1,kmn);
comden(kmn)=1;

kpc=zeros(fn,kmn);
k=zeros(fn*kmn,1);
sf=1;               % when the minimun singular value is almost zero
		    % the scale factor effects the result
		    % a simple serach can be preformed on sf for the
		    % best lamda if desired
[lamda,k(j)]=pdsolv(nli,mwi,sf);
kpc(:)=k;
if nargout==4   % calculate the resulting column dominance
   k=[];
   for i=1:fm     % form a pre-compensator of the correct size.
       k=[k,kpc];
   end
   k=mv2fr(k,comden,w);
   cdomi=fcdom(w,fmulf(w,f,k));
   cdomi=cdomi(:,ci);           % Pick out the ci column
end