transfr.m

来自「线性时变系统控制器设计的工具包」· M 代码 · 共 130 行

% function [a,b1,b2,c1,c2,d11,d12,d21,d22,r12inv,r21inv,q12,q21,fail] = ...
%            transfr(sys,nmeas,nctrl,nsf)
%
% This program is designed to scale the d12 and d21 matrices to satisfy the 
% standard formulas and check the rank conditions.
%
% MODIFICATION (Sep 4, 1996): it now works with the output-and-partial-state
% feedback problem, i.e., the last nsf outputs can be y2 = [0 Ci] x
% (where Ci is square and invertible), i.e. exact state measurements. 
% These are extracted, the rest of the plant is transformed as in the 
% regular output feedback problem, and then the extra outputs are put back 
% (after transforming y2 to Ci\y2). 

 function [a,b1,b2,c1,c2,d11,d12,d21,d22,r12inv,r21inv,q12,q21,fail] = ...
            transfr(sys,nmeas,nctrl,nsf)

 [systype,no,ni,nx] = minfo(sys);
 if ~exist('nsf')
  nsf = 0;
 end
 nx1 = nx - nsf;
 ny1 = nmeas - nsf;
 nd = ni-nctrl;
 nu = nctrl;
 ne = no-nmeas;
 ny = nmeas;

 [a,b,c,d] = unpck(sys);
 b1 = b(:,1:nd);
 b2 = b(:,nd+1:ni);
 c1 = c(1:ne,:);
 c2 = c(ne+1:no,:);
 d11 = d(1:ne,1:nd);
 d12 = d(1:ne,nd+1:ni);
 d21 = d(ne+1:no,1:nd);
 d22 = d(ne+1:no,nd+1:ni);

 fail = 0;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Check the last nsf measurements for the structure y2 = [0 Ci] x
% where Ci is square and invertible.
 if any(any([c2(ny1+1:nmeas,1:nx1) d21(ny1+1:nmeas,:)]))
  disp(' THE LAST OUTPUTS ARE NOT STATE MEASUREMENTS')
  fail = 1;
  return;
 end
 c22 = c2(ny1+1:nmeas,nx1+1:nx);
 if abs(det(c22)) < eps
  disp(' THE EXACT PARTIAL-STATE MEASUREMENT GAIN IS SINGULAR')
  fail = 1;
  return;
 end
 c2 = c2(1:ny1,:);
 d21 = d21(1:ny1,:);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%
% Determine if |A-jwI  B2 | has full column rank at w = 0.
%              |  C1   D12|
%
 ctmp = [a b2;c1 d12];
 [nr,nc] = size(ctmp);
 crk = rank(ctmp,eps);
 if (crk ~= nc)
   disp(' [A B2;C1 D12] DOES NOT HAVE FULL COLUMN RANK AT W = 0 ')
   fail = 1;
   return;
 end
%
% Determine if |A-jwI  B1 | has full row rank at w = 0.
%              |  C2   D21|
%
 rtmp = [a b1;c2 d21];
 [nr,nc] = size(rtmp);
 rrk = rank(rtmp,eps);
 if (rrk ~= nr)
   disp(' [A B1;C2 D21] DOES NOT HAVE FULL ROW RANK AT W = 0 ')
   fail = 1;
   return;
 end
%
% Determine if D12 has full row rank and scale D12 to Q12*D12*R12INV = |0|.
%                                                                      |I|
%
 [q12,r12] = qr(d12);
 rrk = rank(r12,eps);
 if (rrk ~= nctrl)
   disp(' D12 DOES NOT HAVE FULL ROW RANK')
   fail = 1;
   return;
 end
 q12 = [q12(:,(nu+1):ne),q12(:,1:nu)]';
 r12inv = inv(r12(1:nu,:));
%
% Determine if D21 has full column rank and scale D21 to R21INV'*D21*Q21 = [0 I].
%
 [q21,r21] = qr(d21');
 crk = rank(r21,eps);
 if (crk ~= ny1)
   disp(' D21 HAS INSUFFICIENT COLUMN RANK')
   fail = 1;
   return;
 end
 if isempty(d21)
  q21 = eye(nd);
 else
  q21 = [q21(:,(ny1+1):nd),q21(:,1:ny1)];
 end
 r21inv = inv(r21(1:ny1,:));

 c1 = q12*c1;
 c2 = r21inv'*c2;
% cc = [c1;c2];
 b1 = b1*q21;
 b2 = b2*r12inv;
% bb = [b1,b2];
 d11 = q12*d11*q21;
 d12 = [zeros(ne-nctrl,nctrl);eye(nctrl)];
 d21 = [zeros(ny1,nd-ny1) eye(ny1)];
 d22 = d22;
% dd = [d11 d12;d21 d22];
% sys = pck(aa,bb,cc,dd);

%%%% New versions for partial-state measurements:
c2 = [c2; zeros(nsf,nx1) eye(nsf)];
d21 = [d21; zeros(nsf,nd)];
r21inv = daug(r21inv,inv(c22));