transf.m

线性时变系统控制器设计的工具包

% function [a,b1,b2,c1,c2,d11,d12,d21,d22,r12inv,r21inv,q12,q21,fail] = ...
%            transf(sys,nmeas,nctrl)
%
% This program is designed to scale the d12 and d21 matrices to satisfy the 
% standard formulas and check the rank conditions.
%
 function [a,b1,b2,c1,c2,d11,d12,d21,d22,r12inv,r21inv,q12,q21,fail] = ...
            transf(sys,nmeas,nctrl)

 [systype,no,ni,nx] = minfo(sys);
 nd1 = ni-nctrl;
 nd2 = nctrl;
 ne1 = no-nmeas;
 ne2 = nmeas;

 [a,b,c,d] = unpck(sys);
 b1 = b(:,1:nd1);
 b2 = b(:,nd1+1:ni);
 c1 = c(1:ne1,:);
 c2 = c(ne1+1:no,:);
 d11 = d(1:ne1,1:nd1);
 d12 = d(1:ne1,nd1+1:ni);
 d21 = d(ne1+1:no,1:nd1);
 d22 = d(ne1+1:no,nd1+1:ni);

 fail = 0;
%
% 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 ~= nd2)
   disp(' D12 DOES NOT HAVE FULL COLUMN RANK')
   fail = 1;
   return;
 end
 q12 = [q12(:,(nd2+1):ne1),q12(:,1:nd2)]';
 r12inv = inv(r12(1:nd2,:));
%
% 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 ~= ne2)
   disp(' D21 DOES NOT HAVE FULL ROW RANK')
   fail = 1;
   return;
 end
 q21 = [q21(:,(ne2+1):nd1),q21(:,1:ne2)];
 r21inv = inv(r21(1:ne2,:));

 c1 = q12*c1;
 c2 = r21inv'*c2;
% cc = [c1;c2];
 b1 = b1*q21;
 b2 = b2*r12inv;
% bb = [b1,b2];
 d11 = q12*d11*q21;
 d12 = [zeros(ne1-nctrl,nctrl);eye(nctrl)];
 d21 = [zeros(nmeas,nd1-nmeas) eye(nmeas)];
 d22 = d22;
% dd = [d11 d12;d21 d22];
% sys = pck(aa,bb,cc,dd);