routh_app.m

控制系统计算机辅助设计——MATLAB语言与应用(源代码）

function G_red=routh_app(G_Sys,nr)
%ROUTH_APP finds the Routh reduced order model.
%  
%G_red=routh_app(G_Sys,nn)
%     where G_Sys is the original model.
%       nn is the expected orders of reduced order model.
%     Returned G_red is the reduced order model.
%See Also:  PADE_REDC, OPT_RED

%Designed by Professor Dingyu Xue
%Northeastern University, Shenyang 110004, P R China
%first drafted in 1989, revised for LFC book, 2002
num=G_Sys.num{1}; den=G_Sys.den{1};
n0=length(den); n1=length(num); 
a1=den(end:-1:1);
b1=[num(end:-1:1) zeros(1,n0-n1-1)];
for k=1:n0-1, 
   k1=k+2; alpha(k)=a1(k)/a1(k+1); 
   beta(k)=b1(k)/a1(k+1);
   for i=k1:2:n0-1, 
      a1(i)=a1(i)-alpha(k)*a1(i+1); 
      b1(i)=b1(i)-beta(k)*a1(i+1); 
   end, 
end
nn=[]; dd=[1]; nn1=beta(1); 
dd1=[alpha(1),1]; nred=nn1; dred=dd1;
for i=2:nr,
   nred=[alpha(i)*nn1, beta(i)]; 
   dred=[alpha(i)*dd1, 0]; n0=length(dd); 
   n1=length(dred);
   nred=nred+[zeros(1,n1-n0),nn]; 
   dred=dred+[zeros(1,n1-n0),dd];
   nn=nn1; dd=dd1; nn1=nred; dd1=dred;
end
G_red=tf(nred(nr:-1:1),dred(end:-1:1));