rscale.m

function[Nbar]=rscale(a,b,c,d,k)
% Given the single-input linear system: 
%       .
%       x = Ax + Bu
%       y = Cx + Du
% and the feedback matrix K,
% 
% the function rscale(sys,K) or rscale(A,B,C,D,K) 
% finds the scale factor N which will 
% eliminate the steady-state error to a step reference 
% for a continuous-time, single-input system
% with full-state feedback using the schematic below:
%
%                         /---------\
%      R         +     u  | .       |
%      ---> N --->() ---->| X=Ax+Bu |--> y=Cx ---> y
%                -|       \---------/
%                 |             | 
%                 |<---- K <----|
%
%8/21/96 Yanjie Sun of the University of Michigan
%        under the supervision of Prof. D. Tilbury
%6/12/98 John Yook, Dawn Tilbury revised

error(nargchk(2,5,nargin));

% --- Determine which syntax is being used ---
nargin1 = nargin;
if (nargin1==2),	% System form
		[A,B,C,D] = ssdata(a);
		K=b;
elseif (nargin1==5), % A,B,C,D matrices
		A=a; B=b; C=c; D=d; K=k;
else error('Input must be of the form (sys,K) or (A,B,C,D,K)')
end;

% compute Nbar
s = size(A,1);
Z = [zeros([1,s]) 1];
N = inv([A,B;C,D])*Z';
Nx = N(1:s);
Nu = N(1+s);
Nbar=Nu + K*Nx;