towards matlab

matlab/rscale.m

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+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;