Below is the function rscale.m. This function will find the scale factor for a full-state feedback system to eliminate the steady-state error. Copy the following text into a file rscale.m, and put it in the same directory as the Matlab software.
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(A,B,C,D,K) finds the scale factor N which will % eliminate the steady-state error to a step reference % 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 % 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;
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8/29/96 YS