User`s guide

Estimating Linear Grey- Box Models

The following M-ﬁle describes the state-space equation for this model. In

this case, the auxiliary v ariables specify grid-size variables, so that you can

modifythegridsizewithouttheM-ﬁle.

function [A,B, C,D, K,x0] = heatd(pars,T,aux)

% Number of points in the space-discretization

Ngrid = aux(1);

% Length of the rod

L = aux(2);

% Initial rod temperature (un iform)

temp = aux(3);

% Space interval

deltaL = L/Ngrid;

% Heat-diffusio n coefficient

kappa = pars(1);

% Heat transfer coefficient at far end of rod

htf = pars(2);

A = zeros(Ngrid,Ngrid);

for kk = 2 :Ngr id-1

A(kk,kk-1) = 1;

A(kk,kk) = -2;

A(kk,kk+1) = 1;

end

% Boundary condition on insulated end

A(1,1) = -1; A(1,2) = 1;

A(Ngrid,Ngrid-1) = 1;

A(Ngrid,Ngrid) = -1;

A = A*kappa/deltaL/deltaL;

B = zeros(Ngrid,1);

B(Ngrid,1) = htf/deltaL;

C = zeros(1,Ngrid);

C(1,1) = 1;

D=0;

K = zeros(Ngrid,1);

x0 = temp*ones(Ngrid,1);

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