System identification Windkessel - pulse wave

Prashant Kumar answered . 2024-12-21 03:16:08

syms C L R r Pi Po P2 s t 
Z1 = 1/r;
Z2 = s*C + 1/R;
Z3 = 1/(s*L);
Zt = Z1 + Z2 + Z3;

I = Pi/Zt;
Po = Z2*I;
Out = ilaplace(partfrac(Po, s));
Out = simplify(Out, 'Steps',20);
Out_fcn = matlabFunction(Out, 'Vars',{t,Pi,r,C,R,L})

Out_fcn = @(t,Pi,r,C,R,L) Pi.*dirac(t)-(Pi.*exp((t.*(R+r).*(-1.0./2.0))./(C.*R.*r)).*(cosh((1.0./sqrt(L).*t.*sqrt(L.*R.^2+L.*r.^2-C.*R.^2.*r.^2.*4.0+L.*R.*r.*2.0).*(1.0./2.0))./(C.*R.*r))-1.0./sqrt(L).*sinh((1.0./sqrt(L).*t.*sqrt(L.*R.^2+L.*r.^2-C.*R.^2.*r.^2.*4.0+L.*R.*r.*2.0).*(1.0./2.0))./(C.*R.*r)).*(L.*r+L.*R-C.*R.*r.^2.*2.0).*1.0./sqrt(L.*R.^2+L.*r.^2-C.*R.^2.*r.^2.*4.0+L.*R.*r.*2.0)))./(C.*r);

% % % MAPPING: b(1) = r,  b(2) = C,  b(3) = R,  b(4) = L
Out_fcn = @(t,Pi,r,C,R,L) Pi.*dirac(t)-(Pi.*exp((t.*(R+r).*(-1.0./2.0))./(C.*R.*r)).*(cosh((1.0./sqrt(L).*t.*sqrt(L.*R.^2+L.*r.^2-C.*R.^2.*r.^2.*4.0+L.*R.*r.*2.0).*(1.0./2.0))./(C.*R.*r))-1.0./sqrt(L).*sinh((1.0./sqrt(L).*t.*sqrt(L.*R.^2+L.*r.^2-C.*R.^2.*r.^2.*4.0+L.*R.*r.*2.0).*(1.0./2.0))./(C.*R.*r)).*(L.*r+L.*R-C.*R.*r.^2.*2.0).*1.0./sqrt(L.*R.^2+L.*r.^2-C.*R.^2.*r.^2.*4.0+L.*R.*r.*2.0)))./(C.*r);

t = t(:);                                                           % Column Vector
Pi = Pi(:);                                                         % Column Vector
Po = Po(:);                                                         % Column Vector
b0 = ['Initial Parameter Estimates For r,C,R,L — IN THAT ORDER — As A Vector'];
nrmrsd = @(b) norm(Po - Out_fcn(t,Pi,b(1),b(2),b(3),b(4)));         % Norm Of Residuals (Errors)
bvals = fminsearch(nrmrsd, b0);

The ‘bvals’ vector will be the estimated parameters.

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