Fitting a Nonlinear, Dynamic System

Identification Problem for Fitting

The bushing identification is formulated as follows:

$Cost(b)={\displaystyle \sum _{i=1}^{ncase}\left\{{\left(1-\frac{k_{d\_\text{model}}^i}{k_{d\_test}^i}\right)}^2+{\left(1-\frac{{\phi }_{\text{model}}^i}{{\phi }_{test}^i}\right)}^2\right\}}$ , ncase = the number of measurements made

such that the constraints:

$H\left(x_0+x_m{e}^{j\left({\omega }_{0}t+{\phi }_x\right)},j{\omega }_0{x}_m{e}^{j\left({\omega }_{0}t+{\phi }_x\right)},y_0+k_d{u}_m{e}^{j\left({\omega }_{0}t+\phi \right)},u_0+u_m{e}^{j{\omega }_{0}t},p\right)=0$

Subject to limits on the parameters p:

$L_i\le p_i\le U_i,i=1\dots N_p$