# Model Mathematics

### Component: A_B

$A_B = r_B 2 ⁢π$

### Component: r_B

$ddtime r_B = k_for X_b ⁢ xb + 1 X_y ⁢ xy - k_res X_c ⁢ xc + k_rB ⁢ r_B$

### Component: xy

$ddtime xy = k_byp ⁢ xb - X_bss - k_yd ⁢ xy - X_yss$

### Component: F_sti

$F_sti = F_s ⁢ xy 1 +ⅇ- k_Fs ⁢ F_s + k_y ⁢ xy$

### Component: F_s

$F_s = F_a A_B$$F_a = 10000.0 if time ≥ 100.0 ∧ time < 130.0 100.0 otherwise$

### Component: x_no

$ddtime x_no = k_yno ⁢ F_sti + X_noe - k_nod ⁢ x_no$

### Component: x_pge

$ddtime x_pge = k_ypge ⁢ F_sti + k_nopge ⁢ x_no + X_pgex - k_pged ⁢ x_pge$

### Component: x_opg

$ddtime x_opg =K_o_p1⁢ pi_c ⁢ xr + Io + k_nopg ⁢ x_no - k_opgd ⁢ x_opg$

### Component: x_kl

$ddtime x_kl = rl + Il - k_nokl ⁢ x_no + rl ⁢ 1 + k1 k2 ⁢ x_opg + k3 k4 ⁢ K K_l_p ⁢ pi_p ⁢ xb ⁢ x_kl$$pi_L=k3k4⁢K_l_p⁢pi_p⁢xb1+k3⁢Kk4+k1k2⁢ko⁢K_o_p1pi_p⁢xr+Io⁢1+Ilrl$

### Component: xr

$ddtime xr = D_R ⁢ pi_c + k_pger ⁢ x_pge - D_B pi_c ⁢ xr$

### Component: xb

$ddtime xb = D_B pi_c ⁢ xr - k_B ⁢ xb$

### Component: xc

$ddtime xc = D_C ⁢ pi_L - D_A ⁢ pi_c ⁢ xc$

### Component: model_parameters

$D_B=f0⁢dBpi_c=xc+f0⁢C_sxc+C_spi_p=P+P_0P+P_sP=IPkPP_0=SPkPP_s=k6k5$
Source
Derived from workspace Maldonado, Borchers, Findeisen and Allgower, 2006 at changeset d1c385b5e9d2.
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