Model Mathematics

\frac{d}{d time} (Ip) = f1_G - (E (\frac{Ip}{Vp} - (\frac{Ii}{Vi})) + \frac{Ip}{tp}) f1_G = \frac{Rm}{1.0 + ⅇ^{\frac{\frac{C1 - G}{Vg}}{a1}}}

\frac{d}{d time} (Ii) = E (\frac{Ip}{Vp} - (\frac{Ii}{Vi})) - (\frac{Ii}{ti})

\frac{d}{d time} (G) = Gin + f5_x3 f6_G + (- (f2_G + f3_G f4_Ii + f7_G)) f2_G = Ub (1.0 - (ⅇ^{\frac{- G}{C2 Vg}})) f3_G = \frac{G}{C3 Vg} f4_Ii = U0 + \frac{Um - U0}{1.0 + ⅇ^{- (beta \ln (\frac{Ii}{C4 \frac{1.0}{Vi + \frac{1.0}{E ti}}}))}} f5_x3 = \frac{Rg}{1.0 + ⅇ^{alpha \frac{x3}{Vp - C5}}} f6_G = \frac{1.0}{1.0 + ⅇ^{gamma \frac{G}{C3 Vg - C6}}} f7_G = Sb + (Sm - Sb) + 1.0 + ⅇ^{delta \frac{G}{C3 Vg - C7}}

\frac{d}{d time} (x1) = \frac{3.0}{td} (Ip - x1) \frac{d}{d time} (x2) = \frac{3.0}{td} (x1 - x2) \frac{d}{d time} (x3) = \frac{3.0}{td} (x2 - x3)