Model Mathematics

\frac{d}{d time} (G) = Gin + 1 f5_I - (1 f2_G + f3_G f4_I) Gin = \{\begin{matrix} 0.05 + \frac{5.0}{15.0} time if time < 15.0 \land time \geq 0.0 \\ 0.05 + 5.0 \frac{45.0 - time}{45.0 - 15.0} if time < 45.0 \land time \geq 15.0 \\ 0.05 if time ≦ 240.0 \land time \geq 45.0 \\ 0.05 + \frac{5.0}{255.0} time if time > 240.0 \land time < 255.0 \\ 0.05 + 5.0 \frac{285.0 - time}{285.0 - 255.0} if time < 285.0 \land time \geq 255.0 \\ 0.05 if time ≦ 480.0 \land time \geq 285.0 \\ 0.05 + \frac{5.0}{495.0} time if time < 495.0 \land time > 480.0 \\ 0.05 + 5.0 \frac{525.0 - time}{525.0 - 495.0} if time < 525.0 \land time \geq 495.0 \\ 0.05 if time ≦ 720.0 \land time \geq 525.0 \\ 0.05 + \frac{5.0}{735.0} time if time > 720.0 \land time < 735.0 \\ 0.05 + 5.0 \frac{765.0 - time}{765.0 - 735.0} if time < 765.0 \land time \geq 735.0 \\ 0.05 if time ≦ 960.0 \land time \geq 765.0 \end{matrix}

\frac{d}{d time} (I) = Iin - (di I) Iin = \{\begin{matrix} 0.25 if time ≦ 30.0 \land time \geq 0.0 \\ 0.25 + 1.0 (1.0 + \frac{time - 120.0}{90.0}) if time < 120.0 \land time \geq 30.0 \\ 0.25 + 1.0 (1.0 - (0.5 \frac{time - 120.0}{120.0})) if time < 240.0 \land time \geq 120.0 \\ 0.25 + 0.5 (1.0 - (\frac{time - 240.0}{240.0})) if time ≦ 480.0 \land time \geq 240.0 \\ 0.25 if time < 530.0 \land time > 480.0 \\ 0.25 + 1.0 (1.0 + \frac{time - 620.0}{90.0}) if time < 620.0 \land time \geq 530.0 \\ 0.25 + 1.0 (1.0 - (0.5 \frac{time - 620.0}{120.0})) if time < 740.0 \land time \geq 620.0 \\ 0.25 + 0.5 (1.0 - (\frac{time - 740.0}{240.0})) if time ≦ 980.0 \land time \geq 740.0 \end{matrix}

f2_G = Ub (1.0 - (ⅇ^{\frac{- G}{C2 Vg 1.0}}))

f3_G = \frac{G}{C3 Vg}

f4_I = U0 + \frac{Um - U0}{1.0 + ⅇ^{(- beta) \ln (\frac{I}{C4 (\frac{1.0}{Vi} + \frac{1.0}{0.2 ti})})}}

f5_I = \frac{Rg}{1.0 + ⅇ^{alpha \frac{I}{1.0 (1.0 Vp - C5)}}}