Model Mathematics

F_CE = f_L_CE g_V_CE a

f_L_CE = \frac{F_max (1 (1 - L_CE) - ({L_CE_opt}^{2}))}{W^{2} {L_CE_opt}^{2}}

g_V_CE = \{\begin{matrix} \frac{lambda_a V_max + V_CE}{lambda_a V_max - (\frac{V_CE}{A})} if V_CE ≦ 0 \\ \frac{g_max V_CE + d1}{V_CE + d1} if 0 < V_CE \land V_CE ≦ gamma d1 \\ d3 + d2 V_CE if V_CE > gamma d1 \end{matrix}

d1 = \frac{V_max A (g_max - 1)}{S (A + 1)}

d2 = \frac{S (A + 1)}{V_max A {(gamma + 1)}^{2}}

d3 = \frac{(g_max - 1) {gamma}^{2}}{{(gamma + 1)}^{2}} + 1

F_SEE = \{\begin{matrix} 0 if L_SEE ≦ L_slack \\ k_SEE {(L_SEE - L_slack)}^{2} otherwise \end{matrix}

F_PEE = \{\begin{matrix} 0 if L_CE ≦ L_slack \\ k_PEE {(L_CE - L_slack)}^{2} otherwise \end{matrix}

k_PEE = \frac{F_max}{{(W L_CE_opt)}^{2}}

V_CE = 1 \frac{\frac{1}{g_V_CE} (F_SEE (L_m - L_CE) - (F_PEE L_CE))}{a f_L_CE}

F_m = F_SEE

lambda_a = 1 ((1 - (ⅇ^{(- 3.82) a})) + a ⅇ^{- 3.82})

\frac{d}{d time} (L_CE) = 1 V_CE

L_SEE = L_m - L_CE

L_m = \{\begin{matrix} 0.038 if time ≦ 1 \\ 0.038 + 0.002 (time - 1) if time > 1 \land time < 2 \\ 0.04 otherwise \end{matrix}