Model Mathematics

delta_L_sec = L_mtc - delta_L_pec - L_mslack f_sec = \{\begin{matrix} \frac{F_1}{ⅇ^{k_sh} - 1} (ⅇ^{\frac{k_sh delta_L_sec}{delta_L_sec1}} - 1) if delta_L_sec > 0 \land delta_L_sec < delta_L_sec1 \\ F_1 + k (delta_L_sec - delta_L_sec1) if delta_L_sec ≦ delta_L_sec1 \end{matrix} f_pec = \{\begin{matrix} k_1 (ⅇ^{k_2 delta_L_pec} - 1) if delta_L_pec > 0 \\ 0 if delta_L_pec ≦ 0 \end{matrix} v_cc = \frac{1}{f_v} \frac{f_sec - f_pec}{A f_L F_im} \frac{d}{d time} (delta_L_pec) = v_cc f_v = \frac{v_max - v_cc}{v_max + v_cc curv} f_L = \{\begin{matrix} \frac{f_c}{L_2 - L_1} (delta_L_pec - L_1) if delta_L_pec \geq L_1 \land delta_L_pec ≦ L_2 \\ \frac{1 - f_c}{- L_2} (delta_L_pec - L_2) if delta_L_pec > L_2 \land delta_L_pec ≦ 0 \\ 1 if delta_L_pec > 0 \land delta_L_pec ≦ L_3 \\ \frac{- 1}{L_4 - L_3} (delta_L_pec - L_3) if delta_L_pec > L_3 \land delta_L_pec ≦ L_4 \end{matrix} L_mtc = \{\begin{matrix} 0.29 if time ≦ 1 \\ 0.22 if time > 1 \land time < 5 \\ 0.19 otherwise \end{matrix}