Model Mathematics

Tao = \{\begin{matrix} 1 if Pi \geq Po \\ 0 if Pi < Po \end{matrix} Qo = \{\begin{matrix} CV Tao {(| Pi - Po |)}^{0.5} if Pi \geq Po \\ (-1) CV Tao {(| Po - Pi |)}^{0.5} if Pi < Po \end{matrix} \frac{d}{d t} (V) = Qi - Qo Pi = Pini + E (V - Vini)

Tao = \{\begin{matrix} 1 if Pi \geq Po \\ 0 if Pi < Po \end{matrix} Qo = \{\begin{matrix} CV Tao {(| Pi - Po |)}^{0.5} if Pi \geq Po \\ (-1) CV Tao {(| Po - Pi |)}^{0.5} if Pi < Po \end{matrix} \frac{d}{d t} (V) = Qi - Qo Pi = Pini + E (V - Vini)

mt = t - (T ⌊ \frac{t}{T} ⌋) et = \{\begin{matrix} 1 - (\cos (\frac{2 3.14159 (mt - ((Tpwb - 1) T))}{Tpww T})) if mt \geq 0 \land mt ≦ (Tpwb + Tpww - 1) T \\ 0 if mt > (Tpwb + Tpww - 1) T \land mt ≦ Tpwb T \\ 1 - (\cos (\frac{2 3.14159 (mt - (Tpwb T))}{Tpww T})) if mt > Tpwb T \land mt ≦ T \end{matrix} E = Emin + \frac{et (Emax - Emin)}{2}

mt = t - (T ⌊ \frac{t}{T} ⌋) et = \{\begin{matrix} 1 - (\cos (\frac{3.14159 mt}{Ts1 T})) if mt \geq 0 \land mt ≦ Ts1 T \\ 1 + \cos (\frac{3.14159 (mt - (Ts1 T))}{(Ts2 - Ts1) T}) if mt > Ts1 T \land mt ≦ Ts2 T \\ 0 if mt > Ts2 T \land mt < T \end{matrix} E = Emin + \frac{et (Emax - Emin)}{2}

\frac{d}{d t} (Pi) = \frac{Qi - Qo}{C} Qo = \frac{Pi - Po}{R}