# Model Mathematics

### Component: G

$ddtime G = Gin + 1 ⁢ f5_I - 1 ⁢ f2_G + f3_G ⁢ f4_I Gin = 0.05 + 5.0 15.0 ⁢ time if time < 15.0 ∧ time ≥ 0.0 0.05 + 5.0 ⁢ 45.0 - time 45.0 - 15.0 if time < 45.0 ∧ time ≥ 15.0 0.05 if time ≦ 240.0 ∧ time ≥ 45.0 0.05 + 5.0 255.0 ⁢ time if time > 240.0 ∧ time < 255.0 0.05 + 5.0 ⁢ 285.0 - time 285.0 - 255.0 if time < 285.0 ∧ time ≥ 255.0 0.05 if time ≦ 480.0 ∧ time ≥ 285.0 0.05 + 5.0 495.0 ⁢ time if time < 495.0 ∧ time > 480.0 0.05 + 5.0 ⁢ 525.0 - time 525.0 - 495.0 if time < 525.0 ∧ time ≥ 495.0 0.05 if time ≦ 720.0 ∧ time ≥ 525.0 0.05 + 5.0 735.0 ⁢ time if time > 720.0 ∧ time < 735.0 0.05 + 5.0 ⁢ 765.0 - time 765.0 - 735.0 if time < 765.0 ∧ time ≥ 735.0 0.05 if time ≦ 960.0 ∧ time ≥ 765.0$

### Component: I

$ddtime I = Iin - di ⁢ I Iin = 0.25 if time ≦ 30.0 ∧ time ≥ 0.0 0.25 + 1.0 ⁢ 1.0 + time - 120.0 90.0 if time < 120.0 ∧ time ≥ 30.0 0.25 + 1.0 ⁢ 1.0 - 0.5 ⁢ time - 120.0 120.0 if time < 240.0 ∧ time ≥ 120.0 0.25 + 0.5 ⁢ 1.0 - time - 240.0 240.0 if time ≦ 480.0 ∧ time ≥ 240.0 0.25 if time < 530.0 ∧ time > 480.0 0.25 + 1.0 ⁢ 1.0 + time - 620.0 90.0 if time < 620.0 ∧ time ≥ 530.0 0.25 + 1.0 ⁢ 1.0 - 0.5 ⁢ time - 620.0 120.0 if time < 740.0 ∧ time ≥ 620.0 0.25 + 0.5 ⁢ 1.0 - time - 740.0 240.0 if time ≦ 980.0 ∧ time ≥ 740.0$

### Component: f2_G

$f2_G = Ub ⁢ 1.0 -ⅇ- G C2 ⁢ Vg ⁢ 1.0$

### Component: f3_G

$f3_G = G C3 ⁢ Vg$

### Component: f4_I

$f4_I = U0 + Um - U0 1.0 +ⅇ- beta ⁢ln⁡ I C4 ⁢ 1.0 Vi + 1.0 0.2 ⁢ ti$

### Component: f5_I

$f5_I = Rg 1.0 +ⅇ alpha ⁢ I 1.0 ⁢ 1.0 ⁢ Vp - C5$

### Component: model_parameters

Source
Derived from workspace Wang, Li, Kuang, 2007 at changeset b0afdb9fbe31.
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