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Mar 22, 2024
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docs: cleaner and more concise transfer function of Derivative() #277

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13 changes: 6 additions & 7 deletions src/Blocks/continuous.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -35,24 +35,23 @@ end
Derivative(; name, k = 1, T, x = 0.0)

Outputs an approximate derivative of the input. The transfer function of this block is
Initial value of the state ``x`` can be set with `x`

```
k k
─ - ──────────
T 2 ⎛ 1⎞
T ⋅⎜s + ─⎟
⎝ T⎠
k k ks
─ - ─────── = ──────
T sT² + T sT + 1
```

and a state-space realization is given by `ss(-1/T, 1/T, -k/T, k/T)`
where `T` is the time constant of the filter.
A smaller `T` leads to a more ideal approximation of the derivative.

Initial value of the state ``x`` can be set with `x`.

# Parameters:

- `k`: Gain
- `T`: [s] Time constants (T>0 required; T=0 is ideal derivative block)
- `T`: [s] Time constant (T>0 required; T=0 is ideal derivative block)

# Unknowns:

Expand Down