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Derivative(; name, k = 1, T, x = 0.0)
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Outputs an approximate derivative of the input. The transfer function of this block is
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- Initial value of the state ``x`` can be set with `x`
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```
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- k k
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- ─ - ──────────
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- T 2 ⎛ 1⎞
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- T ⋅⎜s + ─⎟
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- ⎝ T⎠
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+ k k ks
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+ ─ - ─────── = ──────
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+ T sT² + T sT + 1
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```
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and a state-space realization is given by `ss(-1/T, 1/T, -k/T, k/T)`
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where `T` is the time constant of the filter.
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A smaller `T` leads to a more ideal approximation of the derivative.
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+ Initial value of the state ``x`` can be set with `x`.
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+
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# Parameters:
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- `k`: Gain
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- - `T`: [s] Time constants (T>0 required; T=0 is ideal derivative block)
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+ - `T`: [s] Time constant (T>0 required; T=0 is ideal derivative block)
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# Unknowns:
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