Derivative Icon

`Derivative`

Outputs an approximate derivative of the input. The transfer function of this block is

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.

This component extends from SISO

Parameters:

Name	Description	Units	Default value
`x0`	Initial value of the derivative-filter state	–	0
`T`	Time constant	–
`k`	Gain	–	1

Connectors

u - This connector represents a real signal as an input to a component (RealInput)
y - This connector represents a real signal as an output from a component (RealOutput)

Variables

Name	Description	Units
`x`	Derivative-filter state	–

\[ \begin{align} \frac{\mathrm{d} x\left( t \right)}{\mathrm{d}t} &= \frac{u\left( t \right) - x\left( t \right)}{T} \\ y\left( t \right) &= \frac{k \left( u\left( t \right) - x\left( t \right) \right)}{T} \end{align} \]

Source

# Outputs an approximate derivative of the input. The transfer function of this block is
#
# ```
# 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.
component Derivative
  extends SISO
  # Derivative-filter state
  variable x::Real
  # Initial value of the derivative-filter state
  parameter x0::Real = 0
  # Time constant
  parameter T::Real
  # Gain
  parameter k::Real = 1.0
relations
  initial x = x0
  der(x) = (u-x)/T
  y = (k/T)*(u-x)
metadata {"JuliaSim": {"icons": {"default": "jsml://BlockComponents/Derivative.svg"}}}
end

Flattened Source

# Outputs an approximate derivative of the input. The transfer function of this block is
#
# ```
# 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.
component Derivative
  u = RealInput() [{
    "JuliaSim": {
      "placement": {"icon": {"iconName": "input", "x1": -50, "y1": 450, "x2": 50, "y2": 550}}
    }
  }]
  y = RealOutput() [{
    "JuliaSim": {
      "placement": {"icon": {"iconName": "output", "x1": 950, "y1": 450, "x2": 1050, "y2": 550}}
    }
  }]
  # Derivative-filter state
  variable x::Real
  # Initial value of the derivative-filter state
  parameter x0::Real = 0
  # Time constant
  parameter T::Real
  # Gain
  parameter k::Real = 1.0
relations
  initial x = x0
  der(x) = (u-x)/T
  y = (k/T)*(u-x)
metadata {"JuliaSim": {"icons": {"default": "jsml://BlockComponents/Derivative.svg"}}}
end

Test Cases

Examples
Experiments
Analyses