FirstOrder Icon

`FirstOrder`

A first-order filter with a single real pole at s = -1/T and gain k. The transfer function is given by $Y(s)/U(s) =$

k
───────
sT + 1

This component extends from SISO

Usage

FirstOrder(T, k=1.0)

Parameters:

Name	Description	Units	Default value
`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`	State of FirstOrder filter	–

Behavior

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

Source

# A first-order filter with a single real pole at `s = -1/T` and gain `k`. The transfer function
# is given by ``Y(s)/U(s) = ``
#
# ```
# k
# ───────
# sT + 1
# ```
component FirstOrder
  extends SISO
  # State of FirstOrder filter
  variable x::Real
  # Time constant
  parameter T::Real
  # Gain
  parameter k::Real = 1.0
relations
  der(x) = (k*u-x)/T
  y = x
metadata {"JuliaSim": {"icons": {"default": "jsml://BlockComponents/FirstOrder.svg"}}}
end

Flattened Source

# A first-order filter with a single real pole at `s = -1/T` and gain `k`. The transfer function
# is given by ``Y(s)/U(s) = ``
#
# ```
# k
# ───────
# sT + 1
# ```
component FirstOrder
  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}}
    }
  }]
  # State of FirstOrder filter
  variable x::Real
  # Time constant
  parameter T::Real
  # Gain
  parameter k::Real = 1.0
relations
  der(x) = (k*u-x)/T
  y = x
metadata {"JuliaSim": {"icons": {"default": "jsml://BlockComponents/FirstOrder.svg"}}}
end

Test Cases

Examples
Experiments
Analyses