Plant

Second-order linear system for testing control designs.

A linear dynamic system with second-order behavior that exhibits damped oscillations in response to inputs.

The system is described by the state-space representation:

$$\begin{array}{rl}{\dot{x}}_1& =x_2\\ {\dot{x}}_2& =-x_1-0.5x_2+u\\ y& =0.5x_1+x_2\end{array}$$

where states x1 and x2 represent position and velocity in a mechanical system analogy.

This component extends from SISO

Usage

BlockComponents.Plant()

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
x1	First state variable (position in mechanical analogy)	–
x2	Second state variable (velocity in mechanical analogy)	–

Behavior

$$\begin{array}{rl}\frac{\mathrm{d}\mathtt{x}\mathtt{1}\left(t\right)}{\mathrm{d}t}& =\mathtt{x}\mathtt{2}\left(t\right)\\ \frac{\mathrm{d}\mathtt{x}\mathtt{2}\left(t\right)}{\mathrm{d}t}& =u\left(t\right)-\mathtt{x}\mathtt{1}\left(t\right)-0.5\mathtt{x}\mathtt{2}\left(t\right)\\ y\left(t\right)& =0.5\mathtt{x}\mathtt{1}\left(t\right)+\mathtt{x}\mathtt{2}\left(t\right)\end{array}$$

Source

"""
Second-order linear system for testing control designs.

A linear dynamic system with second-order behavior that exhibits damped oscillations in response to inputs.

The system is described by the state-space representation:

math \begin{align} \dot{x}_1 &= x_2 MarkdownAST.LineBreak()

\dot{x}_2 &= -x_1 - 0.5x_2 + u MarkdownAST.LineBreak()

y &= 0.5x_1 + x_2 \end

where states `x1` and `x2` represent position and velocity in a mechanical system analogy.
"""
component Plant
  extends SISO
  "First state variable (position in mechanical analogy)"
  variable x1::Real
  "Second state variable (velocity in mechanical analogy)"
  variable x2::Real
relations
  der(x1) = x2
  der(x2) = -x1 - 0.5 * x2 + u
  y = 0.5 * x1 + x2
metadata {
  "Dyad": {
    "icons": {"default": "dyad://BlockComponents/SecondOrder.svg"},
    "labels": [{"label": "$(instance)", "x": 500, "y": 1100, "rot": 0}]
  }
}
end

Flattened Source

"""
Second-order linear system for testing control designs.

A linear dynamic system with second-order behavior that exhibits damped oscillations in response to inputs.

The system is described by the state-space representation:

math \begin{align} \dot{x}_1 &= x_2 MarkdownAST.LineBreak()

\dot{x}_2 &= -x_1 - 0.5x_2 + u MarkdownAST.LineBreak()

y &= 0.5x_1 + x_2 \end

where states `x1` and `x2` represent position and velocity in a mechanical system analogy.
"""
component Plant
  "Input signal port"
  u = RealInput() {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "input", "x1": -100, "y1": 450, "x2": 0, "y2": 550, "rot": 0},
        "diagram": {"iconName": "input", "x1": -100, "y1": 450, "x2": 0, "y2": 550, "rot": 0}
      }
    }
  }
  "Output signal port"
  y = RealOutput() {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "output", "x1": 1000, "y1": 450, "x2": 1100, "y2": 550, "rot": 0},
        "diagram": {"iconName": "output", "x1": 1000, "y1": 450, "x2": 1100, "y2": 550, "rot": 0}
      }
    }
  }
  "First state variable (position in mechanical analogy)"
  variable x1::Real
  "Second state variable (velocity in mechanical analogy)"
  variable x2::Real
relations
  der(x1) = x2
  der(x2) = -x1 - 0.5 * x2 + u
  y = 0.5 * x1 + x2
metadata {
  "Dyad": {
    "labels": [{"label": "$(instance)", "x": 500, "y": 1100, "rot": 0}],
    "icons": {"default": "dyad://BlockComponents/SecondOrder.svg"}
  }
}
end

Test Cases

No test cases defined.

Related

• Examples

• Experiments

• Analyses

• Tests

  • LimPIDTest