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Examples.AircraftPitch.md

Examples.AircraftPitch ​

Simplified pitch-attitude dynamics of an aircraft whose aerodynamic coefficients scale with the dynamic pressure.

The pitch angle and the pitch rate obey

where is the elevator deflection, the airspeed and   the dynamic pressure at the altitude , computed with an exponential model of the air density. The static gain from to is independent of the operating point, whereas the gain at high frequencies is proportional to and the natural frequency is proportional to .

Usage ​

DiscreteComponents.Examples.AircraftPitch(rho0=1.225, H=8500, c_u=6e-4, c_theta=4e-4, c_omega=7.4e-3)

Parameters: ​

NameDescriptionUnitsDefault value
rho0Air density at sea level [kg/m³]–1.225
HScale height of the exponential atmosphere [m]–8500
c_uPitch acceleration per unit elevator deflection and unit dynamic pressure–6e-4
c_thetaPitch acceleration per unit pitch angle and unit dynamic pressure–4e-4
c_omegaPitch damping coefficient–7.4e-3

Connectors ​

  • u - This connector represents a real signal as an input to a component (RealInput)

  • h - This connector represents a real signal as an input to a component (RealInput)

  • V - This connector represents a real signal as an input to a component (RealInput)

  • theta - This connector represents a real signal as an output from a component (RealOutput)

Variables ​

NameDescriptionUnits
pitchPitch angle [rad]–
omegaPitch rate [rad/s]–
qDynamic pressure [Pa]–

Behavior ​

Source ​

dyad
"""
Simplified pitch-attitude dynamics of an aircraft whose aerodynamic coefficients scale with the dynamic pressure.

The pitch angle ``θ`` and the pitch rate ``ω`` obey

```math
\begin{aligned}
\dot θ &= ω \\
\dot ω &= q \left( c_u u - c_θ θ \right) - c_ω \dfrac{q}{V} ω
\end{aligned}
```

where ``u`` is the elevator deflection, ``V`` the airspeed and ``q = \tfrac{1}{2} ρ_0 e^{-h/H} V^2`` the dynamic pressure at the altitude ``h``, computed with an exponential model of the air density. The static gain from ``u`` to ``θ`` is independent of the operating point, whereas the gain at high frequencies is proportional to ``q`` and the natural frequency is proportional to ``\sqrt{q}``.
"""
component AircraftPitch
  "Elevator deflection [rad]"
  u = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -100, "y1": 450, "x2": 0, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Altitude [m]"
  h = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 200, "y1": -100, "x2": 300, "y2": 0, "rot": 90}
      },
      "tags": []
    }
  }
  "Airspeed [m/s]"
  V = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 700, "y1": -100, "x2": 800, "y2": 0, "rot": 90}
      },
      "tags": []
    }
  }
  "Pitch angle [rad]"
  theta = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1000, "y1": 450, "x2": 1100, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Air density at sea level [kg/m³]"
  parameter rho0::Real = 1.225
  "Scale height of the exponential atmosphere [m]"
  parameter H::Real = 8500
  "Pitch acceleration per unit elevator deflection and unit dynamic pressure"
  parameter c_u::Real = 6e-4
  "Pitch acceleration per unit pitch angle and unit dynamic pressure"
  parameter c_theta::Real = 4e-4
  "Pitch damping coefficient"
  parameter c_omega::Real = 7.4e-3
  "Pitch angle [rad]"
  variable pitch::Real
  "Pitch rate [rad/s]"
  variable omega::Real
  "Dynamic pressure [Pa]"
  variable q::Real
relations
  initial pitch = 0
  initial omega = 0
  q = 0.5 * rho0 * exp(-h / H) * V ^ 2
  der(pitch) = omega
  der(omega) = q * (c_u * u - c_theta * pitch) - c_omega * q / V * omega
  theta = pitch
metadata {"Dyad": {"icons": {"default": "dyad://Dyad/Default.svg"}}}
end
Flattened Source
dyad
"""
Simplified pitch-attitude dynamics of an aircraft whose aerodynamic coefficients scale with the dynamic pressure.

The pitch angle ``θ`` and the pitch rate ``ω`` obey

```math
\begin{aligned}
\dot θ &= ω \\
\dot ω &= q \left( c_u u - c_θ θ \right) - c_ω \dfrac{q}{V} ω
\end{aligned}
```

where ``u`` is the elevator deflection, ``V`` the airspeed and ``q = \tfrac{1}{2} ρ_0 e^{-h/H} V^2`` the dynamic pressure at the altitude ``h``, computed with an exponential model of the air density. The static gain from ``u`` to ``θ`` is independent of the operating point, whereas the gain at high frequencies is proportional to ``q`` and the natural frequency is proportional to ``\sqrt{q}``.
"""
component AircraftPitch
  "Elevator deflection [rad]"
  u = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -100, "y1": 450, "x2": 0, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Altitude [m]"
  h = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 200, "y1": -100, "x2": 300, "y2": 0, "rot": 90}
      },
      "tags": []
    }
  }
  "Airspeed [m/s]"
  V = RealInput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 700, "y1": -100, "x2": 800, "y2": 0, "rot": 90}
      },
      "tags": []
    }
  }
  "Pitch angle [rad]"
  theta = RealOutput() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 1000, "y1": 450, "x2": 1100, "y2": 550, "rot": 0}
      },
      "tags": []
    }
  }
  "Air density at sea level [kg/m³]"
  parameter rho0::Real = 1.225
  "Scale height of the exponential atmosphere [m]"
  parameter H::Real = 8500
  "Pitch acceleration per unit elevator deflection and unit dynamic pressure"
  parameter c_u::Real = 6e-4
  "Pitch acceleration per unit pitch angle and unit dynamic pressure"
  parameter c_theta::Real = 4e-4
  "Pitch damping coefficient"
  parameter c_omega::Real = 7.4e-3
  "Pitch angle [rad]"
  variable pitch::Real
  "Pitch rate [rad/s]"
  variable omega::Real
  "Dynamic pressure [Pa]"
  variable q::Real
relations
  initial pitch = 0
  initial omega = 0
  q = 0.5 * rho0 * exp(-h / H) * V ^ 2
  der(pitch) = omega
  der(omega) = q * (c_u * u - c_theta * pitch) - c_omega * q / V * omega
  theta = pitch
metadata {"Dyad": {"icons": {"default": "dyad://Dyad/Default.svg"}}}
end


Test Cases ​

No test cases defined.

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