LIBRARY

`Examples.CompareBrakingTorque`

Compare different braking torques.

Matches MSL Modelica.Mechanics.Rotational.Examples.CompareBrakingTorque.

Four inertias (J=1) start at w=100 rad/s and are braked by different speed-dependent torque sources, all with TorqueDirection=false (torque direction depends on speed direction):

SignTorque (Linear regularization): constant magnitude braking, smooth near zero
LinearSpeedDependentTorque: tau ∝ w → exponential decay w(t) = 100·exp(-t)
QuadraticSpeedDependentTorque: tau ∝ w|w| → w(t) = 100/(1+t)
InverseSpeedDependentTorque: tau ∝ 1/w → rapid braking, w hits 0 at t=0.5

Usage

RotationalComponents.Examples.CompareBrakingTorque()

Behavior

[\begin{matrix} connect (s i g n_{t o r q u e_{+} s p l i n e}, i n e r t i a 1_{+} s p l i n e_{a}) \\ connect (s i g n_{t o r q u e_{+} s u p p o r t}, f i x e d_{+} s p l i n e) \\ connect (l i n e a r_{s p e e d_{+} s p l i n e}, i n e r t i a 2_{+} s p l i n e_{a}) \\ connect (l i n e a r_{s p e e d_{+} s u p p o r t}, f i x e d_{+} s p l i n e) \\ connect (q u a d r a t i c_{s p e e d_{+} s p l i n e}, i n e r t i a 3_{+} s p l i n e_{a}) \\ connect (q u a d r a t i c_{s p e e d_{+} s u p p o r t}, f i x e d_{+} s p l i n e) \\ connect (i n v e r s e_{s p e e d_{+} s p l i n e}, i n e r t i a 4_{+} s p l i n e_{a}) \\ connect (i n v e r s e_{s p e e d_{+} s u p p o r t}, f i x e d_{+} s p l i n e) \\ fixed . spline . phi (t) = fixed . phi 0 \\ inertia 1. phi (t) = {inertia 1. spline}_{a . phi} (t) \\ inertia 1. phi (t) = {inertia 1. spline}_{b . phi} (t) \\ \frac{d \cdot inertia 1. phi (t)}{d t} = inertia 1. w (t) \\ \frac{d \cdot inertia 1. w (t)}{d t} = inertia 1. a (t) \\ inertia 1. J \cdot inertia 1. a (t) = {inertia 1. spline}_{a . tau} (t) + {inertia 1. spline}_{b . tau} (t) \\ {sign}_{torque . support . phi} (t) = {sign}_{torque . phi_support} (t) \\ {sign}_{torque . support . tau} (t) = - {sign}_{torque . spline . tau} (t) \\ {sign}_{torque . phi} (t) = {sign}_{torque . spline . phi} (t) - {sign}_{torque . phi_support} (t) \\ {sign}_{torque . w} (t) = \frac{d \cdot {sign}_{torque . phi} (t)}{d t} \\ {sign}_{torque . tau} (t) = - {sign}_{torque . spline . tau} (t) \\ {sign}_{torque . tau} (t) = {sign}_{torque . tau_nominal} \cdot ifelse (| {sign}_{torque . w} (t) | \geq {sign}_{torque . w 0}, sign ({sign}_{torque . w} (t)), \frac{{sign}_{torque . w} (t)}{{sign}_{torque . w 0}}) \\ inertia 2. phi (t) = {inertia 2. spline}_{a . phi} (t) \\ inertia 2. phi (t) = {inertia 2. spline}_{b . phi} (t) \\ \frac{d \cdot inertia 2. phi (t)}{d t} = inertia 2. w (t) \\ \frac{d \cdot inertia 2. w (t)}{d t} = inertia 2. a (t) \\ inertia 2. J \cdot inertia 2. a (t) = {inertia 2. spline}_{a . tau} (t) + {inertia 2. spline}_{b . tau} (t) \\ {linear}_{speed . support . phi} (t) = {linear}_{speed . phi_support} (t) \\ {linear}_{speed . support . tau} (t) = - {linear}_{speed . spline . tau} (t) \\ {linear}_{speed . phi} (t) = - {linear}_{speed . phi_support} (t) + {linear}_{speed . spline . phi} (t) \\ {linear}_{speed . w} (t) = \frac{d \cdot {linear}_{speed . phi} (t)}{d t} \\ {linear}_{speed . tau} (t) = - {linear}_{speed . spline . tau} (t) \\ {linear}_{speed . tau} (t) = \frac{{linear}_{speed . tau_nominal} \cdot {linear}_{speed . w} (t)}{{linear}_{speed . w_nominal}} \\ inertia 3. phi (t) = {inertia 3. spline}_{a . phi} (t) \\ inertia 3. phi (t) = {inertia 3. spline}_{b . phi} (t) \\ \frac{d \cdot inertia 3. phi (t)}{d t} = inertia 3. w (t) \\ \frac{d \cdot inertia 3. w (t)}{d t} = inertia 3. a (t) \\ inertia 3. J \cdot inertia 3. a (t) = {inertia 3. spline}_{a . tau} (t) + {inertia 3. spline}_{b . tau} (t) \\ {quadratic}_{speed . support . phi} (t) = {quadratic}_{speed . phi_support} (t) \\ {quadratic}_{speed . support . tau} (t) = - {quadratic}_{speed . spline . tau} (t) \\ {quadratic}_{speed . phi} (t) = {quadratic}_{speed . spline . phi} (t) - {quadratic}_{speed . phi_support} (t) \\ {quadratic}_{speed . w} (t) = \frac{d \cdot {quadratic}_{speed . phi} (t)}{d t} \\ {quadratic}_{speed . tau} (t) = - {quadratic}_{speed . spline . tau} (t) \\ {quadratic}_{speed . tau} (t) = \frac{{quadratic}_{speed . tau_nominal} \cdot | {quadratic}_{speed . w} (t) | \cdot {quadratic}_{speed . w} (t)}{{quadratic}_{speed . w_nominal}^{2}} \\ inertia 4. phi (t) = {inertia 4. spline}_{a . phi} (t) \\ inertia 4. phi (t) = {inertia 4. spline}_{b . phi} (t) \\ \frac{d \cdot inertia 4. phi (t)}{d t} = inertia 4. w (t) \\ \frac{d \cdot inertia 4. w (t)}{d t} = inertia 4. a (t) \\ inertia 4. J \cdot inertia 4. a (t) = {inertia 4. spline}_{b . tau} (t) + {inertia 4. spline}_{a . tau} (t) \\ {inverse}_{speed . support . phi} (t) = {inverse}_{speed . phi_support} (t) \\ {inverse}_{speed . support . tau} (t) = - {inverse}_{speed . spline . tau} (t) \\ {inverse}_{speed . phi} (t) = {inverse}_{speed . spline . phi} (t) - {inverse}_{speed . phi_support} (t) \\ {inverse}_{speed . w} (t) = \frac{d \cdot {inverse}_{speed . phi} (t)}{d t} \\ {inverse}_{speed . tau} (t) = - {inverse}_{speed . spline . tau} (t) \\ {inverse}_{speed . tau} (t) = ifelse (| {inverse}_{speed . w} (t) | < {inverse}_{speed . w 0}, \frac{{inverse}_{speed . tau_nominal} \cdot {inverse}_{speed . w} (t)}{{inverse}_{speed . w 0}}, \frac{{inverse}_{speed . tau_nominal} \cdot {inverse}_{speed . w_nominal}}{{inverse}_{speed . w} (t)}) \end{matrix}]

Source

dyad

"""
Compare different braking torques.

Matches MSL Modelica.Mechanics.Rotational.Examples.CompareBrakingTorque.

Four inertias (J=1) start at w=100 rad/s and are braked by different
speed-dependent torque sources, all with TorqueDirection=false (torque
direction depends on speed direction):

1. SignTorque (Linear regularization): constant magnitude braking, smooth near zero
2. LinearSpeedDependentTorque: tau ∝ w → exponential decay w(t) = 100·exp(-t)
3. QuadraticSpeedDependentTorque: tau ∝ w|w| → w(t) = 100/(1+t)
4. InverseSpeedDependentTorque: tau ∝ 1/w → rapid braking, w hits 0 at t=0.5
"""
example component CompareBrakingTorque
  "Fixed ground for all source supports"
  fixed = RotationalComponents.Components.Fixed() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -240, "y1": 400, "x2": -140, "y2": 500, "rot": 90}
      },
      "tags": []
    }
  }
  "Inertia 1 for sign torque braking"
  inertia1 = RotationalComponents.Components.Inertia(J = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 430, "y1": 20, "x2": 530, "y2": 120, "rot": 0}
      },
      "tags": []
    }
  }
  "Sign torque with Linear regularization (tau_nominal=-100, w0=1)"
  sign_torque = RotationalComponents.Sources.SignTorque(tau_nominal = -100, reg = RotationalComponents.Sources.Regularization.Linear(), w0 = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 160, "y1": 20, "x2": 260, "y2": 120, "rot": 0}
      },
      "tags": []
    }
  }
  "Inertia 2 for linear speed dependent braking"
  inertia2 = RotationalComponents.Components.Inertia(J = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 420, "y1": 250, "x2": 520, "y2": 350, "rot": 0}
      },
      "tags": []
    }
  }
  "Linear speed dependent torque (TorqueDirection=false)"
  linear_speed = RotationalComponents.Sources.LinearSpeedDependentTorque(tau_nominal = -100, TorqueDirection = false, w_nominal = 100) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 150, "y1": 250, "x2": 250, "y2": 350, "rot": 0}
      },
      "tags": []
    }
  }
  "Inertia 3 for quadratic speed dependent braking"
  inertia3 = RotationalComponents.Components.Inertia(J = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 420, "y1": 470, "x2": 520, "y2": 570, "rot": 0}
      },
      "tags": []
    }
  }
  "Quadratic speed dependent torque (TorqueDirection=false)"
  quadratic_speed = RotationalComponents.Sources.QuadraticSpeedDependentTorque(tau_nominal = -100, TorqueDirection = false, w_nominal = 100) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 150, "y1": 470, "x2": 250, "y2": 570, "rot": 0}
      },
      "tags": []
    }
  }
  "Inertia 4 for inverse speed dependent braking"
  inertia4 = RotationalComponents.Components.Inertia(J = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 420, "y1": 710, "x2": 520, "y2": 810, "rot": 0}
      },
      "tags": []
    }
  }
  "Inverse speed dependent torque (TorqueDirection=false)"
  inverse_speed = RotationalComponents.Sources.InverseSpeedDependentTorque(tau_nominal = -100, TorqueDirection = false, w_nominal = 100, w0 = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 160, "y1": 710, "x2": 260, "y2": 810, "rot": 0}
      },
      "tags": []
    }
  }
relations
  initial inertia1.phi = 0
  initial inertia1.w = 100
  initial inertia2.phi = 0
  initial inertia2.w = 100
  initial inertia3.phi = 0
  initial inertia3.w = 100
  initial inertia4.phi = 0
  initial inertia4.w = 100
  connect(sign_torque.spline, inertia1.spline_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(sign_torque.support, fixed.spline) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [{"x": 210, "y": 160}, {"x": 0, "y": 160}, {"x": 0, "y": 450}],
          "E": 2
        }
      ],
      "renderStyle": "standard"
    }
  }
  connect(linear_speed.spline, inertia2.spline_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(linear_speed.support, fixed.spline) {
    "Dyad": {
      "edges": [
        {"S": 1, "M": [{"x": 200, "y": 450}], "E": -1},
        {"S": -1, "M": [], "E": -2},
        {"S": -2, "M": [], "E": 2}
      ],
      "junctions": [{"x": -140, "y": 450}, {"x": -140, "y": 450}],
      "renderStyle": "standard"
    }
  }
  connect(quadratic_speed.spline, inertia3.spline_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(quadratic_speed.support, fixed.spline) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [{"x": 200, "y": 700}, {"x": 0, "y": 700}, {"x": 0, "y": 450}],
          "E": -1
        },
        {"S": -1, "M": [], "E": 2}
      ],
      "junctions": [{"x": -140, "y": 450}],
      "renderStyle": "standard"
    }
  }
  connect(inverse_speed.spline, inertia4.spline_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(inverse_speed.support, fixed.spline) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [{"x": 210, "y": 905}, {"x": 0, "y": 905}, {"x": 0, "y": 450}],
          "E": 2
        }
      ],
      "renderStyle": "standard"
    }
  }
metadata {
  "Dyad": {
    "icons": {"default": "dyad://RotationalComponents/Example.svg"},
    "tests": {
      "case1": {
        "stop": 5,
        "atol": {
          "inertia1.w": 0.001,
          "inertia2.w": 0.001,
          "inertia3.w": 0.001,
          "inertia4.w": 0.001
        },
        "expect": {
          "initial": {"inertia1.w": 100, "inertia2.w": 100, "inertia3.w": 100, "inertia4.w": 100},
          "signals": ["inertia1.w", "inertia2.w", "inertia3.w", "inertia4.w"]
        }
      }
    }
  }
}
end

Flattened Source

dyad

"""
Compare different braking torques.

Matches MSL Modelica.Mechanics.Rotational.Examples.CompareBrakingTorque.

Four inertias (J=1) start at w=100 rad/s and are braked by different
speed-dependent torque sources, all with TorqueDirection=false (torque
direction depends on speed direction):

1. SignTorque (Linear regularization): constant magnitude braking, smooth near zero
2. LinearSpeedDependentTorque: tau ∝ w → exponential decay w(t) = 100·exp(-t)
3. QuadraticSpeedDependentTorque: tau ∝ w|w| → w(t) = 100/(1+t)
4. InverseSpeedDependentTorque: tau ∝ 1/w → rapid braking, w hits 0 at t=0.5
"""
example component CompareBrakingTorque
  "Fixed ground for all source supports"
  fixed = RotationalComponents.Components.Fixed() {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": -240, "y1": 400, "x2": -140, "y2": 500, "rot": 90}
      },
      "tags": []
    }
  }
  "Inertia 1 for sign torque braking"
  inertia1 = RotationalComponents.Components.Inertia(J = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 430, "y1": 20, "x2": 530, "y2": 120, "rot": 0}
      },
      "tags": []
    }
  }
  "Sign torque with Linear regularization (tau_nominal=-100, w0=1)"
  sign_torque = RotationalComponents.Sources.SignTorque(tau_nominal = -100, reg = RotationalComponents.Sources.Regularization.Linear(), w0 = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 160, "y1": 20, "x2": 260, "y2": 120, "rot": 0}
      },
      "tags": []
    }
  }
  "Inertia 2 for linear speed dependent braking"
  inertia2 = RotationalComponents.Components.Inertia(J = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 420, "y1": 250, "x2": 520, "y2": 350, "rot": 0}
      },
      "tags": []
    }
  }
  "Linear speed dependent torque (TorqueDirection=false)"
  linear_speed = RotationalComponents.Sources.LinearSpeedDependentTorque(tau_nominal = -100, TorqueDirection = false, w_nominal = 100) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 150, "y1": 250, "x2": 250, "y2": 350, "rot": 0}
      },
      "tags": []
    }
  }
  "Inertia 3 for quadratic speed dependent braking"
  inertia3 = RotationalComponents.Components.Inertia(J = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 420, "y1": 470, "x2": 520, "y2": 570, "rot": 0}
      },
      "tags": []
    }
  }
  "Quadratic speed dependent torque (TorqueDirection=false)"
  quadratic_speed = RotationalComponents.Sources.QuadraticSpeedDependentTorque(tau_nominal = -100, TorqueDirection = false, w_nominal = 100) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 150, "y1": 470, "x2": 250, "y2": 570, "rot": 0}
      },
      "tags": []
    }
  }
  "Inertia 4 for inverse speed dependent braking"
  inertia4 = RotationalComponents.Components.Inertia(J = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 420, "y1": 710, "x2": 520, "y2": 810, "rot": 0}
      },
      "tags": []
    }
  }
  "Inverse speed dependent torque (TorqueDirection=false)"
  inverse_speed = RotationalComponents.Sources.InverseSpeedDependentTorque(tau_nominal = -100, TorqueDirection = false, w_nominal = 100, w0 = 1) {
    "Dyad": {
      "placement": {
        "diagram": {"iconName": "default", "x1": 160, "y1": 710, "x2": 260, "y2": 810, "rot": 0}
      },
      "tags": []
    }
  }
relations
  initial inertia1.phi = 0
  initial inertia1.w = 100
  initial inertia2.phi = 0
  initial inertia2.w = 100
  initial inertia3.phi = 0
  initial inertia3.w = 100
  initial inertia4.phi = 0
  initial inertia4.w = 100
  connect(sign_torque.spline, inertia1.spline_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(sign_torque.support, fixed.spline) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [{"x": 210, "y": 160}, {"x": 0, "y": 160}, {"x": 0, "y": 450}],
          "E": 2
        }
      ],
      "renderStyle": "standard"
    }
  }
  connect(linear_speed.spline, inertia2.spline_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(linear_speed.support, fixed.spline) {
    "Dyad": {
      "edges": [
        {"S": 1, "M": [{"x": 200, "y": 450}], "E": -1},
        {"S": -1, "M": [], "E": -2},
        {"S": -2, "M": [], "E": 2}
      ],
      "junctions": [{"x": -140, "y": 450}, {"x": -140, "y": 450}],
      "renderStyle": "standard"
    }
  }
  connect(quadratic_speed.spline, inertia3.spline_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(quadratic_speed.support, fixed.spline) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [{"x": 200, "y": 700}, {"x": 0, "y": 700}, {"x": 0, "y": 450}],
          "E": -1
        },
        {"S": -1, "M": [], "E": 2}
      ],
      "junctions": [{"x": -140, "y": 450}],
      "renderStyle": "standard"
    }
  }
  connect(inverse_speed.spline, inertia4.spline_a) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(inverse_speed.support, fixed.spline) {
    "Dyad": {
      "edges": [
        {
          "S": 1,
          "M": [{"x": 210, "y": 905}, {"x": 0, "y": 905}, {"x": 0, "y": 450}],
          "E": 2
        }
      ],
      "renderStyle": "standard"
    }
  }
metadata {
  "Dyad": {
    "icons": {"default": "dyad://RotationalComponents/Example.svg"},
    "tests": {
      "case1": {
        "stop": 5,
        "atol": {
          "inertia1.w": 0.001,
          "inertia2.w": 0.001,
          "inertia3.w": 0.001,
          "inertia4.w": 0.001
        },
        "expect": {
          "initial": {"inertia1.w": 100, "inertia2.w": 100, "inertia3.w": 100, "inertia4.w": 100},
          "signals": ["inertia1.w", "inertia2.w", "inertia3.w", "inertia4.w"]
        }
      }
    }
  }
}
end

Test Cases

Test Case `case1`

julia

plt

julia

plt

julia

plt

julia

plt

Examples
Experiments
Analyses

Scalar Types

Partial Types

Enumerated Types

Function Types

Partial Types

Enumerated Types

Partial Types

Enumerated Types

Partial Types

Enumerated Types

Partial Types

Scalar Types

Partial Types

Partial Types

Types

Partial Types

Enumerated Types

Components

Analyses

Examples

Tests

Scalar Types

Partial Types

Enumerated Types

Examples.CompareBrakingTorque ​

Usage ​

Behavior ​

Source ​

Test Cases ​

Test Case case1 ​

Related ​

`Examples.CompareBrakingTorque`

Usage

Behavior

Source

Test Cases

Test Case `case1`

Related