{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# UDD Alpha Controller (Constant CL)\n", "\n", "In this tutorial the `UserDefinedDynamic` will be used to implement a PI controller that manipulates the angle of attack to achieve a constant given lift coefficient. The project will be started from an example volume mesh and basic python post-processing of the results will be showcased.\n", "\n", "![Mesh](figures/om6_wing_vm.png)\n", "\n", "## 1. Imports and Project creation\n", "\n", "At first the **flow360** library must be imported.\n", "\n", "**Note:** The settings in this example are by no means a validation setup; they are crafted to showcase the capabilities of Flow360 and we have intentionally reduced node count and example FC cost. For rigorous validation, modify the settings as needed." ], "id": "932b5b72" }, { "cell_type": "code", "metadata": {}, "source": [ "import flow360 as fl\n", "from flow360.examples import OM6wing" ], "execution_count": 1, "outputs": [], "id": "eca4f647" }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then the `Project` has to be created. In this case it will be started from the volume mesh." ], "id": "f6626322" }, { "cell_type": "code", "metadata": {}, "source": [ "OM6wing.get_files()\n", "\n", "project = fl.Project.from_volume_mesh(\n", " OM6wing.mesh_filename, name=\"UDD Alpha Controller (Constant CL)\"\n", ")" ], "execution_count": 2, "outputs": [ { "output_type": "display_data", "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "69ec07b4a6464e0e946d5a559fa29f7a", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {} }, { "output_type": "display_data", "data": { "text/html": [ "
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     "metadata": {}
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       "version_minor": 0
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      "text/plain": [
       "Output()"
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       "
[15:27:34] WARNING: The expected mapbc file                                                                        \n",
       "           c:\\Code\\Flow360Documentation\\.venv\\Lib\\site-packages\\flow360\\examples\\om6wing\\wing_tetra.1.mapbc        \n",
       "           specifying user-specified boundary names doesn't exist.                                                 \n",
       "
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      ],
      "text/plain": [
       "\u001b[2;36m[15:27:34]\u001b[0m\u001b[2;36m \u001b[0m\u001b[33mWARNING\u001b[0m: \u001b[37mThe expected mapbc file \u001b[0m                                                                       \n",
       "\u001b[2;36m           \u001b[0m\u001b[37mc:\\Code\\Flow360Documentation\\.venv\\Lib\\site-packages\\flow360\\examples\\om6wing\\wing_tetra.\u001b[0m\u001b[1;37m1.\u001b[0m\u001b[37mmapbc \u001b[0m       \n",
       "\u001b[2;36m           \u001b[0m\u001b[37mspecifying user-specified boundary names doesn't exist.\u001b[0m                                                 \n"
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[15:27:46] INFO: VolumeMesh successfully submitted:                                                                \n",
       "                   type        = Volume Mesh                                                                       \n",
       "                   name        = Tutorial UDD alpha controller from Python                                         \n",
       "                   id          = vm-70f5a518-3df9-49f1-9b3e-a4d6c5a5a04e                                           \n",
       "                   status      = uploaded                                                                          \n",
       "                   project id  = prj-52037feb-d308-4ee7-ab53-d7163a45358f                                          \n",
       "                                                                                                                   \n",
       "
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      ],
      "text/plain": [
       "\u001b[2;36m[15:27:46]\u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: VolumeMesh successfully submitted:                                                                \n",
       "\u001b[2;36m           \u001b[0m        type        = Volume Mesh                                                                       \n",
       "\u001b[2;36m           \u001b[0m        name        = Tutorial UDD alpha controller from Python                                         \n",
       "\u001b[2;36m           \u001b[0m        id          = vm-\u001b[93m70f5a518-3df9-49f1-9b3e-a4d6c5a5a04e\u001b[0m                                           \n",
       "\u001b[2;36m           \u001b[0m        status      = uploaded                                                                          \n",
       "\u001b[2;36m           \u001b[0m        project id  = prj-\u001b[93m52037feb-d308-4ee7-ab53-d7163a45358f\u001b[0m                                          \n",
       "\u001b[2;36m           \u001b[0m                                                                                                        \n"
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     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "539e5763c5d7412a972a6fc8bf43ddcd",
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       "version_minor": 0
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       "Output()"
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     "data": {
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       "
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      ],
      "text/plain": []
     },
     "metadata": {}
    }
   ],
   "id": "4ce29035"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The project can also be referenced by its unique ID if it was already created."
   ],
   "id": "b5bf87b1"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "# project = fl.Project.from_cloud(project_id=\"prj-your_id_here\")"
   ],
   "execution_count": 3,
   "outputs": [],
   "id": "63aa15e1"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `Project` entity stores all of the information about the root asset it was created from such as boundary names."
   ],
   "id": "7df37d65"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "volume_mesh = project.volume_mesh\n",
    "\n",
    "print(\"Volume mesh boundaries:\")\n",
    "for boundary in volume_mesh.boundary_names:\n",
    "    print(f\"  - {boundary}\")"
   ],
   "execution_count": 4,
   "outputs": [
    {
     "output_type": "stream",
     "text": [
      "Volume mesh boundaries:\n",
      "  - 3\n",
      "  - 1\n",
      "  - 2\n"
     ],
     "name": "stdout"
    }
   ],
   "id": "64474d5a"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Setting up the base of `SimulationParams`\n",
    "\n",
    "As the project is started from the volume mesh, the `meshing` part is not required. \n",
    "The basic case setup consists of:\n",
    "- setting appropriate operating conditions in `operating_condition`,\n",
    "- specifying the reference values for coefficient calculation in `reference_geometry`,\n",
    "- choosing between the transient vs a steady simulation in `time_stepping`,\n",
    "- setting appropriate boundary conditions in the `models` section,\n",
    "- specifying wanted outputs in `outputs`."
   ],
   "id": "e94a070a"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `operating_condition` is set using a given *Reynolds number* and *Mach*."
   ],
   "id": "d594e2af"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "with fl.SI_unit_system:\n",
    "    operating_condition = fl.AerospaceCondition.from_mach_reynolds(\n",
    "        reynolds_mesh_unit=11.72e6,\n",
    "        mach=0.84,\n",
    "        project_length_unit=0.80167 * fl.u.m,\n",
    "        temperature=297.78,\n",
    "        alpha=3.06 * fl.u.deg,\n",
    "        beta=0 * fl.u.deg,\n",
    "    )"
   ],
   "execution_count": 5,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
[15:28:04] INFO: using: SI unit system for unit inference.                                                         \n",
       "
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      ],
      "text/plain": [
       "\u001b[2;36m[15:28:04]\u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: using: SI unit system for unit inference.                                                         \n"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
[15:28:05] INFO: Density and viscosity were calculated based on input data, ThermalState will be automatically     \n",
       "           created.                                                                                                \n",
       "
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      ],
      "text/plain": [
       "\u001b[2;36m[15:28:05]\u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: Density and viscosity were calculated based on input data, ThermalState will be automatically     \n",
       "\u001b[2;36m           \u001b[0mcreated.                                                                                                \n"
      ]
     },
     "metadata": {}
    }
   ],
   "id": "5e9efb56"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `reference_geometry` is set according to the input geometry and `time_stepping` is set to `Steady`."
   ],
   "id": "049f1462"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "with fl.SI_unit_system:\n",
    "    reference_geometry = fl.ReferenceGeometry(\n",
    "        area=1.15315,\n",
    "        moment_center=[0, 0, 0],\n",
    "        moment_length=[1.47601, 0.80167, 1.47601],\n",
    "    )\n",
    "    time_stepping = fl.Steady(\n",
    "        max_steps=2000,\n",
    "    )"
   ],
   "execution_count": 6,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
           INFO: using: SI unit system for unit inference.                                                         \n",
       "
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      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: using: SI unit system for unit inference.                                                         \n"
      ]
     },
     "metadata": {}
    }
   ],
   "id": "b06a4113"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The boundary conditions are assigned to given volume mesh boundaries by specifying them in the models section."
   ],
   "id": "d3344d10"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "with fl.SI_unit_system:\n",
    "    models = [\n",
    "        fl.Wall(surfaces=[volume_mesh[\"1\"]]),\n",
    "        fl.SlipWall(surfaces=[volume_mesh[\"2\"]]),\n",
    "        fl.Freestream(surfaces=[volume_mesh[\"3\"]]),\n",
    "    ]"
   ],
   "execution_count": 7,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
           INFO: using: SI unit system for unit inference.                                                         \n",
       "
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      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: using: SI unit system for unit inference.                                                         \n"
      ]
     },
     "metadata": {}
    }
   ],
   "id": "5077062e"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the `outputs` basic `SurfaceOutput` is specified focusing on the pressure coefficient and the wall shear stress."
   ],
   "id": "765f0875"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "with fl.SI_unit_system:\n",
    "    outputs = [\n",
    "        fl.SurfaceOutput(\n",
    "            surfaces=volume_mesh[\"1\"],\n",
    "            output_fields=[\n",
    "                \"Cp\",\n",
    "                \"Cf\",\n",
    "                \"CfVec\",\n",
    "                \"yPlus\",\n",
    "            ],\n",
    "        )\n",
    "    ]"
   ],
   "execution_count": 8,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
           INFO: using: SI unit system for unit inference.                                                         \n",
       "
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      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: using: SI unit system for unit inference.                                                         \n"
      ]
     },
     "metadata": {}
    }
   ],
   "id": "0f1c208a"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally all the fields can be input into the `SimulationParams` class that is used as a setup data source for the simulation."
   ],
   "id": "234b17a0"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "with fl.SI_unit_system:\n",
    "    params = fl.SimulationParams(\n",
    "        operating_condition=operating_condition,\n",
    "        reference_geometry=reference_geometry,\n",
    "        time_stepping=time_stepping,\n",
    "        models=models,\n",
    "        outputs=outputs,\n",
    "    )"
   ],
   "execution_count": 9,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
           INFO: using: SI unit system for unit inference.                                                         \n",
       "
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      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: using: SI unit system for unit inference.                                                         \n"
      ]
     },
     "metadata": {}
    }
   ],
   "id": "7ce2ff78"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Adding `UserDefinedDynamic`\n",
    "\n",
    "The goal of the `UserDefinedDynamic` object will be to \"search\" for a specified angle of attach for which the lift coefficient of the wing is a certain value (0.4 in this case). To achieve that the PI controller will be used to update the value of the `alpha` variable in each pseudo_step.\n",
    "\n",
    "The `UserDefinedDynamic` requires the specification of a few parameters:\n",
    "- `name` is the name of the dynamic, will be used to access the variables present in it in post-processing,\n",
    "- `input_vars` is the list of variables from the solution that will be used in calculations ,\n",
    "- `constants` are the predefined constants used in calculations, in this case those include the CL target and PI controller constants,\n",
    "- `output_vars` are the variables in the case that are controlled, they are defined using a dictionary where the key is the name of the controlled variable and the value is a formula using the predefined constants, state variables or solution variables such as `pseudo_step`; the formula should be written using C syntax, \n",
    "- `state_vars_initial_value` define initial values of the state variables, in this case the initial state of `state[0]` is the `alphaAngle` and the initial state of `state[1]` is `0.0`,\n",
    "- `update_law` is a list of expression used to calculate the state variables in each `pseudo_step` those expressions also should use C syntax,\n",
    "- `input_boundary_patches` is a list of boundaries that are used in the calculation of the `input_vars` meaning the `CL` used for calculation will be only taken from the `volume_mesh[\"1\"]` boundary.\n",
    "\n",
    "The PI controller in this case is formulated so that it does not turn on until 500 pseudo steps, which allows the simulation to converge initially before applying corrections. After this number of steps the `state[0]` calculates the new `alphaAngle` to set and `state[1]` gets the numerical integral part of the controller.\n",
    "\n",
    "The `state` is a vector of values that can be referenced in the expressions and is updated at each step according to `update_law`."
   ],
   "id": "0dc0e74a"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "alpha_controller = fl.UserDefinedDynamic(\n",
    "    name=\"alphaController\",\n",
    "    input_vars=[\"CL\"],\n",
    "    constants={\"CLTarget\": 0.4, \"Kp\": 0.2, \"Ki\": 0.002},\n",
    "    output_vars={\"alphaAngle\": \"if (pseudoStep > 500) state[0]; else alphaAngle;\"},\n",
    "    state_vars_initial_value=[\"alphaAngle\", \"0.0\"],\n",
    "    update_law=[\n",
    "        \"if (pseudoStep > 500) state[0] + Kp * (CLTarget - CL) + Ki * state[1]; else state[0];\",\n",
    "        \"if (pseudoStep > 500) state[1] + (CLTarget - CL); else state[1];\",\n",
    "    ],\n",
    "    input_boundary_patches=[volume_mesh[\"1\"]],\n",
    ")\n",
    "params.user_defined_dynamics = [alpha_controller]"
   ],
   "execution_count": 10,
   "outputs": [],
   "id": "7e92a7b6"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Running the simulation\n",
    "\n",
    "The simulation is then run using the `run_case` function of the `Project`."
   ],
   "id": "3fe7c3d0"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "case = project.run_case(params=params, name=\"Steady (constant-CL controller)\")"
   ],
   "execution_count": 11,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
           INFO: Density and viscosity were calculated based on input data, ThermalState will be automatically     \n",
       "           created.                                                                                                \n",
       "
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      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: Density and viscosity were calculated based on input data, ThermalState will be automatically     \n",
       "\u001b[2;36m           \u001b[0mcreated.                                                                                                \n"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
           INFO: using: SI unit system for unit inference.                                                         \n",
       "
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      ],
      "text/plain": [
       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: using: SI unit system for unit inference.                                                         \n"
      ]
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     "metadata": {}
    },
    {
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     "data": {
      "text/html": [
       "
[15:28:07] INFO: Successfully submitted:                                                                           \n",
       "                   type        = Case                                                                              \n",
       "                   name        = Case of tutorial UDD alpha controller from Python                                 \n",
       "                   id          = case-79b42c52-01a4-44fd-b410-3c6c67082df0                                         \n",
       "                   status      = pending                                                                           \n",
       "                   project id  = prj-52037feb-d308-4ee7-ab53-d7163a45358f                                          \n",
       "                                                                                                                   \n",
       "
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      ],
      "text/plain": [
       "\u001b[2;36m[15:28:07]\u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: Successfully submitted:                                                                           \n",
       "\u001b[2;36m           \u001b[0m        type        = Case                                                                              \n",
       "\u001b[2;36m           \u001b[0m        name        = Case of tutorial UDD alpha controller from Python                                 \n",
       "\u001b[2;36m           \u001b[0m        id          = case-\u001b[93m79b42c52-01a4-44fd-b410-3c6c67082df0\u001b[0m                                         \n",
       "\u001b[2;36m           \u001b[0m        status      = pending                                                                           \n",
       "\u001b[2;36m           \u001b[0m        project id  = prj-\u001b[93m52037feb-d308-4ee7-ab53-d7163a45358f\u001b[0m                                          \n",
       "\u001b[2;36m           \u001b[0m                                                                                                        \n"
      ]
     },
     "metadata": {}
    }
   ],
   "id": "10827f4c"
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Post-processing\n",
    "\n",
    "To access the results of the simulation it has to be finished. They can be found in the `results` parameter. Below the state of the controller and calculated alpha is plotted."
   ],
   "id": "7d46af77"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "case.wait()\n",
    "\n",
    "udd_data = case.results.user_defined_dynamics[\"alphaController\"]\n",
    "\n",
    "ax0 = udd_data.as_dataframe().plot(\n",
    "    x=\"pseudo_step\",\n",
    "    y=\"alphaAngle\",\n",
    "    title=\"AoA\",\n",
    "    ylabel=\"AoA [deg] - blue\",\n",
    "    legend=False,\n",
    ")\n",
    "ax1 = ax0.twinx()\n",
    "udd_data.as_dataframe().plot(\n",
    "    x=\"pseudo_step\", y=\"CL\", ylabel=\"CL - orange\", ax=ax1, color=\"orange\", legend=False\n",
    ")"
   ],
   "execution_count": 12,
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "0d99e7efff71405dbed1653d1e682e7d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
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       "version_minor": 0
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      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "display_data",
     "data": {
      "text/html": [
       "
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      ],
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     },
     "metadata": {}
    },
    {
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      "text/html": [
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       "
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      ],
      "text/plain": [
       "\u001b[2;36m[15:29:27]\u001b[0m\u001b[2;36m \u001b[0m\u001b[36mINFO\u001b[0m: Saved to C:\\Users\\user\\AppData\\Local\\Temp\\tmpvdihtq8f\\\u001b[93m1eba06e3-b226-42da-9f23-b992ec6362e3\u001b[0m.csv   \n"
      ]
     },
     "metadata": {}
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       ""
      ]
     },
     "metadata": {},
     "execution_count": null
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "
"
      ]
     },
     "metadata": {}
    }
   ],
   "id": "c2e31696"
  },
  {
   "cell_type": "code",
   "metadata": {},
   "source": [
    "ax0 = udd_data.as_dataframe().plot(\n",
    "    x=\"pseudo_step\", y=\"state[0]\", title=\"state\", ylabel=\"state[0] - blue\", legend=False\n",
    ")\n",
    "ax1 = ax0.twinx()\n",
    "udd_data.as_dataframe().plot(\n",
    "    x=\"pseudo_step\",\n",
    "    y=\"state[1]\",\n",
    "    ylabel=\"state[1] - orange\",\n",
    "    ax=ax1,\n",
    "    color=\"orange\",\n",
    "    legend=False,\n",
    ")"
   ],
   "execution_count": 13,
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       ""
      ]
     },
     "metadata": {},
     "execution_count": null
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
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 ],
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  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "pygments_lexer": "ipython3",
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 },
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}