finback-at/GenerationOfFMUs_with_linear_correction.ipynb

## GenerationOfFMUs_with_linear_correction.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### GenerationOfFMUs (2) - with_linear_correction\n",
    "[CO-SIMULATION USING THE OPEN-SOURCE PYTHON PACKAGE PYFMI](https://www.modelon.com/co-simulation-using-the-open-source-python-package-pyfmi/) の最後の方に記述された linear_correction = True にしたシミュレーションを試みます。\n",
    "\n",
    "サブシステムモデルをコンパイルしてFMUを生成します。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pymodelica import compile_fmu\n",
    "fmu1 = compile_fmu('Modelica.Mechanics.Rotational.Examples.Utilities.DirectInertia',target='cs', version='2.0', compile_to='DirectInertia.fmu')\n",
    "fmu2 = compile_fmu('Modelica.Mechanics.Rotational.Examples.Utilities.InverseInertia',target='cs',version='2.0', compile_to='InverseInertia.fmu')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "サブシステムモデルをロードします。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyfmi import load_fmu\n",
    "directInertia = load_fmu(\"DirectInertia.fmu\")\n",
    "inverseInertia = load_fmu(\"InverseInertia.fmu\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "パラメータを設定します。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "directInertia.set(\"J\", 1.1)\n",
    "inverseInertia.set(\"J\", 2.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "サブシステムモデルのリストと接続関係のリストを作成します。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "models = [directInertia, inverseInertia]\n",
    "connections = [\n",
    "    (directInertia, \"phi\", inverseInertia, \"phi\"),\n",
    "    (directInertia, \"w\", inverseInertia, \"w\"),\n",
    "    (directInertia, \"a\", inverseInertia, \"a\"),\n",
    "    (inverseInertia, \"tau\", directInertia, \"tau\")]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Co-Simulationモデルを作成します。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/dist-packages/ipykernel_launcher.py:2: UserWarning: The model, DirectInertia, does not support directional derivatives which is necessary in-case of an algebraic loop. The simulation might become unstable...\n",
      "  \n",
      "/usr/local/lib/python2.7/dist-packages/ipykernel_launcher.py:2: UserWarning: The model, InverseInertia, does not support directional derivatives which is necessary in-case of an algebraic loop. The simulation might become unstable...\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "from pyfmi.master import Master\n",
    "coupled_simulation = Master(models, connections)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "directional derivatives を計算する機能がサポートされていないというワーニングが出ています。この機能はモデルどうしの接続で代数ループがある場合は必要になるようです。\n",
    "\n",
    "オプションを設定します。コミュニケーションステップサイズを設定し、linear_correction を False にします。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "opts = coupled_simulation.simulate_options()\n",
    "opts[\"step_size\"] = 0.01\n",
    "opts[\"linear_correction\"] = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "directInertia モデルの入力信号用オブジェクトを生成します。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "f = lambda time: 10*np.sin(2*np.pi*2*time)\n",
    "input_object = ((directInertia, \"tauDrive\"), f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Co-Simulation を実行します。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/dist-packages/ipykernel_launcher.py:1: UserWarning: Linear correction only supported if directional derivatives are available.\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Elapsed initialization time: 0.00193905830383 seconds.\n",
      "Master Algorithm options:\n",
      " Algorithm             : Jacobi (fixed-step)\n",
      "  Execution            : Serial\n",
      " Extrapolation Order   : 0\n",
      " Step-size             : 0.01\n",
      " Algebraic loop        : True\n",
      "  Linear Correction    : False\n",
      "\n",
      "Statistics: \n",
      " Number of global steps        : 100\n",
      "\n",
      "Simulation interval      : 0.0 - 1.0 seconds.\n",
      "Elapsed simulation time  : 0.0547690391541 seconds.\n",
      " 0.002795 seconds spent in DirectInertia.\n",
      " 0.000860 seconds spent in InverseInertia.\n",
      " 0.042885 seconds spent saving simulation result.\n"
     ]
    }
   ],
   "source": [
    "res = coupled_simulation.simulate(options=opts, input=input_object)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "linear correction は、directional derivative が計算できる場合のみサポートされるという旨のワーニングがでます。\n",
    "シミュレーション結果を抽出してプロットします。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "inverseInertia_time = res[inverseInertia][\"time\"]\n",
    "inverseInertia_phi = res[inverseInertia][\"inertia.flange_b.phi\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f728c326850>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f728c3b8990>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(1)\n",
    "plt.plot(inverseInertia_time, inverseInertia_phi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "結局、linear_correction が有効になりませんでした。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.17"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
	{
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"### GenerationOfFMUs (2) - with_linear_correction\n",
	"[CO-SIMULATION USING THE OPEN-SOURCE PYTHON PACKAGE PYFMI](https://www.modelon.com/co-simulation-using-the-open-source-python-package-pyfmi/) の最後の方に記述された linear_correction = True にしたシミュレーションを試みます。\n",
	"\n",
	"サブシステムモデルをコンパイルしてFMUを生成します。"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 1,
	"metadata": {},
	"outputs": [],
	"source": [
	"from pymodelica import compile_fmu\n",
	"fmu1 = compile_fmu('Modelica.Mechanics.Rotational.Examples.Utilities.DirectInertia',target='cs', version='2.0', compile_to='DirectInertia.fmu')\n",
	"fmu2 = compile_fmu('Modelica.Mechanics.Rotational.Examples.Utilities.InverseInertia',target='cs',version='2.0', compile_to='InverseInertia.fmu')"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"サブシステムモデルをロードします。"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 2,
	"metadata": {},
	"outputs": [],
	"source": [
	"from pyfmi import load_fmu\n",
	"directInertia = load_fmu(\"DirectInertia.fmu\")\n",
	"inverseInertia = load_fmu(\"InverseInertia.fmu\")"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"パラメータを設定します。"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 3,
	"metadata": {},
	"outputs": [],
	"source": [
	"directInertia.set(\"J\", 1.1)\n",
	"inverseInertia.set(\"J\", 2.2)"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"サブシステムモデルのリストと接続関係のリストを作成します。"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 4,
	"metadata": {},
	"outputs": [],
	"source": [
	"models = [directInertia, inverseInertia]\n",
	"connections = [\n",
	" (directInertia, \"phi\", inverseInertia, \"phi\"),\n",
	" (directInertia, \"w\", inverseInertia, \"w\"),\n",
	" (directInertia, \"a\", inverseInertia, \"a\"),\n",
	" (inverseInertia, \"tau\", directInertia, \"tau\")]"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"Co-Simulationモデルを作成します。"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 5,
	"metadata": {},
	"outputs": [
	{
	"name": "stderr",
	"output_type": "stream",
	"text": [
	"/usr/local/lib/python2.7/dist-packages/ipykernel_launcher.py:2: UserWarning: The model, DirectInertia, does not support directional derivatives which is necessary in-case of an algebraic loop. The simulation might become unstable...\n",
	" \n",
	"/usr/local/lib/python2.7/dist-packages/ipykernel_launcher.py:2: UserWarning: The model, InverseInertia, does not support directional derivatives which is necessary in-case of an algebraic loop. The simulation might become unstable...\n",
	" \n"
	]
	}
	],
	"source": [
	"from pyfmi.master import Master\n",
	"coupled_simulation = Master(models, connections)"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"directional derivatives を計算する機能がサポートされていないというワーニングが出ています。この機能はモデルどうしの接続で代数ループがある場合は必要になるようです。\n",
	"\n",
	"オプションを設定します。コミュニケーションステップサイズを設定し、linear_correction を False にします。"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 6,
	"metadata": {},
	"outputs": [],
	"source": [
	"opts = coupled_simulation.simulate_options()\n",
	"opts[\"step_size\"] = 0.01\n",
	"opts[\"linear_correction\"] = True"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"directInertia モデルの入力信号用オブジェクトを生成します。"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 7,
	"metadata": {},
	"outputs": [],
	"source": [
	"import numpy as np\n",
	"f = lambda time: 10np.sin(2np.pi2time)\n",
	"input_object = ((directInertia, \"tauDrive\"), f)"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"Co-Simulation を実行します。"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 8,
	"metadata": {},
	"outputs": [
	{
	"name": "stderr",
	"output_type": "stream",
	"text": [
	"/usr/local/lib/python2.7/dist-packages/ipykernel_launcher.py:1: UserWarning: Linear correction only supported if directional derivatives are available.\n",
	" \"\"\"Entry point for launching an IPython kernel.\n"
	]
	},
	{
	"name": "stdout",
	"output_type": "stream",
	"text": [
	"Elapsed initialization time: 0.00193905830383 seconds.\n",
	"Master Algorithm options:\n",
	" Algorithm : Jacobi (fixed-step)\n",
	" Execution : Serial\n",
	" Extrapolation Order : 0\n",
	" Step-size : 0.01\n",
	" Algebraic loop : True\n",
	" Linear Correction : False\n",
	"\n",
	"Statistics: \n",
	" Number of global steps : 100\n",
	"\n",
	"Simulation interval : 0.0 - 1.0 seconds.\n",
	"Elapsed simulation time : 0.0547690391541 seconds.\n",
	" 0.002795 seconds spent in DirectInertia.\n",
	" 0.000860 seconds spent in InverseInertia.\n",
	" 0.042885 seconds spent saving simulation result.\n"
	]
	}
	],
	"source": [
	"res = coupled_simulation.simulate(options=opts, input=input_object)"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"linear correction は、directional derivative が計算できる場合のみサポートされるという旨のワーニングがでます。\n",
	"シミュレーション結果を抽出してプロットします。"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 9,
	"metadata": {},
	"outputs": [],
	"source": [
	"inverseInertia_time = res[inverseInertia][\"time\"]\n",
	"inverseInertia_phi = res[inverseInertia][\"inertia.flange_b.phi\"]"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 10,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"[<matplotlib.lines.Line2D at 0x7f728c326850>]"
	]
	},
	"execution_count": 10,
	"metadata": {},
	"output_type": "execute_result"
	},
	{
	"data": {
	"image/png": 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\n",
	"text/plain": [
	"<matplotlib.figure.Figure at 0x7f728c3b8990>"
	]
	},
	"metadata": {
	"needs_background": "light"
	},
	"output_type": "display_data"
	}
	],
	"source": [
	"%matplotlib inline\n",
	"import matplotlib.pyplot as plt\n",
	"plt.figure(1)\n",
	"plt.plot(inverseInertia_time, inverseInertia_phi)"
	]
	},
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"結局、linear_correction が有効になりませんでした。"
	]
	},
	{
	"cell_type": "code",
	"execution_count": null,
	"metadata": {},
	"outputs": [],
	"source": []
	}
	],
	"metadata": {
	"kernelspec": {
	"display_name": "Python 2",
	"language": "python",
	"name": "python2"
	},
	"language_info": {
	"codemirror_mode": {
	"name": "ipython",
	"version": 2
	},
	"file_extension": ".py",
	"mimetype": "text/x-python",
	"name": "python",
	"nbconvert_exporter": "python",
	"pygments_lexer": "ipython2",
	"version": "2.7.17"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 2
	}