{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a1b2c3d4",
   "metadata": {},
   "source": [
    "# JSBSim Trim and Elevator Doublet with PathSim\n",
    "\n",
    "This notebook demonstrates how to embed a [JSBSim](https://github.com/JSBSim-Team/jsbsim)\n",
    "flight dynamics model (FDM) directly inside a [PathSim](https://github.com/pathsim/pathsim)\n",
    "block diagram using a `DynamicalFunction` block — without any additional wrapper library.\n",
    "\n",
    "The example is adapted from\n",
    "[test_pathsim_01_Trim_Elevator_Doublet.ipynb](https://github.com/agodemar/jsbsim/blob/master/examples/python/test_pathsim_01_Trim_Elevator_Doublet.ipynb)\n",
    "and covers:\n",
    "\n",
    "1. Instantiating and trimming a JSBSim FDM (Global 5000 business jet).\n",
    "2. Wrapping the FDM step inside a PathSim `DynamicalFunction` block.\n",
    "3. Assembling a block diagram that applies a **doublet elevator input** and records\n",
    "   the angle-of-attack response.\n",
    "4. Plotting the results.\n",
    "\n",
    "**Prerequisites:** `jsbsim` and `pathsim` must be installed.\n",
    "\n",
    "```bash\n",
    "pip install jsbsim\n",
    "pip install pathsim\n",
    "```\n",
    "\n",
    "**Previous notebook:** [03_pathsim_intro.ipynb](03_pathsim_intro.ipynb) – PathSim block-diagram basics.  \n",
    "**Next notebook:** [05_pathsim_flight.ipynb](05_pathsim_flight.ipynb) – higher-level `pathsim-flight` integration."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2c3d4e5",
   "metadata": {},
   "source": [
    "## 1. Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "colab-install",
   "metadata": {},
   "outputs": [],
   "source": [
    "# If running on Google Colab, install the required packages.\n",
    "\n",
    "import sys\n",
    "\n",
    "if 'google.colab' in sys.modules:\n",
    "    print('Running on Google Colab \\u2013 installing jsbsim, pathsim \\u2026')\n",
    "    !pip install jsbsim pathsim\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c3d4e5f6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "JSBSim version  : 1.3.0\n",
      "PathSim version : 0.20.0\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "import xml.etree.ElementTree as ET\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import jsbsim\n",
    "import pathsim\n",
    "\n",
    "matplotlib.rcParams.update({'figure.dpi': 120, 'axes.grid': True, 'grid.alpha': 0.4})\n",
    "\n",
    "# Suppress JSBSim console output\n",
    "# jsbsim.FGJSBBase().debug_lvl = 0\n",
    "\n",
    "print(f\"JSBSim version  : {jsbsim.__version__}\")\n",
    "print(f\"PathSim version : {pathsim.__version__}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4e5f6a7",
   "metadata": {},
   "source": [
    "## 2. Initialize the JSBSim FDM\n",
    "\n",
    "Instantiate an `FGFDMExec` object and load the **Global 5000** business-jet model\n",
    "(`global5000`) from the JSBSim Python-package data directory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e5f6a7b8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "     JSBSim Flight Dynamics Model v1.3.0 Apr  9 2026 10:00:08\n",
      "            [JSBSim-ML v2.0]\n",
      "\n",
      "JSBSim startup beginning ...\n",
      "\n",
      "Aircraft loaded  : global5000\n",
      "JSBSim root dir  : /home/vscode/.local/lib/python3.11/site-packages/jsbsim\n",
      "Load status      : True\n"
     ]
    }
   ],
   "source": [
    "AIRCRAFT_NAME = \"global5000\"\n",
    "\n",
    "# Use the aircraft data bundled with the jsbsim Python package\n",
    "fdm = jsbsim.FGFDMExec(jsbsim.get_default_root_dir())\n",
    "\n",
    "fdm.set_debug_level(0) # Suppress verbose JSBSim console output\n",
    "\n",
    "load_status = fdm.load_model(AIRCRAFT_NAME)\n",
    "\n",
    "# Property manager gives direct node access (used later to read alpha)\n",
    "pm = fdm.get_property_manager()\n",
    "\n",
    "print(f\"Aircraft loaded  : {AIRCRAFT_NAME}\")\n",
    "print(f\"JSBSim root dir  : {fdm.get_root_dir()}\")\n",
    "print(f\"Load status      : {load_status}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6a7b8c9",
   "metadata": {},
   "source": [
    "## 3. Aircraft Parameters and Trim Conditions\n",
    "\n",
    "Parse the aircraft XML to extract the empty weight and centre-of-gravity location,\n",
    "then define payload, fuel, and initial flight conditions for the trim."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a7b8c9d0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Empty weight        : 48235 lb\n",
      "Total weight (est.) : 67967 lb\n",
      "CG x (original)     : 790.82 in\n",
      "Trim altitude       : 15000 ft\n",
      "Trim CAS            : 250 kts\n"
     ]
    }
   ],
   "source": [
    "# Parse aircraft XML to get empty weight and CG\n",
    "ac_xml_path = os.path.join(\n",
    "    fdm.get_root_dir(), f\"aircraft/{AIRCRAFT_NAME}/{AIRCRAFT_NAME}.xml\"\n",
    ")\n",
    "ac_xml_root = ET.parse(ac_xml_path).getroot()\n",
    "\n",
    "# Empty weight [lbs]\n",
    "empty_weight = float(\n",
    "    ac_xml_root.find(\"mass_balance/emptywt\").text\n",
    ")\n",
    "\n",
    "# Original CG x-location [inches from construction-axes origin]\n",
    "x_cg_0 = float(\n",
    "    ac_xml_root.find(\"mass_balance/location/x\").text\n",
    ")\n",
    "\n",
    "# --- Payload and fuel ---\n",
    "payload_0     = 15172 / 2      # half payload [lb]\n",
    "fuelmax       = 8097.63        # Global 5000 max fuel [lb]\n",
    "fuel_per_tank = fuelmax / 2    # each of the three tanks loaded to half its capacity\n",
    "\n",
    "# --- Initial flight conditions ---\n",
    "speed_cas = 250.0   # calibrated airspeed [kts]\n",
    "h_ft_0    = 15000.0 # altitude [ft]\n",
    "gamma_0   = 0.0     # flight-path angle [deg]\n",
    "\n",
    "weight_0 = empty_weight + payload_0 + fuel_per_tank * 3\n",
    "\n",
    "print(f\"Empty weight        : {empty_weight:.0f} lb\")\n",
    "print(f\"Total weight (est.) : {weight_0:.0f} lb\")\n",
    "print(f\"CG x (original)     : {x_cg_0:.2f} in\")\n",
    "print(f\"Trim altitude       : {h_ft_0:.0f} ft\")\n",
    "print(f\"Trim CAS            : {speed_cas:.0f} kts\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8c9d0e1",
   "metadata": {},
   "source": [
    "## 4. Level-Flight Trim\n",
    "\n",
    "Apply the initial conditions, start the engines, and ask JSBSim's built-in trimmer\n",
    "(`simulation/do_simple_trim`) to find the steady level-flight equilibrium.\n",
    "The resulting elevator position and throttle are saved as the trim reference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c9d0e1f2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trim results:\n",
      "  CAS               : 250.00 kts\n",
      "  Angle of attack   : 4.3176 deg\n",
      "=========\n",
      "  Elevator (rad)    : -0.051721 rad\n",
      "  Elevator (deg)    : -2.9634 deg\n",
      "  Elevator (norm)   : -0.147775\n",
      "=========\n",
      "  Elevator Autopilot Cmd (norm) : -0.000000\n",
      "  Elevator Trim Tab Cmd (norm) : 0.000000\n",
      "=========\n",
      "  Throttle cmd norm : 0.772610\n"
     ]
    }
   ],
   "source": [
    "# Set engines running\n",
    "fdm['propulsion/set-running'] = -1\n",
    "\n",
    "# Initial conditions\n",
    "fdm['ic/h-sl-ft']   = h_ft_0\n",
    "fdm['ic/vc-kts']    = speed_cas\n",
    "fdm['ic/gamma-deg'] = gamma_0\n",
    "\n",
    "# Fuel load (three tanks)\n",
    "fdm['propulsion/tank[0]/contents-lbs'] = fuel_per_tank\n",
    "fdm['propulsion/tank[1]/contents-lbs'] = fuel_per_tank\n",
    "fdm['propulsion/tank[2]/contents-lbs'] = fuel_per_tank\n",
    "\n",
    "# Payload pointmass\n",
    "fdm['inertia/pointmass-weight-lbs[0]'] = payload_0\n",
    "\n",
    "# Initialise and trim\n",
    "fdm.run_ic()\n",
    "fdm.run()\n",
    "fdm['simulation/do_simple_trim'] = 1\n",
    "fdm.run()\n",
    "\n",
    "# Trim results\n",
    "trim_vc_kts       = fdm['velocities/vc-kts']\n",
    "trim_alpha_deg    = fdm['aero/alpha-deg']\n",
    "trim_elev_rad     = fdm['fcs/elevator-pos-rad']\n",
    "trim_elev_deg     = fdm['fcs/elevator-pos-deg']\n",
    "trim_elev_norm    = fdm['fcs/elevator-pos-norm']\n",
    "throttle_cmd_0    = fdm['fcs/throttle-cmd-norm']\n",
    "\n",
    "print(\"Trim results:\")\n",
    "print(f\"  CAS               : {trim_vc_kts:.2f} kts\")\n",
    "print(f\"  Angle of attack   : {trim_alpha_deg:.4f} deg\")\n",
    "print(f\"=========\")\n",
    "print(f\"  Elevator (rad)    : {trim_elev_rad:.6f} rad\")\n",
    "print(f\"  Elevator (deg)    : {trim_elev_deg:.4f} deg\")\n",
    "print(f\"  Elevator (norm)   : {trim_elev_norm:.6f}\")\n",
    "print(f\"=========\")\n",
    "print(f\"  Elevator Autopilot Cmd (norm) : {fdm['ap/elevator_cmd']:.6f}\")\n",
    "print(f\"  Elevator Trim Tab Cmd (norm) : {fdm['fcs/elevator-cmd-norm']:.6f}\")\n",
    "print(f\"=========\")\n",
    "print(f\"  Throttle cmd norm : {throttle_cmd_0:.6f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0e1f2a3",
   "metadata": {},
   "source": [
    "## 5. PathSim Block Diagram\n",
    "\n",
    "The flight-dynamics model is embedded as a PathSim\n",
    "[DynamicalFunction](https://docs.pathsim.org/pathsim/) block whose\n",
    "**input** is the normalised elevator command and whose **output** is the\n",
    "angle of attack in degrees.\n",
    "\n",
    "The total elevator command is the sum of two sources:\n",
    "\n",
    "| Block | Role |\n",
    "|-------|------|\n",
    "| `srcElevatorAtTrim` | Constant source — elevator position at trim |\n",
    "| `srcStepElevator` | `StepSource` — doublet perturbation (±10 % of full deflection) |\n",
    "| `addedElevatorSignals` | `Adder` — sums the two signals |\n",
    "| `dynFunAircraft` | `DynamicalFunction` — calls `fdm.run()` and returns α |\n",
    "| `ampElevatorNormalized` | `DynamicalFunction` — scales command × 100 for display |\n",
    "| `sco` | `Scope` — records both channels for plotting |\n",
    "\n",
    "The doublet shape: see code below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e1f2a3b4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15:15:34 - INFO - LOGGING (log: True)\n",
      "15:15:34 - INFO - BLOCKS (total: 6, dynamic: 0, static: 6, eventful: 1)\n",
      "15:15:34 - INFO - GRAPH (nodes: 6, edges: 6, alg. depth: 3, loop depth: 0, runtime: 0.083ms)\n",
      "Running 40-second simulation …\n",
      "15:15:34 - INFO - STARTING -> TRANSIENT (Duration: 40.00s)\n",
      "15:15:34 - INFO - --------------------   1% | 0.0s<0.7s | 7178.7 it/s\n",
      "15:15:35 - INFO - ####----------------  20% | 0.1s<0.2s | 18680.5 it/s\n",
      "15:15:35 - INFO - ########------------  40% | 0.2s<0.1s | 19257.6 it/s\n",
      "15:15:35 - INFO - ############--------  60% | 0.2s<0.1s | 15004.6 it/s\n",
      "15:15:35 - INFO - ################----  80% | 0.3s<0.1s | 18916.7 it/s\n",
      "15:15:35 - INFO - #################### 100% | 0.3s<--:-- | 10187.1 it/s\n",
      "15:15:35 - INFO - FINISHED -> TRANSIENT (total steps: 4801, successful: 4801, runtime: 334.44 ms)\n",
      "Done.\n"
     ]
    }
   ],
   "source": [
    "from pathsim import Simulation, Connection\n",
    "from pathsim.blocks import DynamicalFunction, Source, StepSource, Adder, Scope\n",
    "\n",
    "# -----------------------------------------------------------------------\n",
    "# Aircraft block: receives elevator command, advances JSBSim by one step,\n",
    "# and returns the angle of attack.\n",
    "# -----------------------------------------------------------------------\n",
    "def f_aircraft(u, t):\n",
    "    # Hold throttle at trim power to isolate the elevator response\n",
    "    fdm['fcs/throttle-cmd-norm'] = throttle_cmd_0\n",
    "    # PathSim passes u as a 1-D array; recent numpy rejects float() on non-0-d arrays,\n",
    "    # so .flat[0] reliably extracts the scalar regardless of array shape.\n",
    "    fdm['fcs/elevator-cmd-norm'] = float(np.asarray(u).flat[0])\n",
    "    fdm.run()\n",
    "    return pm.get_node('aero/alpha-deg').get_double_value()\n",
    "\n",
    "dynFunAircraft = DynamicalFunction(f_aircraft)\n",
    "\n",
    "# -----------------------------------------------------------------------\n",
    "# Signal sources\n",
    "# -----------------------------------------------------------------------\n",
    "\n",
    "# Constant: normalised elevator position at trim\n",
    "def f_elevator_command_at_trim(t):\n",
    "    return 0 # already set to: trim_elev_norm ... Why?\n",
    "\n",
    "srcElevatorAtTrim = Source(f_elevator_command_at_trim)\n",
    "\n",
    "# Doublet: −0.10 at t=10 s, 0 at t=11 s, +0.10 at t=12 s, 0 at t=13 s\n",
    "srcStepElevator = StepSource(\n",
    "    amplitude=[-0.1, 0, 0.1, 0],\n",
    "    tau=[10, 11, 12, 13]\n",
    ")\n",
    "\n",
    "# -----------------------------------------------------------------------\n",
    "# Signal processing blocks\n",
    "# -----------------------------------------------------------------------\n",
    "\n",
    "# Sum trim command and doublet perturbation\n",
    "addedElevatorSignals = Adder('++')\n",
    "\n",
    "# Scale elevator command × 100 so both traces fit on a similar y-scale\n",
    "def f_gain_100x(u, t):\n",
    "    return 100.0 * u\n",
    "\n",
    "ampElevatorNormalized = DynamicalFunction(f_gain_100x)\n",
    "\n",
    "# Scope records two channels: scaled elevator command and alpha\n",
    "sco = Scope(labels=[\"Elevator Command (% of full deflection)\", \"Angle of Attack (deg)\"])\n",
    "\n",
    "# -----------------------------------------------------------------------\n",
    "# Assemble the block diagram\n",
    "# -----------------------------------------------------------------------\n",
    "blocks = [\n",
    "    srcElevatorAtTrim,\n",
    "    srcStepElevator,\n",
    "    addedElevatorSignals,\n",
    "    dynFunAircraft,\n",
    "    ampElevatorNormalized,\n",
    "    sco,\n",
    "]\n",
    "\n",
    "connections = [\n",
    "    Connection(srcElevatorAtTrim,      addedElevatorSignals[0]),\n",
    "    Connection(srcStepElevator,        addedElevatorSignals[1]),\n",
    "    Connection(addedElevatorSignals,   dynFunAircraft),\n",
    "    Connection(addedElevatorSignals,   ampElevatorNormalized),\n",
    "    Connection(ampElevatorNormalized,  sco[0]),\n",
    "    Connection(dynFunAircraft,         sco[1]),\n",
    "]\n",
    "\n",
    "# -----------------------------------------------------------------------\n",
    "# Run the simulation for 40 s with a JSBSim standard dt (60 Hz)\n",
    "# -----------------------------------------------------------------------\n",
    "sim = Simulation(blocks, connections, \n",
    "                 dt=fdm.get_delta_t(), \n",
    "                 log=True)\n",
    "\n",
    "print(\"Running 40-second simulation …\")\n",
    "sim.run(40.0)\n",
    "print(\"Done.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2a3b4c5",
   "metadata": {},
   "source": [
    "## 6. Simulation Results\n",
    "\n",
    "The upper panel shows the normalised elevator command (scaled to percent of full\n",
    "deflection) and the lower panel shows the resulting angle-of-attack response."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a3b4c5d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MPeItZ0cEAAAAAA7nkGKjJNWtW1dLly5VSkqKoqOjJUmBgYFycXHIndwAgNxozxbp4G7zcouOUun0E43lGEWDpEah0uZfpN3h5slscnK8AAAAAJANHF7pc3Fxkbe3t4oVK0ahEQCQscQEacGn5mUfP6nbIOfGY4sO/cwjMCXp5++cGwsAAAAAOIHDqn07d+5U+/bt5ePjoyJFimjDhg2SpIsXL6pbt25av369o0IBAOQGq76XLp4zL3cfJPkVdG48tiheQmrY0ry8a7MUecq58QAAAACAgzmk2BgeHq6mTZvqyJEjGjhwoFJSUizrihYtqqtXr2rWrFmOCAUAkBtERUg/zzcvlywnNe/k1HCypGM/83MlDeOfcwAAAACAfMIhz2x87bXXVL16dW3dulXXr1/X7Nmz06xv2bKlvvzyS0eEAgDI6VJSpK+mSkmJ5qLd4OclV1dnR2W74NLSw82k7RvMry4DpKBSzo4qd7p4TrpyQUpMlJKTzDmR9PdXSSpVXipbSXJzd26cAAAAACwcUmzcsWOH3nvvPXl6eio2Njbd+pIlS+rcuXOOCAUAkNNtXCkd2W9eDu0mVajq3HjuRaf+5kKjkSKtmC89Nc7ZEeUe12PksnWdgjb/Io+zJzLv7+Epla8qVQ6RKteUKlSTvH2zP04AAAAAVjmk2Oju7p7m1uk7nT17Vn5+fo4IBQCQk125KP3wuXk5IFDqPti58dyrkuWkB5uan9u4bb3U51nJr4Czo8q5EuKlPVulrf+T9u+UW3Ky7b+gJMRLf/1hfknmCXpKlzcXHqvWlmrUlbx8sityAAAAAHdwSLGxYcOGWrRokcaOHZtu3Y0bNzRnzhw1b97cEaEAAHIqw5DmfSLduml+//goycvbuTHdjxadzcXG5CRp1yapeUdnR5QzHT0gzZpkLjTfJqlQgEwNQ+X6QH3Jw0tyczO/XN3NXxMTpBN/mUfBHtknnT1p3tBIkU4fM79+XSK5uklVakq1G0i160vFSzr+HAEAAIB8xCHFxgkTJqh58+bq1KmT+vfvL0nau3evjh8/rg8++EAXLlzQm2++6YhQAAA51e+/SXu2mJcbtJRqPezceO5X1VqSfxEp5pK0bR3FxjsZhrkY+P1nUnKyuc3HT3roESU+1ExnvQupRMlScvXwyHgfgSXMuSJJsdelYwfMxcej+6STR8zPdkxOkg7uMb8WzDIXG2vXN78q1+R5jwAAAICdOaTY2KBBA61YsULPPfecBg0aJEl68cUXJUkVK1bUihUrVLt2bUeEAgDIiW5cl779xLzsW0Dq+6xz47EHF1epfgvplx+kw39Kl6KlIoHOjipniLtlngRo+wbze1c3qc8zUrMOkruHjIQEKTIya/v0KyA90MD8ksy3Vx/aK/25Xfpju/nzl6TzZ6U1i80vLx/zbda1G0i1HpIKBdjtFAEAAID8yiHFRklq1aqV/vrrL+3Zs0dHjhxRSkqKKlasqAcffFAmk8lRYQAAcprkZOnrj6WrV8zv+z4rFfR3akh207CludgoSdvXSx36ODWcHCEqQprxjhR52vw+oJg07A37TwTk4fnPCMbHDCnylLno+Md28wjIlBQp7qZ5RO3vv5m3KVf5n9uty1SSXFzsGxMAAACQDzis2JiqTp06qlOnjqMPCwDIiZKSpNn/lXZuNL+vUU9qFOrcmOypdEUpuIwUddp8K3V+Lzbu3CTNmSLF3zK/r1FPeuZlqUCh7D2uyWSetKdkOfP3IPa6tH+nufC4b6d5ZK1kvvX65BFp6TdSocJSzYfNhceQekwyAwAAANgoW4qNGzduvKftmjVrZudIAAA5VmKCNOu9f57TWLqC9MxL5sJQXmEySQ1aSD99JZ05YZ7EpGQ5JwflJNs3SJ++98/7zv2lrgPNt5s7ml8B87MeG7SUUpKl439Jf2wzFx/PnDD3uXpF+u0X84tJZgAAAACbZUuxsUWLFmlujTYMw6ZbpZNTHxAPIHcwDPNLMv/BnpJsnowhyfRP++19Ut/r7zZDdyzf9l5/t93e39px0+3vzn1a25/S7tPa/iztGe1PSh/j7X1tOOd052Ntf1b2afP5WOuT0f6snc9dvodWz/mOeK3szyU5WYWuXZdLAT/zrayH9po3KVdFev5d8/Ma85oGLc3FRkna+j+p51POjccZzp6U5k4xL3v7SENe/ufZis7m4ipVqmF+9XjS/GzHP3eYC4+H9pif/Whtkpla9aUHmGQGAAAAuFO2FBvXrVuX5n18fLxeeukl3bx5U0OHDlXVqubnMh06dEifffaZfH199d///jc7QoEduKxbpsJnTsrV18/8/KqsFELSvM+gEJJum3sohKT7mkFhJ8Piky3nY62Ykk3nkyMKVbf1tbRbOf7fPCSVS9cKpOUmqfCdjZVqSGPekbx9nRCRAxQLlipWl44dlLatlx59In89C/BmrPTJRHPRzmSSnn1NqvmQs6PKWJFAqUUn8yshXvrrj39GPd4+ycz5xdLaxbljkpmUFPNI4sQE8wzdiYn/LKe+EhPM7be/T+2bZEv/O5ZT+ycnWY/J6n9CW2mz2s3c6G4YKpmULDc317/brG1v40hpa/3uZ1vzChuPcx/bZiWe+/nM7X0uGW5/P+eYvs1NhoLiE+Tm6fHPNrZ+Dvcbj70/7wyPY+P2dviZs+/2jsrxzPu5pqSoWFycXL280/77nB05bmu/3JA/+ewa6ZqSrMKxsXL1KyC53vl7nIOukXb/mbN124y2z+v/xmb9M3NJSlbBa1eljr0lDw9rB883sqXY2Lx58zTvX3jhBXl4eGjr1q3y8vKytHfp0kUjRoxQ8+bNtWrVKrVp0yY7wsF9ctn6PxWKOObsMADkNSaT9GBT6YkXJC9vZ0eTvRq0NBcbL0dLRw+Yb8nND1JSpNmTpei/Z5bu9njOLjTeycNTqvWw+WWZZGaHufh4t0lmqteVChY257W3j7kg6eVz27K3+avrXW4hT0mREuLMM3ffumk+TtzNv5dvWX9vWb5x23a3/nlGZh5jksSYUtyNiySvTHshv3OVlEf/uxN25CqpkLODQI7nJilAUkLz9ubnf+djDpkgZt68eXrjjTfSFBpT+fj46PHHH9e7776rDz/80BHhIKvc3ZXi5i6TyWS+HT519IDJdFtl3/RPRT9NnzvWm25fvvN/mP9ef/v+b1+f5quV/VkOdefxb99XRse/LVZrx7flfKzu4x7P587193Q+Vvrcub90+7iH8/l7fVJKiq5fv64CBQvKzdUtg/O5cx93rE8Xo+6I1dpnYOP53Jkj95JD6b7/GZ3bXWJMd85WPnNbfiZsPh8rn3kG38OMczKjGK3lSEbfQ/M+EhITFRkVpRIlSsjD0zNtDHnZw82k+TPNBaRt/8s/xcafvzMX5iSpTkOpYz/nxnM/TKbbJpnpbZ5UZv8uae8265PM2MLD858ipKeXlJBgLgzeumn+amUUuVO5uplvGXd3l9w9zMupL/c7v/693tXttuvI36ydltVztdJ2W1NySrJu3bwlbx9vuVobLWxtn7Z+pvcQz71tfx/xZCU/7iceq4e5n22zsL2tn3kG26akGIqPj5enp6dcXEz3H4/d8yeD/d3PZ25rPA7Lcasb27a/bMlxK00pKUpMSpK7m5v+efRXNsTjiPy57585G+PJh/ljGOZcMbmYZLr9HzZ7X+8z6ptb8wf5lkOKjTdu3FBUVFSG66OionTz5k1HhIJ7kDTuv4qMjDQXB/L5UGBkLCUhQVcjI+VbokS+HzKOu0hJMd+i5OKSfwqNklTAXwp50PwswJ2bpP7P5f3n/P25wzyrs2R+xuFT/8pbt4/7FpDqtzC/LJPMbDcXV1MnmclMQrz5de3Kvcfh6mpl1KTvHaMqvc3FTEsx0OOfouDthcE7C4W3t7m557jvX3JCgi7+/fuJK//uwIqkhASd53dYZCIxIYG/dZAp8uQeObVY7YD/0LujX0JCgqLORSk4INC27fMwhxQbW7durWnTpumhhx5Sjx490qz74YcfNG3aNLVr184RodzVu+++qzfeeEMhISHat2+fs8MBAOQlDVuZC3A3rptHwtVp5OyIsk90pPTZ++ZfwDy9pOFvSj55+Ca1NJPMPCElJ/9zm/PdboO+vT0uzlzYS3fbtbf127BTl93c81fhHgAA5B7387zG3MjFVYaHV477D1pncEix8ZNPPlGrVq3Uu3dvBQcHq1KlSpKkY8eOKTIyUhUrVtTHH3/siFAydObMGU2aNEm+vnn4jyEAgPPUaWS+bTYh3jxRTF4tNsbHSWHvmCeGkczP5CxZzqkhOZyrq3nkY16cXR0AAADIhEPKrSVLltTevXs1ZcoU1axZU+fPn9f58+cVEhKijz76SHv37lWpUqUcEUqGxo0bp4YNG+qhh3LRg+sBALmHp5dUt7F5ee9W82i2vMYwpK+m/XMbcdue5udVAgAAAMg3HDKyUZK8vLw0ZswYjRkzxlGHtNnGjRu1aNEi7d69W6NGjXJ2OACAvKpBS2nbOvPoxt/DpcatnR2Rfe3Zaj4/SapaW+r5lHPjAQAAAOBwDis25lTJyckaNWqUhgwZolq1atm0TXR0tC5cuJCm7ejRo5KkxMREJSQk2D1OZ0pMTFRSUpISExOdHQpyMPIEtsj3eVK5ptz9CsoUe00pW35V0kN5aNRfcrLcF82WSZLh7avEp8aZn12YnJzlXeX7PIFNyBNkhhyBLcgT2II8gS3ycp5k9ZyypdjYrl07vf7662rWLGt/RK1bt07/+c9/tHr16uwIy6qZM2fq1KlTWrt2rc3bhIWFacKECVbXRUdHy9/f307R5QxJSUm6evWqJMnNLd/Xp5EB8gS2IE+kgGp1VXDnBpkO7dH5wweV7FfI2SHZhd+ujSp6/qwk6Urjdrp2/aZ0/d5uFSdPYAvyBJkhR2AL8gS2IE9gi7ycJ9HR0Vnqny1nX7FiRbVp00YVKlRQ3759FRoaqrp168rPzy9Nv+vXr2vXrl1au3atvv/+e506dUpPP/10doRk1aVLl/TWW2/pzTffVLFixWzebvjw4erdu3eatqNHj6p79+4KDAxUiRIl7B2qU6VWsIODg+Xu7u7kaJBTkSewBXkimVp0knZukMkwFHzmiFJadXV2SPcv7pbcf1shSTICAuXX9TH5uXvc8+7IE9iCPEFmyBHYgjyBLcgT2CIv50lMTEyW+mdLsTEsLEz/+te/NG3aNIWFhemdd96RyWRSQECAChcuLMMwdOXKFV25ckWGYSggIEADBgzQmDFjVL58+ewIyao33nhDAQEBWX5OY2BgoAIDA62uc3d3l4fHvf+BlVO5ubnl2XOD/ZAnsEW+z5OqtaRiwdKFKLnt3Ci17+XsiO7fqoXStRhJkqnHE/Lw9bt7fxvk+zyBTcgTZIYcgS3IE9iCPIEt8mqeZLV4mm3jOsuXL6+pU6fqgw8+0KZNm7RlyxYdOnRIly5dkiQVKVJE1apVU6NGjdS0aVOHV32PHDmiTz/9VFOnTlVkZKSlPS4uTomJiTp58qQKFiyogIAAh8YFAMjjTCapQQtp+XfSycPS+bNS8ZLOjureXb0srV5kXi5TUarfwqnhAAAAAHCubL+J3M3NTS1btlTLli2z+1BZcvbsWaWkpGj06NEaPXp0uvXly5fXmDFjNHXqVMcHBwDI2+q3NBcbJfPszV0HOjee+7H0Gyk+zrzce4jk4uLceAAAAAA4Vd56YmUW1KxZU4sXL07X/sYbb+j69euaNm2aKlas6ITIAAB5Xoky5lGAp4+Zi41dBphHPOY2kaelTavMyzUflqrXdW48AAAAAJwu3xYbixYtqu7du6drTx3JaG0dAAB206CVudh4/qz5duryVZ0dUdb9OEdKSTEXSns95exoAAAAAOQA3OsEAIAz1G/+z2jGbeucG8u9OLxP2rPFvNy4jVTKcRO8AQAAAMi5KDbeYf369dq3b5+zwwAA5HWFi0pVHzAvb1svJSU5NZwsMQxp0WzzsruH1O1x58YDAAAAIMeg2AgAgLM0amX+ej1G2rfTqaFkya7N0vFD5uU2j0oBxZwbDwAAAIAcI0cUG5OTk7V8+XJnhwEAgGM9+Ijk6WVe/u0X58Ziq6RE6YcvzMt+haT2fZwbDwAAAIAcxanFxvDwcI0YMULBwcHq1q2bM0MBAMDxvLzNBUdJ+mObeYRjTrdhhXQhyrzc5THJx9e58QAAAADIURw+G/XBgwc1b948ffvttzp16pR8fX3Vrl07denSxdGhAADgfE3bSuFrpORk87MbW3d3dkQZu3lDWvateblYsNS8o3PjAQAAAJDjOKTYGBkZqe+++07z5s3T3r175e3trVu3bunf//63XnzxRXl4eDgiDAAAcp7KNc2FuwtR5lupc3KxcdX3UuxV83LPJyU3d+fGAwAAACDHybbbqK9du6YvvvhCoaGhKlu2rCZMmKAaNWpo6dKl2rFjhwzDUNWqVSk0AgDyN5NJatLGvBxxXDp9zLnxZOTyBWnNj+blCtX+uf0bAAAAAG6TbSMbg4KCJEkdO3bUt99+qy5dusjLy/wQ/GPHcugfUgAAOEOj1tKSryXDMI9uLPOcsyNKb8nXUmKCebnXEHORFAAAAADukG0jG+Pi4lS4cGGVL19eFSpUsBQaAQDAHYoEStXqmJe3rTPP+JyTnD1pfq6kJNVpJFWp6dRwAAAAAORc2VZsPHDggJ588kn98MMPql+/vqpUqaLx48fr0KFD2XVIAAByr6ZtzV9jr0l7tzk3ljstm2cedWlykXo86exoAAAAAORg2VZsrFatmv7973/r+PHj2rBhg0JDQxUWFqaQkBC1a9dOJpNJly5dyq7DAwCQu9RtLHn7mJd/W+PcWG539qS0a7N5uWFLqUQZp4YDAAAAIGfLtmLj7Zo2baoZM2YoKipKixcvVr169eTp6alhw4apcuXKGjdunNavX++IUAAAyJk8PKWHm5uX9+2Qrl52bjypfv7un1GNnfo5OxoAAAAAOZxDio2p3Nzc1LVrVy1cuFDnz5/X559/rnLlymnq1KkKDQ11ZCgAAOQ8Tf6+lTolRdryq3NjkaTI09KOjebl+s2loNLOjQcAAABAjufQYuPtChQooCeeeEJr1qzR6dOn9cEHHzgrFAAAcoYK1f4p6IWvMY8odCbLqEaT1Km/c2MBAAAAkCs4vNh44MABrVy5UitXrtSBAwckSSVKlNDzzz/v6FAAAMhZTKZ/RjdGnpZOHHZeLOfOSNs3mJcfasazGgEAAADYxGHFxiVLlqhixYqqVauWOnfurM6dO6tWrVqqVKmSli5d6qgwAADI2Rq1Mj8fUZJ++8V5cfz8nWSkmAugnRnVCAAAAMA2Dik2rlixQj179pQkTZo0SYsXL9bixYs1adIkGYahHj16aNWqVY4IBQCAnM2/iFTzQfPy9vVSYoLjYzgfKW1dZ15+sKlUspzjYwAAAACQK7k54iDvvPOOateurU2bNsnX19fS3rVrV40cOVJNmzbVhAkT1L59e0eEAwBAztakrfTnDunWDWl3uFS/hWOPnzqqUZI6P+bYYwMAAADI1RwysvGPP/7Q4MGD0xQaU/n6+uqJJ57QH3/84YhQAADI+R5oIPkWMC87+lbq6Ehp698zYddrIpUq79jjAwAAAMjVHFJs9PLy0uXLlzNcf/nyZXl5eTkiFAAAcj53D6lBS/Pygd3S5QuOO/aKBVIKoxoBAAAA3BuHFBtbtWqladOmacuWLenWbdu2Tf/3f/+n1q1bOyIUAAByhyZtzF8NQ9ryq2OOefGctGWteblOI6lMRcccFwAAAECe4ZBnNv73v/9Vo0aN1LRpU9WvX19Vq1aVJP3111/avn27AgMD9f777zsiFAAAcocylcy3MJ85Yb6VumNf88zQ2WnFAik52bzchVGNAAAAALLOISMby5cvrz/++EOjR4/WlStXtGDBAi1YsEBXrlzRmDFjtHfvXpUrV84RoQAAkDuYTFLjv0c3RkdKR/dn7/EunZd+W2NefqCBVLZy9h4PAAAAQJ7kkJGNkhQYGKiPPvpIH330kdX1V65cUeHChR0VDgAAOV+jVtIPn5tHG/62RqpcM/uOtWKhlJxkXu4yIPuOAwAAACBPc8jIxozEx8fr+++/V/fu3RUcHOzMUAAAyHkK+Eu1G5iXd2yU4uOy5ziXL0ibV5uXaz0slauSPccBAAAAkOc5vNhoGIbWrl2rJ598UsWLF1ffvn21ZcsWPfYYz4YCACCd1Ili4m9JuzZnzzFWMqoRAAAAgH047DbqXbt2ad68eZo/f77OnTsnk8mkfv36aeTIkWrYsKFM2f3QewAAcqOaD5tHOF6PkcLXSI1b23f/Vy5Km1aZl0MelCpUs+/+AQAAAOQr2Tqy8fjx43rnnXdUrVo11a9fX4sWLdKAAQO0YMECGYahnj17qlGjRhQaAQDIiJub1LCVefnQXunCOfvuf+VCKSnRvNyVUY0AAAAA7k+2jWxs1KiRtm/frqJFi6pXr16aPXu2mjZtKkk6duxYdh0WAIC8p0kbac2P5uXffpG6D7LPfmMuSRtXmper15Uq1rDPfgEAAADkW9lWbNy2bZvKly+vKVOmqFOnTnJzc9gd2wAA5C2lypsnbTl5WPp1idS6u+RX8P73u/w7RjUCAAAAsKtsu416+vTpCg4O1qOPPqqgoCA9++yzWrdunQzDyK5DAgCQd6VO3HLrhvTz/Pvf37ED0oafzcvV60qVa97/PgEAAADke9lWbBw+fLg2b96sY8eOaezYsdq0aZNCQ0NVsmRJvfXWWzKZTDyrEQAAW9WuL1WpZV5et+z+nt2YlCh9OVUyDMnNXRowwi4hAgAAAEC2ThAjSeXLl9cbb7yhAwcOaMeOHerXr5/Wr18vwzA0fPhwDR06VMuXL1dcXFx2hwIAQO5lMkm9hpiXkxKln768932tXChFnjYvdx0gBZW6//gAAAAAQA4oNt7uwQcf1JQpUxQREaFffvlF7dq104IFC9S1a1cVLVrUkaFox44dGjlypEJCQuTr66syZcqoT58+Onz4sEPjAADAZhWqSg83Ny9vWyedPJL1fUSeMj+rUTI/C7JtL/vFBwAAACDfc2ix0XJQFxe1bt1ac+fO1fnz5/Xdd98pNDTUoTG8//77+uGHHxQaGqpp06Zp6NCh2rhxo+rVq6d9+/Y5NBYAAGz26GDJ9e9J1xbNNt8KbauUFOnLaVJykmRykQaPlZjADQAAAIAdOf0vDC8vL/Xt21d9+/Z16HFfeOEFffvtt/Lw8LC09e3bV7Vq1dJ//vMfffPNNw6NBwAAmwSWkFp0Ms9KfWivtG+nVOth27bd8LN5YhjJPKN1+arZFiYAAACA/MkpIxtzgsaNG6cpNEpS5cqVFRISooMHDzopKgAAbNC5v+TtY15e9LmUkpz5NpcvSD/MMS8XLS51H5R98QEAAADIt5w+sjEnMQxD58+fV0hIyF37RUdH68KFC2najh49KklKTExUQkJCtsXoDImJiUpKSlJiYqKzQ0EORp7AFuSJnXj6yKVNT7kt/Vo6e1JJm1YrpVHrjPvHXpPb9AlyibspSUrsN1yGyUXKof9ekSewBXmCzJAjsAV5AluQJ7BFXs6TrJ4TxcbbzJs3T2fPntXEiRPv2i8sLEwTJkywui46Olr+/v7ZEJ3zJCUl6erVq5IkN57thQyQJ7AFeWI/puoPq+S6ZXK7HiP99JWiSlSS4e6Rrp/r9RgVnzdNLhejJEnXH2isS/7FpchIB0dsO/IEtiBPkBlyBLYgT2AL8gS2yMt5Eh0dnaX+eevs78OhQ4c0YsQINWrUSIMHD75r3+HDh6t3795p2o4eParu3bsrMDBQJUqUyM5QHS61gh0cHCx3d3cnR4OcijyBLcgTO+s+SPr6/+R2PUaldq1TcrdBkqvrP+svnpP7vKkyXTwnSUp+uLk8B41RCdec/c8/eQJbkCfIDDkCW5AnsAV5Alvk5TyJiYnJUv+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      "text/plain": [
       "<Figure size 1320x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "t_rec   = sco.recording_time\n",
    "data    = np.array(sco.recording_data[:])\n",
    "\n",
    "label = (\n",
    "    f\"Weight {weight_0:.0f} lb, \"\n",
    "    f\"Alt {h_ft_0/1000:.0f} kft, \"\n",
    "    f\"CoG-x {x_cg_0:.2f} in\"\n",
    ")\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(11, 6), sharex=True)\n",
    "\n",
    "ax1.plot(t_rec, data[:, 0], color='steelblue', linewidth=1.5, label=label)\n",
    "ax1.set_title(\n",
    "    f\"Normalised Elevator Command — trim altitude {h_ft_0/1000:.0f} kft\"\n",
    ")\n",
    "ax1.set_ylabel('Elevator Command (% full deflection)')\n",
    "ax1.set_ylim(-30, 30)\n",
    "ax1.legend(loc='upper right', fontsize=8)\n",
    "\n",
    "ax2.plot(t_rec, data[:, 1], color='tomato', linewidth=1.5, label=label)\n",
    "ax2.set_title(\n",
    "    f\"Angle of Attack — trim altitude {h_ft_0/1000:.0f} kft\"\n",
    ")\n",
    "ax2.set_xlabel('Time (s)')\n",
    "ax2.set_ylabel('AoA (deg)')\n",
    "ax2.set_ylim(-2, 10)\n",
    "ax2.legend(loc='lower right', fontsize=8)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4c5d6e7",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "In this notebook you:\n",
    "\n",
    "1. **Initialised** a JSBSim FDM for the Global 5000 business jet using the data\n",
    "   bundled with the `jsbsim` Python package.\n",
    "2. **Trimmed** the aircraft to steady level flight at 15 000 ft / 250 KCAS.\n",
    "3. **Wrapped** the JSBSim step function inside a PathSim `DynamicalFunction`\n",
    "   block — no additional library required.\n",
    "4. **Built a block diagram** that superimposes a doublet elevator perturbation on\n",
    "   the trim elevator command and records the angle-of-attack response.\n",
    "5. **Plotted** the two-channel scope output.\n",
    "\n",
    "**Next:** [05_pathsim_flight.ipynb](05_pathsim_flight.ipynb) – using the\n",
    "higher-level `pathsim-flight` library (`JSBSimWrapper`, `ISAtmosphere`) to build\n",
    "a closed-loop altitude-hold autopilot."
   ]
  }
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