{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tilt Sensor Calibration Report 2019-6-19\n",
    "\n",
    "\n",
    "## Introduction\n",
    "\n",
    "This calibration report covers the first installation of the reworked level sensor in the sled constructed for the ROV Doc Ricketts. The sensor was rebuilt with more sensitive allegro hall sensors, and stronger magnets, which should lead to a well defined magnetic field. \n",
    "\n",
    "<img src=\"sledhanging.png\" width=\"200\" />\n",
    "\n",
    "## Setup \n",
    "\n",
    "Calibration was done in the Building B high bay with the sled flat on the ground. Angle measurements were taken with the digital level, clamped to the front of the sled and manually recorded, while stopping the movement at about every 5 degrees."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "%matplotlib inline\n",
    "matplotlib.rcParams['figure.dpi'] = 300"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "raw_angle = np.array([180.-78.3, 180.-80.1, 180.-86.9, 90., 81.3, 75.6, \n",
    "                68.3, 61.5, 55.5, 50.4, 44.4, 40.3, 35.9, 30.8, \n",
    "                25.9, 20.9, 15.4, 9.97, 7.30, 4.01, 0.57, -2.59,\n",
    "                -6.20, -9.64, -13.1, -15.4, -18.5, -19.0])\n",
    "raw_counts = np.array([136., 146., 171., 180., 225., 255., 294., 333., 369.,\n",
    "                400., 438., 465., 494., 529., 561., 596., 631., 668., \n",
    "                686., 707., 728., 746., 768., 785., 803., 814., 827., 832.])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b9bba90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots(figsize=(10,4))\n",
    "ax1.plot(raw_counts, raw_angle,'.');\n",
    "ax1.set_xlabel('ADC Counts');\n",
    "ax1.set_ylabel('Angle From Vertical (degrees)')\n",
    "ax1.set_title('Raw Data');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -0.1654825 , 119.36475706])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_model = np.polyfit(raw_counts, raw_angle, 1)\n",
    "lin_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.90947004e-05, -1.94146092e-01,  1.24838146e+02])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sec_model = np.polyfit(raw_counts, raw_angle, 2)\n",
    "sec_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "counts = np.linspace(np.min(raw_counts), np.max(raw_counts), 100)\n",
    "angles_lin = lin_model[0]*counts + lin_model[1]\n",
    "angles_sec = sec_model[0]*counts**2 + sec_model[1]*counts + sec_model[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b9f14a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax2 = plt.subplots(figsize=(10,10))\n",
    "ax2.plot(raw_counts, raw_angle, '.', label='raw')\n",
    "ax2.plot(counts, angles_lin, '-', label='linear fit');\n",
    "ax2.plot(counts, angles_sec, '-', label='2nd order fit');\n",
    "ax2.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import leastsq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#optimize a lsq fit on a sinusoid\n",
    "raw_rads = raw_angle*np.pi/180\n",
    "guess_mean = np.mean(raw_counts)\n",
    "guess_std = np.std(raw_counts)/2**0.5\n",
    "guess_phase = 0\n",
    "guess_freq = 1\n",
    "guess_amp = 400\n",
    "\n",
    "data_first_guess = guess_std*np.sin(raw_rads+guess_phase) + guess_mean\n",
    "\n",
    "optimize_func = lambda x: x[0]*np.sin(x[1]*raw_rads+x[2]) + x[3] - raw_counts\n",
    "est_amp, est_freq, est_phase, est_mean = leastsq(optimize_func, [guess_amp, guess_freq, guess_phase, guess_mean])[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "fine_rads = np.arange(np.min(raw_rads), np.max(raw_rads),.1)\n",
    "data_fit = est_amp*np.sin(est_freq*fine_rads+est_phase)+est_mean\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ADC = -446.6 sin\\(0.859 theta + -0.468)+527.6\n"
     ]
    }
   ],
   "source": [
    "print(f'ADC = {est_amp:2.1f} sin\\({est_freq:4.3} theta + {est_phase:4.3})+{est_mean:4.1f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(20,700,'ADC {=} -446.6 sin(0.859 \\\\theta - 0.468)+527.6')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11786aac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rc('text', usetex=True)\n",
    "plt.rc('font', family='serif', size=18)\n",
    "fig, ax4 = plt.subplots(figsize=(10,10));\n",
    "ax4.plot(raw_rads*180/np.pi, raw_counts,'.', label='raw')\n",
    "ax4.plot(fine_rads*180/np.pi, data_fit, label='sinusoid lsq fit')\n",
    "ax4.legend()\n",
    "ax4.set(xlabel=r'\\theta (degrees)', ylabel='ADC',title='Tilt Sensor Calibration 2019-06-19')\n",
    "ax4.text(20, 700, r'ADC {=} -446.6 sin(0.859 \\theta - 0.468)+527.6')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Resultant transfer function is:\n",
    "\n",
    "$$\\theta = \\frac{sin^{-1}\\left(\\frac{ADC-527.6}{-446.6}\\right)+0.468}{0.859}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simplified equation is 1.164 * ( arcsin(-0.00224*(ADC-527.575)) + 0.468)\n"
     ]
    }
   ],
   "source": [
    "print(f'Simplified equation is {1/est_freq:4.3f} * ( arcsin({1/est_amp:4.3}*(ADC-{est_mean:.3f})) + {-1*est_phase:.3f})')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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