{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab Assignment 1: Step Test of a First-Order System\n",
    "\n",
    "This notebook outlines a process for fitting a first-order model of a heater/sensor assembly to data taken during a step test. The learning goals for this notebook are:\n",
    "\n",
    "* Read and plot a previously saved step test data using the `Pandas` library.\n",
    "* By inspection, identify the gain and dominant time constant of the step test.\n",
    "* Simulate the response of a first-order model to step test.\n",
    "* Through iteration, adjust model parameters to fit the first order model to step test data. \n",
    "* Understand the relationship of model parameters to gain and time constant.\n",
    "* Determine if a first-order model provides an adequate description of the observed response."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Background and Starter Code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First-order lumped model for heater/sensor device.\n",
    "\n",
    "We have previously developed a first-order model for one heater/sensor pair on the temperature control lab device.  An energy balance gives\n",
    "\n",
    "\\begin{align}\n",
    "C_p\\frac{dT_1}{dt} & = U_a(T_{amb} - T_1) + \\alpha P_1u_1 \\\\\n",
    "\\end{align}\n",
    "\n",
    "where $T_1$ is the average temperature of heater/sensor one, $T_{amb}$ is the ambient temperature of the surroundings. The unknown parameters are the heat capacity $C_p$ and the heat transfer coefficient $U_a$.\n",
    "\n",
    "The parameters describing the heat input are as follows:\n",
    "\n",
    "* $\\alpha$ is a system calibration constant  The measured value of $\\alpha$ is 0.16 milliwatts per unit of $P_1$ per percent.\n",
    "* $P_1$ is a constant integer value in the range 0 to 255 that controls the operating range of heater 1. It is set using the `tclab` library.\n",
    "* $u_1$ is a floating point value in the range 0 to 100 that specify the percentage of available power for heater 1.\n",
    "\n",
    "For example, if $P_1 = 255$ and $u_1 = 100$, then the total applied power is\n",
    "\n",
    "$$\\alpha_1 P_1 u_1 = 0.16 \\times 200 \\times 50 = 4080\\ \\text{milliwatts} = 4.08\\ \\text{watts}$$\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reading previously saved experimental data\n",
    "\n",
    "A step test was performed where the temperature control laboratory was initially at steady state at ambient temperature. The heater range $P_1$ was set to 200, then  heater 1 was set to 50% of full range with $\\bar{u}_1 = 50$. Temperatures $T_1$ and $T_2$ were recorded for 800 seconds. The has been saved to the course Github repository where it can be located with the url\n",
    "\n",
    "[https://raw.githubusercontent.com/jckantor/CBE30338-book/main/tclab/data/tclab-data.csv](\"https://raw.githubusercontent.com/jckantor/CBE30338-book/main/notebooks/data/step-test-data.csv\")\n",
    "\n",
    "The following cell reads the step test data using the `Pandas` library. The data is stored in a Pandas DataFrame called `data`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>T1</th>\n",
       "      <th>T2</th>\n",
       "      <th>Q1</th>\n",
       "      <th>Q2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Time</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.00</th>\n",
       "      <td>23.81</td>\n",
       "      <td>23.48</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.00</th>\n",
       "      <td>23.81</td>\n",
       "      <td>23.48</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.00</th>\n",
       "      <td>23.81</td>\n",
       "      <td>23.48</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3.00</th>\n",
       "      <td>23.81</td>\n",
       "      <td>23.48</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4.01</th>\n",
       "      <td>23.81</td>\n",
       "      <td>23.48</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>796.00</th>\n",
       "      <td>54.75</td>\n",
       "      <td>34.44</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>797.00</th>\n",
       "      <td>54.75</td>\n",
       "      <td>34.44</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>798.01</th>\n",
       "      <td>54.75</td>\n",
       "      <td>34.76</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>799.00</th>\n",
       "      <td>54.75</td>\n",
       "      <td>34.76</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>800.00</th>\n",
       "      <td>54.75</td>\n",
       "      <td>34.76</td>\n",
       "      <td>50.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>800 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           T1     T2    Q1   Q2\n",
       "Time                           \n",
       "0.00    23.81  23.48  50.0  0.0\n",
       "1.00    23.81  23.48  50.0  0.0\n",
       "2.00    23.81  23.48  50.0  0.0\n",
       "3.00    23.81  23.48  50.0  0.0\n",
       "4.01    23.81  23.48  50.0  0.0\n",
       "...       ...    ...   ...  ...\n",
       "796.00  54.75  34.44  50.0  0.0\n",
       "797.00  54.75  34.44  50.0  0.0\n",
       "798.01  54.75  34.76  50.0  0.0\n",
       "799.00  54.75  34.76  50.0  0.0\n",
       "800.00  54.75  34.76  50.0  0.0\n",
       "\n",
       "[800 rows x 4 columns]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "# parameter values\n",
    "P1 = 200\n",
    "U1 = 50\n",
    "\n",
    "# file location\n",
    "github_repo = \"https://raw.githubusercontent.com/jckantor/CBE30338-book/main/\"\n",
    "file_path = \"tclab/data/tclab-data.csv\"\n",
    "url = github_repo + file_path\n",
    "\n",
    "# read file\n",
    "data = pd.read_csv(url, index_col=\"Time\")\n",
    "\n",
    "# display the step test data\n",
    "display(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we plot the data using the `.plot()` method associated with every Pandas DataFrame. The Pandas plot method provides a concise and intuitive means of plotting data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot: title={'center': 'P1=200, U1=50'}, xlabel='seconds', ylabel='% of full range'>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x250 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x150 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot(y=[\"T1\", \"T2\"], \n",
    "          title=f\"{P1=}, {U1=}\",\n",
    "          xlabel=\"seconds\", \n",
    "          ylabel=\"deg C\", \n",
    "          grid=True, \n",
    "          figsize=(8, 2.5)\n",
    "         )\n",
    "\n",
    "data.plot(y=[\"Q1\", \"Q2\"],\n",
    "          title=f\"{P1=}, {U1=}\",\n",
    "          xlabel=\"seconds\", \n",
    "          ylabel=\"% of full range\", \n",
    "          grid=True, \n",
    "          figsize=(8, 1.5),\n",
    "          ylim=(0, 100)\n",
    "         )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Analytical Solution for a Step Test\n",
    "\n",
    "The goal of this assignment is to fit a first-order model to the step test. The strategy we use will be use an analytical solution for a first-order model subject to a step change in the input. Then, by trail-and-error, find a set of model parameters that provide a good fit to the experimental data.\n",
    "\n",
    "We start with a first-order model written in gain/time-constant form\n",
    "\n",
    "$$\\tau\\frac{dx}{dt} = -x + K \\bar{u}$$\n",
    "\n",
    "where $x = T_1 - T_{amb}$ and the $\\bar{u}$ is a constant value for the input $u_1(t)$. The analytical solution consists of two parts\n",
    "\n",
    "$$x(t) = \\underbrace{x_0e^{-t/\\tau}}_{\\text{initial condition }x_0} + \\underbrace{(1 - e^{-t/\\tau}) K \\bar{u}}_{\\text{input }\\bar{u}}$$\n",
    "\n",
    "The solution depends on three parameters:\n",
    "\n",
    "* $x_0$: initial condition\n",
    "* $K$: steady-state gain\n",
    "* $\\tau$: time constant\n",
    "\n",
    "The initial condition $x_0 = 0$ if the step test starts at steady-state. In that case there are two parameters to fit, $K$ and $\\tau$. The following cell demonstrates the calculation and plotting of the analytical solution.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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k4OPjc9kFfRyRtK+UUoq8vDxSU1MBiIiIsEWIQgghKuGqTmZMJpMlkQkKCqry681mM0VFRXh4eDjtH3tpXylPT08AUlNTCQ0NlSEnIYSoI5zvL1QVlMyR8fLysnMkwlGUfFeqOr9KCCFE7bmqk5kSMv9BVJZ8V4QQou6RZEYIIYQQDk2SGWE3Op2O77//HoDExER0Oh07duyweRx33303N910k83fVwghRM2QZMbB6HS6f/yZMGECANOmTaNnz554eXkREBBg15grIzo6muTkZNq0aVOp8hMmTJAERAghBHCV383kiJKTky3HixYt4uWXX+bAgQOWcyV33BQVFTFmzBji4uKYPXt2rcVjNBprZHMxvV5PeHh4DUQkhBCitpnNisJiM5l5RZwvhPS8IkL97beRpiQzDubiP/j+/v7odLpyk4ApU6YAMHfu3ErX3bBhQ+6991727dvHjz/+iJ+fHxMnTuTpp5+2lNHpdMyaNYtly5axatUqnn76aaZMmcJPP/1EfHw8e/bsITIykvHjx/PCCy/g6qp9xQ4dOsS9997L5s2bady4Me+++67VeycmJtKoUSO2b99Ohw4dANizZw/PPvssv/32G0opOnTowNy5c/niiy+YN2+eJR6ANWvW0K9fP06dOsWTTz7JypUrcXFx4ZprruHdd9+lYcOGgHY7/jPPPMP//vc/9Ho9t99+O0qpSv+OhBDCkSilJR25hcXkFZnIKSwmr6iY3EITuYXF5BaZyCsq1s4XmsgtKi49f+GxwGgir8hEfpGJfGPpYylX0vxO8Mx1Le3WTklmLqGUuuRDqpjZbCa/yIRrUfEVr8PiadDXiTtl3nzzTSZPnkx8fDzLly/nySefpH379gwZMsRS5pVXXmHGjBn83//9H3q9nhUrVnDHHXfw3nvv0bt3b44cOcL9999vKWs2mxk1ahTBwcFs3LiRrKwsJk6c+I9xnDp1ij59+tCvXz9+/fVX/Pz8+OOPPyguLubpp59m3759ZGVlMWfOHADq1atHXl4e/fv3p3fv3qxfvx5XV1emTp3Kddddx86dO3Fzc+Ptt9/mf//7H7Nnz6ZFixa8/vrrfP/991x77bW19jsVQoiqUkqRW2Qiu8BIdkExWfkXHi88136MVo+5RRclLBcSk7wiEyZz7f4Pm0GnsPf/E0oyc4l8o4lWL6+w+fvu/c8QvNzs/3H06tWL5557DoCmTZuydu1aZs6caZXMjBs3jnvuucfy/M477+S5555j/PjxADRu3JhXX32VZ599lldeeYVVq1axb98+EhMTiYqKAmD69OkMHTq0wjg+/PBD/P39WbhwoWUYKzY21nLd09OTwsJCq16p+fPn4+LiwmeffWZJDOfMmUNAQABr165l8ODBzJw5k+eff57Ro0djNpt55513WLNmzZX+2oQQooyiYjPncgpJyYOtx9PJKVJk5BvJyCsiM99IZr7RkqRYJypGcgqLqekcxNOgx9tdj7e7K15urni7acfe7nq83FzxcXfFq+Scm3bOy12Pl5seD4P23NNw8XM9esysWL6MYQOb1mywVWTXv57x8fGW4ZASYWFhpKSkANokz5LhhBLdu3dn48aNNovxahMXF2f1vFu3bnz88cdW57p06WL1fOvWrWzZsoVp06ZZzplMJgoKCsjLy2Pfvn00aNDAksiU9z6X2rFjB717967SfJytW7dy+PBhfH19rc4XFBRw5MgRMjMzSU5OtnpvV1dXOnfuXOn3EEJcfZRSZBUUcy6nkPO5RZzLLSIjr4iMPOOF5MRIZv6F53lakpKRV0RuUUkvvyv8vaVa7+3qosPXwxVfD8OFx9Jjv0vOebu74nMhMfF2c70ocdHO6V1qvve/riwgaveugNatW7Nq1SrL80uXiL/uuussQwkAbm5utRqPp0HP3v8MuXxBtGGm7KxsfP18a2SYqa66dPjL29vb6rnZbGbKlCmMGjWqzGs9PDzKnZNyuSG1konMVWE2m+ncuTNffvllmWshISFVrk8I4ZyUUmTlF3Mut5BzuUWcyynifG4R53MLSbMcF5F2IXlJzyvCaKpeN4lOB54uimB/LwK93PD3ciPA00CAlwF/T8NFCYl1YuJ34dHD4FInpiDUdXZPZlxdXf/xLhZ3d3eb3uWi0+kqPdxjNpspvpDxOsveRZf2em3ZsoXmzZv/42s6derEgQMHaNq0/G7GVq1aceLECU6fPk1kZCQAf/755z/W2a5dO+bNm1fh3VJubm6YTNZzmzp16sSiRYsIDQ3Fz8+v3HojIiLYuHEjffr0AaC4uJht27bRqVOnf4xHCFH3GU1m0nIKSc0qJDW7kNTsAsvx2exCzmYXkJpdSFpOYbWSEx93V+p5u1l+AjwN+HsZCPB0I8CrNEEJuChh8dCjDcMMq1pPs6gauyczhw4dIjIyEnd3d7p378706dNp3Lix5fratWsJDQ0lICCAvn37Mm3aNEJDQyusr7CwkMLCQsvzrKwsQOsKu7Q7zGg0opTCbDZjNpurHHtJj0NJHbZW8p7lvfeJEyc4f/48x48fx2QysW3bNkCbB+Pj41NhnX/88Qevv/46I0aMICEhgR9++IEff/zR6j0u/X29+OKL3HjjjURFRXHzzTfj4uLCzp072b17N6+++irXXnstzZs356677uLNN98kKyuLF154waqui9tiNpt5+OGHef/997n11lt57rnn8Pf3Z+PGjXTr1o3mzZsTExPDihUr2LdvH0FBQfj7+zN27FjefPNNRowYQXx8PFFRUZw4cYLvvvuOp59+mqioKB5//HFee+01mjRpQosWLXjzzTfJyMio9GdoNptRSmE0Gh1io8mS73xd6QquadI+x1eZNiqlOJ9nJCWzgOTMAlKyCkjJLCQ1pyRJKeRsTiHpecYqTUT1dtcTVJKceLkR5KM91vM2UM/brfSatxv1vAy4V6MH3dk/w9psX1Xq1Ck73pe6bNky8vLyiI2N5cyZM0ydOpX9+/ezZ88egoKCWLRoET4+PsTExHDs2DFeeukliouL2bp1K+7u7uXWWd48HIAFCxaU2VCypFcoOjq61oevasOCBQt4/vnnOX78eJlrDz/8MF999VWZ8z/99BPXXHNNufW1a9eOO+64g/3797NixQp8fHz497//zYMPPmgpExgYyPz58xk+fLjVa1evXs0bb7zBrl27cHV1JTY2ljvvvNMyKfjw4cM89thjbNu2jQYNGvDaa69x8803W+o6ceIE7du3Z/369bRt2xaA3bt388orr7Bx40b0ej1t2rTho48+omHDhqSlpXH//fezZcsWcnJyLO06c+YM8fHxJCQkkJOTQ0REBH379uU///kPfn5+FBcX89JLL/Hll1/i4uLCHXfcwblz58jKyip3eOpSRUVFJCUlkZKSQnFx8WXLCyH+mVKQVwzpRZBRpCOjENKLdGQWXjhXqCOjCIpV5YZaXHQKXwP4GcDfTeFnAD838LMca48+BjA4R4e608rLy2PcuHFkZmZW2Ntewq7JzKVyc3Np0qQJzz77LE8++WSZ68nJycTExLBw4cJy52dA+T0z0dHRpKWllfllFBQUkJSURMOGDfHw8KhyvEopsrOz8fX1dYoxzcaNG/PEE0/wxBNPAM7XvktVp30FBQUkJiYSHR1dre+MrRmNRhISEhg0aJBTdnFL++o+pRSZ+cWcTM8nKT2Pkxn5nEovuPA8n9MZ+RQUV65nO9jHjQh/D8L9PAj3cyfU150QX+0x2MedUF83Ar3ccKmFia7VVWc+w5xUdOlHa7za4uJitmzZQpdrR+Aa3PjyL6iCrKwsgoODK5XM2H2Y6WLe3t60bduWQ4cOlXs9IiKCmJiYCq+DNsemvF4bg8FQ5otkMpnQ6XS4uLhUa85LybBESR3O4OK2OGP7Llad9rm4aJPxyvs+1WWOFm9VSfvsq7DYxIlzeRw/l0dSeh5J5/MvPOZxKj2f7MLL92LW8zYQ4e9JhL8nkQEeF449iPD3IDLAk1A/d9xd6/7QbkXs+hkWZMF/46Aws8ardgV6A6aQXPSDy46KXImq/L7qVDJTWFjIvn376N27d7nXz507R1JSEhERETaOTAghrm5Gk5mT6fkkpuVy7MJP4jnt8VRG/mXnqgT7uBNdz5PoQC+i63kSFehFdKAX4b4Gdvy5lhHXD67TCZtDS9mlJTJ6N/CPrtGqFYrc3Fw8PQNrtN6qsmsy8/TTT3PDDTfQoEEDUlNTmTp1KllZWYwfP56cnBzi4+MZPXo0ERERJCYmMnnyZIKDgxk5cqQ9w3ZaiYmJ9g5BCGFHSinO5RZx6EwOh1OzOZqWS2JaLonntF6W4n9Yxc3H3ZWYIC9LshJdTzuOCtQSF0+38ntVjEYje5yv47duObtPe2zcH27/ukarLjYaWb10KcN6DMOe/WZ2TWZOnjzJ2LFjSUtLIyQkhB49erBx40ZiYmLIz89n165dfP7552RkZBAREUH//v1ZtGhRmUXRhBBCVJ5SijNZhRxKzdYSl7M5HD6Tw6HUbNLzKr6DxMPgQsMgbxoFe9Mw2JtGQdpjw2AvQnzcnXJuXRlFuTD3ejh3pPzrJUM5ejdw9cQVxYjCLNRuLzDmlZZz96/9WEsUF2iPofbbO6m22TWZWbhwYYXXPD09WbHC9tsKCCGEMzmfW8S+5Cz2JWdx8Ew2h1K1xKWieSw6HUQHetE01IcmIReSlgs/Yb4edWpyrV0c/xNOb7t8OVMRmIoo+W3pLk5koFbmr/wzHTRx3j3o6tScGSGEENVjMiuOpeWwNznbkrzsS87iTFZhueX1LjpigrxoFupDs1Bfmob6XEhgfCocEhLA2f3aY9NBcN1r1tf+NwTy0kqfj/8Z88qXcEneXraea56EDrfXXpyX8vAHH+ddCV2SGSGEcDAFRhN7k7PYdTKTvaez2JeSxYGUbAoruMU5JsiLluF+xIb7EhumJS8Ng72qdnfQuSOwYwGYyxmG0um1ngiXy9Tn4goNekLSRjBrPUMuRXm0OnUSl1+3QMldhT7h0HYMbJsL+Rll6y33/XRanRef8w6B7g9C0ibIPAntb4Pcc7DlMzDmVr7tFzu6Vnus3wmCL1n1XH/JBOaYXmCoYGuWBnFlXy+qTZIZIYSow4rNsPtUFnvP5LDrZCY7T2Zy8Ex2uZNxvdz0NA/3pWWEHy0j/GgV4UvzcD983Gvgn/oVL8DBZVdeD29bPdMDzQBSLym2Kh5M5fcqVYlfJHx7j3Yc2hJ2L4E/Zl55veFty55rPRI2flT63MUF1XQgnNhQtmxI7JXHICwkmRFCiDrCbFYcPpvDjqQMdp7MYGdSBntO6zFt2limbLCPG+2iAmgd6WdJXmLqedXenJbkv7XH9mPBK6j0fHoi7P9ZO47qCtHdy399fgbsmF/upUyPaHza34DexQWOrdNuJb44kYnurtUNUJgN2+Zpx4ENocX1YDLC5o+1c571oMM4OP4HnN4OBy+ae3lmb2k7mg2B4GaVbb01nzCIHVr2fP8XtGs5ZyxDSOZuD7LvwCGaX/84hrS9cGqb1qsT2LB67y3KJcmMEBeZO3cuEydOJCMjw96hiKtATmExfydlsPV4OluPp7PtRDrZBZdOzNUR4GmgbZQ/7aL8aVs/gPbR/oT7eVT/7qH045B1qvLljfmQfVo7Hvq6Nv+ixJk9pclMp7u0n/IU5VaYzKT4d6TxwP+gNxjgj/e0ZOZiXe6F9rdqx8VFpclMWBsYMk3bE6EkmfGN0M5t/lRLZvb9XFpP4u9wZrd23OcZiO5ayV9AJbn7wDUTrc/p3TgSOpTmwc0gohW0vblm31MAksw4nMv94zV+/Hjmzp3LtGnT+OWXX9ixYwdubm7yx1kIO1NKcTI935K4bD2ezv6ULC4dLfJy09Muyp/2UQG0Cvch7dA27hw5qOb2jzt/DN7vDMp0+bKX8qtvncgABF3UuxHQoOLXunmDmy8UZZe5VGC4aMG10FZlX3txL4arW9nzF/+7WDIPpeQ25IvnxlycTIU0rzhW4XAkmXEwycnJluNFixbx8ssvc+DAAcs5T09tsllRURFjxowhLi6O2bNn2zxOe7p4mwoh7EUpxdG0XDYePcemo+fZePQcqdll54BEBXrSOSaQzjGBdGoQSItwX1z12nfXaDSyNOny/xNTJUmbtETG4K3NJ6ksnQt0f6DseVc36PucdpdPTPmb2FoMmQYbZ2m9N4XZsHY65iYDSfK5BksK0/AabQjo/FE4dwja3Fw6xFTipv/C319pdwSVuPVL2PRfGDxVex7VTRuCOnsACjIhN7U08WoxDDz+ea8f4VgkmXEw4eHhlmN/f390Op3VuRIlO4fPnTu30nU3bNiQf/3rXxw8eJAlS5YQFBTEjBkzGDBgAPfffz+rV6+mUaNGzJkzhy5dulhet2HDBp577jm2bNliWaF5xowZeHt7AzB//nxmzpzJgQMH8Pb25tprr2XmzJmEhoYCkJ6ezqOPPsrKlSvJyckhKiqKyZMnc/fdd7N27Vr69+9Peno6AQEBAOzYsYOOHTty7NgxGjZsaBkamj9/Ps8++ywHDx7k0KFD1K9fnxdffJEvv/ySjIwM2rRpw+uvv06/fv0ssS9YsIDXXnuNtLQ0hgwZUuGO4kJczsXJy8YLycvZS5IXg15H60h/S/LSOSaQMD8bb1iauld77DAWhr/9z2Urq//zlSvXebz2U6LfJExGI6alS0vPGTwuv0pth7Haz8VaXq/9lHB1g9u+rFxcwuFJMnMppaxXafwnZrNWtkhfekthdRm8rLtK7eT//u//mD59Oi+99BLvvPMODz74ID179uTee+/lzTffZNKkSdx1113s2bMHnU7Hrl27GDJkCK+++iqzZ8/m7NmzPProozz66KPMmTMH0HqJXn31VZo3b05qair//ve/mTBhAksv/AP20ksvsXfvXpYtW0ZwcDCHDx8mPz+/SnHn5eUxY8YMPvvsM4KCgggNDeXuu+8mMTGRhQsXEhkZyXfffcd1113Hrl27aNasGZs2beLRRx9l2rRpjB49muXLl/PKK6/U+O9UOK9TGfn8dvAsfxw5V27y4ubqQqcGAfRoHESPxkF0iA7Aw1ADa7ic3g4L7wB3X22eRsPeMPAVyDsP826EFsO1BCPhZfhrLnDRWFbJv29OvBqsuPpIMnMpYx5Mr1zXqwsQUFPvO/m0NqZsZ8OGDeOBB7Su5Jdeeon//ve/dO3alTFjxgAwadIk4uLiOHPmDOHh4bz55puMGzeOiRMnAtCsWTPee+89+vbty6xZs/Dw8OCee+6x1N+4cWPee+89unXrRk5ODj4+Ppw4cYKOHTtaensaNmxY5biNRiMfffQR7du3B+DIkSN89dVXnDx5kshI7fN8+umnWb58OXPmzGH69Om89957XHvttUyaNAkXFxdiY2PZsGEDy5cvr+6vTzi53MJiNh49x2+H0lh/6CxHz1qvVVJrycul9nwHWSdLn5/cAte+CNs+hzO7tJ++k2BzBeup6N2gUd+aj0sIO5FkRlhp166d5TgsLAyANm3alDmXmppKeHg4W7du5fDhw3z5ZWl3rlIKs9nMsWPHaNmyJdu3byc+Pp4dO3Zw/vx5zGZtYa8TJ07QqlUrHnroIUaPHs22bdsYPHgwN910Ez179qxS3G5ublaxb9u2DaUUsbHWazkUFhYSFKTdVrp//36GDrW+vTIuLk6SGWFhNit2n87UkpeDZ9l2Ih2jqbSXQ++io0N0ANc0DSauSS0mL5dK3Vf2XHqi9eqzp7driYzeDR7607rn1ysIPANqO0ohbEaSmUsZvLRekkowm81kZWfj5+t75ZNNDV5X9voaYjCUrmBZMumwvHMlCYnZbOaBBx7g8ccfL1NXgwYNyM3NZfDgwQwePJj58+cTEhLCiRMnGDJkCEVFRQAMHTqU48eP88svv7Bq1SoGDBjAI488wltvvWX5vSpV+gfEaCy7Aqmnp6fVJEmz2Yxer2fr1q3o9dZ/XHx8fMrUKUSJnMJifj90ltX7UllzIJW0nCKr69H1POnTLITezUKIaxKEv6ehgpoqaefXcChBS0SCm0NgDJzaCoDebKbT6dPov//Beij7xKay9fw8Ubvl+uLnAMGxstKscHqSzFxKp6v8cI/ZDAaTVv4qvXOmU6dO7Nmzh6ZNy//HcteuXaSlpfHaa68RHR0NwF9//VWmXEhICBMmTGDChAn07t2bZ555hrfeeouQEG0vkeTkZAIDtds3d+zYcdm4OnbsiMlkIjU1ld69e5dbpmXLlmzZssXq3MaNZRcnE87vZHoeq/elsmrfGTYdPU+RqXRbAB93V3o2CaJ3bAh9mgUTE1SDw8HFhbDkvtLnR361uuwCRAOkV6KuY+utn6fs1B4jO1Q/PiEchCQzTurEiROcP3+eEydOYDKZLAlA06ZNLT0TNWHSpEn06NGDRx55hPvuuw9vb2/27dtHQkIC77//Pg0aNMDNzY3333+fBx98kN27d/Pqq69a1fHyyy/TuXNnWrduTWFhIT///DMtW7a0xBsdHU18fDxTp07l0KFDvP325e/AiI2N5fbbb+euu+7i7bffpmPHjqSlpfHrr7/Stm1bhg0bxmOPPcY111zDm2++yciRI1m5cqUMMV0llFLsSMogYe8ZVu9L5cAZ67VPYoK8GNAijIEtQ+nSsB5urrX0PyvnDpd/3isIej+NyWxi7969tGrVCv2l+xNFdoDsZG3Sr06nLSYHpfsDmYzaHT2tbqqd2IWoQySZcVIvv/wy8+bNszzv2LEjAGvWrLG6NflKtWvXjnXr1vHCCy/Qu3dvlFI0adKEW2/VVusMCQlh7ty5TJ48mffee49OnTrx1ltvceONN1rqcHNz4/nnnycxMRFPT0969+7NwoULAW2I66uvvuKhhx6iffv2dO3alalTp1omJP+TOXPmMHXqVJ566ilOnTpFUFAQcXFxDBs2DIAePXrw3nvv8frrrzNlyhQGDhzIiy++WCbZEs7BbFZsPZHO0l3JrNidwunMAss1Fx10aViPAS1CGdAyjCYh3tVb2yU/o3SF2co4Xs6ePQAR7SHuYcxGI0fTltKi2zBtdVwhRLl0ysknDmRlZeHv709mZiZ+ftaLJBUUFHDs2DEaNWqEh0fV13owm81kZWXh5+fnlAu0SfvKutLvjK0ZjUaWLl3KsGHDrOY+OYvLta/YZGbzsfMs253C8j0pVrdOe7vp6dcilEEtw+jXPIQArxpYYfejuNJ1XK5Ej4fhuhlO//mBfEcdXW2275/+fl9KemaEEE7FbFZsPHaOn/4+zYo9ZzifWzqB19fDlUEtwxjaNoLezYJr9s6j3HOliUxwFZbKd/PSyuedAxdXyD0LHe+oubiEuApIMiOEcHhKKXafyuSHHaf46e9kUrJKh5ACvQwMbhXOdW3D6dUkuPbmv5y9cLt0QAN4dHPtvIcQolySzAghHNaJ83msOKnjvfc3cOSiBez8PFwZ1jaC69tF0qNxPcteRzWiuBA+H1F2Z2fThSUDytsoUQhRqySZEUI4lKwCIz/9fZrFW0+y7UQGoAdycXN1YWDLUEZ0qE+/5iG4u9bS4nXJf8OJPyu+3mxQ7byvEKJCkswgi6eJypPvin2UzIP55q+TLN2VTGGxtg6Miw6a+pm559q2DGtfHz8PG0ywLJkXE3MNjPjA+prBE3zLbvwqhKhdV3UyUzLzOi8vD09PTztHIxxBXp62SZ8z3pVQF53OyGfx1pN8s/UkJ86XbgDbLNSHW7pEM6xNKH/9tpphnepX/Jls/xKOrNbWYwlpDv5R2lL/1XVmj/YY2QHqNap+PUKIGnNVJzN6vZ6AgABSU1MB8PLyqtLaEmazmaKiIgoKCpz21mVpn0YpRV5eHqmpqQQEBJTZIkHUnGKTmdX7U1mw6QTrD52lpDPM192VGzpEckuXaNpH+aPT6crd2sJKUR788HDp86Nrai7QyI41V5cQ4opc1ckMQHi41iVcktBUhVKK/Pz8MvsCOQtpX1kBAQGW74yoWanZBSzanMSCzSdIvmhBu+6N6nFr12iGtonA062KSWTagfLP+4TBNU9WP1ivIFlZV4g65KpPZnQ6HREREYSGhl7+//IuYTQaWb9+PX369HHKYQdpnzWDwSA9MjVMKcXmY+f5YuNxlu9OodisdcPU83bjli7R3NY1mobBFeyFdHoHuF64lnce0g9BTC/IOA5JF26NTqrgFun6naHHgzXbGCGE3Vz1yUwJvV5f5T9Uer2e4uJiPDw8nPKPvbRP1JbcwmKWbD/F/D+PW+2L1KlBAHfFNWRo2/B/vhsp8xR80hcDQId56L8aAyl/w9hFsOxZLaH5J6Eta6QdQoi6QZIZIYTNnMkqYO6GRBZsOkFmvtYT6mnQc1PHSG7vHkOb+v6Vq+j0Nsuhe3EmLil/a0/+mHkhkdFB437aOTdvCG8LOWdA56KtsNt5Qk01SQhRB0gyI4SodXtOZzL7t2P8tPM0RpM2lNQwyIu74hoyunMU/p5V7Bk7f8xyGJRz0byYlAubPAY2hLu+v7KghRAOQ5IZIUStMJsV6w6e5dPfjrLhyDnL+W4N6/Gv3o0YeGQGLuu+hnXVqNxUut9S58T/lp4vujBkJcNIQlxVJJkRQtSoYpOZX3Yl8+Gawxw8kwOA3kXHsLYR/OuaRrSPDgBjAXz7BSjTFb+fC+XUIavwCnFVkWRGCFEjiorNLNl2klnrjnD8nLbAnY+7K2O7RTO+Z0OiAr1KC587pCUy7v7w4PrqvaG7H8bCPNYmLKfftQMw+IVq82FcPcE3rAZaJIRwFJLMCCGuSH6RiYVbTvDJ+qOW9WECvQzce00j7oxriL8xDX59GgoyQX9hbkx2ivYY2lKb31JdBl/y3EO0VX0NBm2yrxDiqiPJjBCiWvKKipm34Tif/XaUc7naHJZQX3fu79OYcd0b4OV24Z+Xz2/VNmcsT/1ONopWCOHMJJkRQlRJgdHEl5tOMGvtYdJytCQmKtCTB/s24ebOUXgYLlkf5uJEpsX10KiPduzqAa1G2ChqIYQzk2RGCFEpRcVmvv4riQ9+PUxKljacFBPkxWPXNmNEh0gM+gv7W53ZAym7yq+kwzhoMdxGEQshrhaSzAgh/lGxycx320/x7upDnEzPByDS34PHBzRjdOeo0iQGoDAbPhsExtzyKwuOtUHEQoirjSQzQohyKaVYtS+V15bt48hZLTkJ8XXn0f5Nua1bdPnbDZzZqyUyBm9o0L30fEYStBkFwc1sFL0Q4moiyYwQooy/kzKYtnQfm4+dB7S7kx7q14Q7ezQs3bm6IBOU2fqFp7drjw16wJ1LbBixEOJqJsmMEMIi6Xweb6w4wE9/nwbA3dWFe69pxIP9muDncdGWAz8+DtvmVVyRrMArhLAhSWaEEGTmGflgzSHmbThOkcmMTgejOkbx1OBYIgM8rQsrBXu/r7gyNx/triUhhLARuyYz8fHxTJkyxepcWFgYKSnaglpKKaZMmcInn3xCeno63bt358MPP6R169b2CFcIp2MyK77+K4k3Vxzg/IW1Yq5pGszzw1rQOrKCHayzk7UhJp0enjsBru7W13Uu4FLOfBohhKgldu+Zad26NatWrbI81+tL/xF84403eOedd5g7dy6xsbFMnTqVQYMGceDAAXx9fe0RrhBOY+vxdOJ/3MOuU5kANAv14YXhLekbG4JOp9MKnT8GS5+BwqzSFxZq+y0R1ATcfWwctRBClGX3ZMbV1ZXw8PAy55VSzJw5kxdeeIFRo0YBMG/ePMLCwliwYAEPPPCArUMVwimkZhfw2rL9LNl2CgBfD1f+PTCWO+NirG+zBtj+BRxOKL+i6O7lnxdCCBuzezJz6NAhIiMjcXd3p3v37kyfPp3GjRtz7NgxUlJSGDx4sKWsu7s7ffv2ZcOGDZLMCFFFRpOZuX8k8u7qQ+QUFgNwS5conr2uBcE+7uW/KHW/9tj5bmg6oPS8iwEaXlPLEQshROXYNZnp3r07n3/+ObGxsZw5c4apU6fSs2dP9uzZY5k3ExZmvfttWFgYx48fr7DOwsJCCgsLLc+zsrTucaPRiNForNH4S+qr6XrrCmmf4ytp21/H0oj/5SAHzmhDRO2i/Hh5eEvaR/mXlkvZie78UW3Oi1FbHE9/ehs6oLj5DaiSbQis38Am7aiIs3+Gzt4+cP42SvuuvO7K0CmlVI1HUE25ubk0adKEZ599lh49etCrVy9Onz5NRESEpcx9991HUlISy5cvL7eO8iYVAyxYsAAvL69ai12Iuii/GH4+4cIfZ3QodHi7Km6MMdMtROGiKy1nKM7hul2P4YKp3HqWt3mPQkOAbYIWQgggLy+PcePGkZmZiZ+f3z+Wtfsw08W8vb1p27Ythw4d4qabbgIgJSXFKplJTU0t01tzseeff54nn3zS8jwrK4vo6GgGDx582V9GVRmNRhISEhg0aBAGg+HyL3Aw0j7HpZRi5d5U3vllH6nZ2l1KIztG8tyQWOp5u5Upr0tcj8uu0kRGBTZCBTbWjmN6MqDnONsEXkXO/BmC87cPnL+N0r7qKxlZqYw6lcwUFhayb98+evfuTaNGjQgPDychIYGOHTsCUFRUxLp163j99dcrrMPd3R1397Lj/waDoda+SLVZd10g7XMspzPyefmHPazadwaAYA/FO2O70Kf5JRPtzWYoyNCOz+y0uqTr8wy6jrdbntf1G62d7TO8lLO3D5y/jdK+6tVZWXZNZp5++mluuOEGGjRoQGpqKlOnTiUrK4vx48ej0+mYOHEi06dPp1mzZjRr1ozp06fj5eXFuHF18/8ShbAnpRQLNp9g+i/7yC0yYdDruO+aRjQuOEhc4yDrwqZi+KQfnKlgd+t6jWs9XiGEqCl2TWZOnjzJ2LFjSUtLIyQkhB49erBx40ZiYmIAePbZZ8nPz+fhhx+2LJq3cuVKWWNGiEucysjnucU7+e1QGgCdYwKZMaotjep5sHTpwbIvOH+0bCLj7g9u3uAdBPU72SBqIYSoGXZNZhYuXPiP13U6HfHx8cTHx9smICEcjFLaCr6v/ryPnMJi3F1dePa6Fkzo2RC9i67iuwHO7tMeIzvCv1ZfOKkDFxdtuwKdrvzXCSFEHVSn5swIISovOTOf5xbvYt3BswB0ahDAm2Pa0yTkolV5iwvonPgR+rnvWycoOdrSB4S2Krv1gCQyQggHI8mMEA7ohx2nePH73WQXFOPm6sLTg2O595rG6F2sExHd0TVEpW+E9AoqklV8hRBOQJIZIRxIVoGRV37Yw3fbta0I2kcH8PaYdjQNLX8eme6stoKvuWEfXHo8aH3R3Q9ietZqvEIIYQuSzAjhILYeP88TC3dwMj0fFx08PqAZj/ZviuvhFbB/T7mv0e3/GQDVqB+0GG67YIUQwoYkmRGijis2mXn/18O8/+shzAqiAj1597YOdI6pB+nH4avbKnxtybaRKqy1bYIVQgg7kGRGiDos6XweExftYOtxbdLLyI71mTKiNX4eFxaTSrlwe7VPGMQOKfN6s9nMgZQ8mjbqZ5uAhRDCDiSZEaKOSth7hqe+3kFWQTG+7q5MHdmGER3qQ0Em5Gq7XnN6u/bYuB/c+H6ZOkxGIweXLqXppXcsCSGEE5FkRog6xmgy89aKA3y8/iigTfL9YGxHout5wZ8fworJZV8U0sLGUQohRN0hyYwQdUhyZj6PLdjOXxeGle7p1YjnhrbAzfXC7Jd9P5V9kWcgNB9qwyiFEKJukWRGiDpi/cGzTFy0g/O5Rfi6u/LGze0Y2rZ0x3iUgtQLK/c+sB7C2mrHOp0sdCeEuKpJMiOEnZnNivd+PcS7qw+hFLSO9OPzDvsJ2vQmbFSlBdWFXa51LhDcXNt6QAghhCQzQthTdoGRfy/6m1X7zgBwe/cGvHR9Kzxm3gO5qeW/KLITGDxsGKUQQtRtkswIYSdHz+Zw/xdbOZyag5urC9NHtuXmzlGQm1aayNzyBbhc9J+pTgdR3ewTsBBC1FGSzAhhB2v2p/L4wu1kFxQT7ufBnBsCaJm+ENYpyNK2KiAgBlrdaN9AhRDCAUgyI4QNKaWYte4Ib644gFLQJSaQj+7oROiiG+DkZuvC4W3tE6QQQjgYSWaEsJECo4mnv/mbn3cmAzCuewPib2iNm4uClJ1aoba3gMET9G7Q7T47RiuEEI5DkhkhbOBsdiH3ff4XO5IyMOh1xN/Ymtvb+sLZ3ZCdDMUF4OoJI/8LslqvEEJUiSQzQtSyg2eyuXvOFk5l5OPvaeDjOzvTI9QM/9cGjLmlBUNiJZERQohqkGRGiFr026GzPDx/G9mFxTQM8uJ/E7rSOMQHDizTEhkXA3gFaXcsdbvf3uEKIYRDkmRGiFqyYNMJXvphNyazolvDenx8Z2cCvd20i2f3a4+tRsDNs+0XpBBCOAFJZoSoYUopXl9+gP+uOwLAyI71eW10W9xTd8E3L4IxDzKStMKyQaQQQlwxSWaEqEFGk5lJi3eyZJu2Vsy/B8by+ICm6HQ62PwpJP5m/YJoWQBPCCGulCQzQtSQvKJiHv5yG2sPnEXvomPGqLbc0iW6tEDqXu2xz7NQvzN4h0D9TvYJVgghnIgkM0LUgPO5Rdwzdws7kjLwMLjw4bhODGgZBklb4OgarVDJjtftboHgZvYLVgghnIwkM0JcoZPpedz1v80cPZtLgJeB2eO70jkmEJSCr26FvHOlhQ1eENjIfsEKIYQTkmRGiCtw6Ew2d8zexJmsQiL9Pfj83m40DfXVLmYmaYmMiyt0vFM712ww6OU/OyGEqEnyr6oQ1bT7VCZ3zt5Eep6R2DAf5t3TjQhvF0jeCShIurDXUnAs3DDTnqEKIYRTk2RGiGrYejydCXM2k11QTPsof+bd040ALzeYe33ZO5ZCW9onSCGEuEpIMiNEFW04ksa/5v1FXpGJrg0D+d+Ervh6GMBYAMc3aIV8IwCdtmlkp7vsGq8QQjg7SWaEqII1+1N5cP5WCovN9G4WzMd3dsbL7cJ/RucOgTKBhz88uQ90OvsGK4QQVwlJZoSopOW7k3nsq+0YTYqBLcP4YFxHPAx6+Hsh/DoNirK1gqGtJZERQggbkmRGiEpYtiuZR7/ajsmsuL5dBP93awcMehft4uZPIPNEaeHG/ewSoxBCXK0kmRHiMpbvTuGxC4nMqI71eXNMe/QuF3pezGY4e0A7vm0BBDXV7l4SQghhM5LMCPEPVu5J4dEF2yg2K0ZenMhsnw8nt0BxIRTlgN7twhoyBnuHLIQQVx1JZoSowKq9Z3jkQiIzokMkb5UkMlnJ8MMj1oXDWksiI4QQdiLJjBDlWL3vDA99uRWjSXFD+0jevnhoKXWP9ugTDl3/pU32bXmD/YIVQoirnCQzQlxi3cGzPDR/G0aTYnjbCP7vlva46l3g3BEozIKja7WC0d2g7zN2jVUIIYQkM0JY2ZJ4nge++Isik5mhbcKZeVsHLZHZvQS+vdu6sKzsK4QQdYIkM0JcsPtUJvfM2UKB0Uz/5iG8e1vH0tuvj63THt39wd0XPAOgzWi7xSqEEKKUJDNCAIdTc7jrf5vJLiymW6N6fHR7Z9xcXUoLpO7THq9/B9rebJ8ghRBClEuSGXHVO5WRz52zt3A+t4i29f2ZPb4LnllHYdEdkJ+uFco9qz2GtrJfoEIIIcrlcvkitjFjxgx0Oh0TJ060nJswYQI6nc7qp0ePHvYLUjidrCIYP2cryZkFNA31Yd493bRNI3cvgbP7IeeM9qPM4FdfWxRPCCFEnVInema2bNnCJ598Qrt27cpcu+6665gzZ47luZubmy1DE04sK9/IrH16TuflERXoyfx7u1PP+8L36+yFYaWej0O7W7XjwIbgKt8/IYSoa+zeM5OTk8Ptt9/Op59+SmBgYJnr7u7uhIeHW37q1atnhyiFsyksNvHwVzs4nacj2MeN+fd2J9zfQ7v41xzY85123KgPhLfRftx97BewEEKICtm9Z+aRRx5h+PDhDBw4kKlTp5a5vnbtWkJDQwkICKBv375MmzaN0NDQCusrLCyksLDQ8jwrKwsAo9GI0Wis0dhL6qvpeusKZ22f2ax48ttdbDqWjrte8fG4dtT3d9PamXkSw88TAVA6F4qDmoMDt99ZP8MS0j7H5+xtlPZded2VoVNKqRqPoJIWLlzItGnT2LJlCx4eHvTr148OHTowc+ZMABYtWoSPjw8xMTEcO3aMl156ieLiYrZu3Yq7u3u5dcbHxzNlypQy5xcsWICXl1dtNkc4iB8SXfg12QUXneKBFmZaBJT+JxCWuZ0eR/8PgD8bP0Wqf3t7hSmEEFe1vLw8xo0bR2ZmJn5+fv9Y1m7JTFJSEl26dGHlypW0b6/9wbg0mblUcnIyMTExLFy4kFGjRpVbpryemejoaNLS0i77y6gqo9FIQkICgwYNwmBwvn15nLF98/48ztSl2i7Xr93UEs8zu7T2FZ5Hd2orLgeX47JzAeY2N2Ma8V87R3vlnPEzvJi0z/E5exulfdWXlZVFcHBwpZIZuw0zbd26ldTUVDp37mw5ZzKZWL9+PR988AGFhYXo9Xqr10RERBATE8OhQ4cqrNfd3b3cXhuDwVBrX6TarLsucJb2LduVzLRlWiLzzJDmjO4czdKlu7T2/W8kpB20lHUJa42LE7S5hLN8hhWR9jk+Z2+jtK96dVaW3ZKZAQMGsGvXLqtzd999Ny1atGDSpEllEhmAc+fOkZSUREREhK3CFE5iS+J5nli0A6Xgjh4NeLhfE4qLi7WL+emliUxUN/AMhPa32S9YIYQQVWK3ZMbX15c2bdpYnfP29iYoKIg2bdqQk5NDfHw8o0ePJiIigsTERCZPnkxwcDAjR460U9TCER0/l8t9n/9FUbGZQa3CmHJjG3Q6neW6Lk3rrcE/Gv6VYKcohRBCVJfd72aqiF6vZ9euXXz++edkZGQQERFB//79WbRoEb6+vvYOTziIzHwj98zdQkaekfZR/rx3W0f0Lloio9v+OYN3v4p+74UempDmdoxUCCFEddWpZGbt2rWWY09PT1asWGG/YITDKzaZeXTBNo6czSXC34NP7+qCp1vp8KX+r9m4GtNLX9C4n+2DFEIIccXqVDIjRE169ee9/HYoDU+Dnk/v6kKon0fpRZMRzmkTyYvHfotrcGOo19hOkQohhLgSkswIp/TFn4nM+/M4AP93awfa1PfXLmz+FJJ3QFEeOlMRxS4eqEZ9wK38dYuEEELUfZLMCKfz26GzxP+0F4Bnr2vOdW3CtQvnj8LSp63KZng1xF9n9109hBBCXAFJZoRTOXI2h4e/3IbJrBjVqT4P9W1SejFlt/YY0AA6T8CkYEeKL33tE6oQQogaIsmMcBrZBUbu//wvsguK6RwTyIxRbbVbsJWCE3/C/p+1gg17Q++nMBuN5C5dat+ghRBCXDFJZoRTMJsVT3/zN0fO5hLu58F/7+iMu+uFO5cOroCvbi0tHNrSPkEKIYSoFZLMCKcwa90RVuw5g5vehVl3dCLE96IJvUkbtUffSIhoD21vsU+QQgghaoUkM8LhrT2QylsrtVV8p4xoTccGgaUXTcVwRpsMTO8nodt9dohQCCFEbZJkRji0E+fyeGKhtufS2G7RjO3WoPTiti/g54lgvrDCrwwvCSGEU5J7UoXDyisq5v4v/iIz30iH6ADib2xtXWD34tJEJqABRHSweYxCCCFqn/TMCIeklOK5xbvYn5JNsI8bs+7oVDrht8TZ/drjnd9Bwz6gl6+7EEI4I/nXXTik+RuP8+Pfp3F10fHhuE5E+HtqF/LOw/q3ID8dspO1c/U7SyIjhBBOTP6FFw5n18lMXv15HwDPDW1B98ZBpRe3zoWNH5Y+D2wEHv62DVAIIYRNSTIjHEpWgZFHFmyjyGRmYMsw7r2mkXWBMxdW+W0+DKK7Q7NBtg9SCCGETUkyIxyGUopJ3+7kxPk86gd48vaY9toKv7nntBV+lRlObdUKd54AsUPsGq8QQgjbkGRGOIx5GxJZtjsFg17Hh7d3wt/LoF34+i44/rt1YbkNWwghrhqSzAiHsPNkBtOWavNknh/akg7RAdoFUzGc3KId1+8CegM06KHdii2EEOKqIMmMqPNK5skYTYohrcO4u1fD0ovnDoGpEAxecG8CuMjSSUIIcbWRf/lFnaaU4sXvdpN0Pp+oQE/euPnCPBnQNpD8qId2HNJCEhkhhLhKyb/+ok77bvspfvz7NHoXHe+N7Yi/p6H04t4fSo9b32Tz2IQQQtQNMswk6qwT5/J4+Yc9ADwxoBmdLt5AEiD1wgaSIz+G9rfZODohhBB1hSQzok4ymsw8sWg7OYXFdG0YyCP9m2oXCrJg6dOQkwopF9aUqd/FfoEKIYSwO0lmRJ30/upDbD+Rga+HK/93awf0Lhfmyez9AXYuKi3oFQz1GpVfiRBCiKuCJDOiztl87DwfrDkMwPSRbYkK9Cq9WDK0FDsU2ozS9l1y0ZdTixBCiKuFJDOiTskqMPLvRTswKxjdKYob2keWXjz5F2z8SDtuMRza3WKfIIUQQtQpcjeTqFOm/LiXUxn5NKjnxZQRrUsvFOXBvBtKn4e1sn1wQggh6iRJZkSdsXJPCou3ncRFB/93a3t83C/qOEw7CMY87bjfZIjsZJ8ghRBC1DkyzCTqhHM5hUz+bhcA9/VpTOeYeqUXzabS3bBjekG/SXaIUAghRF0lyYywO6UUL36/m7ScImLDfPj3wNjSi5kn4eO+kJemPQ9pYZ8ghRBC1FkyzCTs7se/T7NsdwquLjreuaUDHoaL7k46vLo0kdG7QYth9glSCCFEnSU9M8KuzmQVWFb5fezaZrSp729d4Ox+7bHrfTB4Khg8bByhEEKIuk6SGWE3SikmLd5JZr6RtvX9ebh/k5ILsHoKnNoGZ7REh4h2ksgIIYQolyQzwm6+2XqStQfO4ubqwju3tMegvzDqee4w/P5/1oWjuto+QCGEEA6h0nNmTp8+zdNPP01WVlaZa5mZmTzzzDOcOXOmRoMTzis1q4CpP2ur+T45KJZmYb4XXbywym9QUxj1GdyzEkJb2iFKIYQQjqDSycw777xDVlYWfn5+Za75+/uTnZ3NO++8U6PBCef18g97yCoopm19f/51zUV7K6Unws9PasfRPaDdGGjQ3S4xCiGEcAyVTmaWL1/OXXfdVeH1u+66i59//rlGghLObdmuZJbv0e5een10O1z1F30Nv3uo9O6lsNblVyCEEEJcpNLJzLFjx2jQoEGF16OiokhMTKyJmIQTy8wz8tKFu5ce6teEVpEX9fSZzXB6u3bcuD90GGuHCIUQQjiaSicznp6e/5isJCYm4unpWRMxCSc29Ze9pOUU0iTEm0evbVp6wVgAx/+A4nzQu8Mdi8Ez0H6BCiGEcBiVTma6d+/OF198UeH1zz//nG7dutVIUMI5/XboLN9sPYlOB2/c3A531wuL45mM8FF3mHe99jwkFlz0FVckhBBCXKTSt2Y//fTTDBo0CH9/f5555hnCwsIAOHPmDG+88QZz585l5cqVtRaocGx5RcU8v0Tbe2l8XEPrvZfOHdYm/gJ4BEDnCbYOTwghhAOrdM9M//79+fDDD/nggw+IjIwkMDCQevXqERkZyYcffsj777/PtddeW+1AZsyYgU6nY+LEiZZzSini4+OJjIzE09OTfv36sWfPnmq/h7CfmasOcTI9n/oBnjwzpLn1xZJVfut3geeOQ9d/2T5AIYQQDqtKi+Y98MADXH/99Xz99dccPnwYpRSxsbHcfPPNREVFVTuILVu28Mknn9CuXTur82+88QbvvPMOc+fOJTY2lqlTpzJo0CAOHDiAr69vBbWJumZfchazfz8GwNSb2uDtftHX7tAq+GaCdiybSAohhKiGKq8AXL9+ff7973/XWAA5OTncfvvtfPrpp0ydOtVyXinFzJkzeeGFFxg1ahQA8+bNIywsjAULFvDAAw/UWAyi9pjN2o7YJrNiaJtw+rcItS6wZlrpcVQX2wYnhBDCKdh91+xHHnmE4cOHM3DgQKvzx44dIyUlhcGDB1vOubu707dvXzZs2GDrMEU1ff1XEluPp+PtpuflG1pZXzSbS4eYrnsNOt5p+wCFEEI4PLvuzbRw4UK2bdvGli1bylxLSUkBsEw0LhEWFsbx48crrLOwsJDCwkLL85LtF4xGI0ajsSbCtiipr6brrSuutH3ncouYsWwfAE8MaEqwl2tpXcWFuPzxDnpjHkrvTnHHu8GswGy736Wzf37g/G2U9jk+Z2+jtO/K664MuyUzSUlJPPHEE6xcuRIPj4p3Q9bpdFbPlVJlzl1sxowZTJkypcz5lStX4uXlVf2A/0FCQkKt1FtXVLd9Xx52ITPfhfpeiuD0PSxdWjp5OyZtDR2S5gCQ6RbBuuUraiTW6nD2zw+cv43SPsfn7G2U9lVdXl5epcvqlFKqxiOohO+//56RI0ei15euJ2IymdDpdLi4uHDgwAGaNm3Ktm3b6Nixo6XMiBEjCAgIYN68eeXWW17PTHR0NGlpaeXuK3UljEYjCQkJDBo0CIPBUKN11wVX0r5Nx85zx//+QqeDr+/rRofoAKvr+l/+jcsObd2i4jt/QjWIq6mwK83ZPz9w/jZK+xyfs7dR2ld9WVlZBAcHk5mZedm/33brmRkwYAC7du2yOnf33XfTokULJk2aROPGjQkPDychIcGSzBQVFbFu3Tpef/31Cut1d3fH3d29zHmDwVBrX6TarLsuqGr7iorNxP+szYUZ260BXRuHlF5UCjJOQOpu7fno2bg26VOT4VaZs39+4PxtlPY5Pmdvo7SvenVWVpWTmcDAwHKHeXQ6HR4eHjRt2pQJEyZw9913/2M9vr6+tGnTxuqct7c3QUFBlvMTJ05k+vTpNGvWjGbNmjF9+nS8vLwYN25cVcMWNjT792McTs0hyNuNSUMuud169X/g94t2Vw9tadvghBBCOJ0qJzMvv/wy06ZNY+jQoXTr1g2lFFu2bGH58uU88sgjHDt2jIceeoji4mLuu+++Kwru2WefJT8/n4cffpj09HS6d+/OypUrZY2ZOuxMVgHv/3oIgOeHtcTf65LM+vCFcVWDNzToLmvLCCGEuGJVTmZ+//13pk6dyoMPPmh1/uOPP2blypUsXryYdu3a8d5771U5mVm7dq3Vc51OR3x8PPHx8VUNU9jJa8v2k1dkomODAEZ1rG990WyCswe144d+h3qNbR+gEEIIp1PldWZWrFhRZk0Y0ObArFih3ZEybNgwjh49euXRCYfyV+J5vtt+Cp0OptzYGheXS4YjV08BUyG4ekJAQ7vEKIQQwvlUOZmpV68eP/30U5nzP/30E/XqaZsH5ubmylDQVcZkVsT/pN16fWuXaNpFBZQttHuJ9livMbjYfb1GIYQQTqLKw0wvvfQSDz30EGvWrKFbt27odDo2b97M0qVL+e9//wto95v37du3xoMVddfXfyWx+1QWvh6uPH3pRpIAhdmQmaQd3/GtbYMTQgjh1KqczNx33320atWKDz74gCVLlqCUokWLFqxbt46ePXsC8NRTT9V4oKLuyswz8uaKAwD8e2AswT6X3BpfmAPLn9eOfcLAL9LGEQohhHBm1VpnplevXvTq1aumYxEO6v9WHeR8bhHNQn24My6mbIHNH8N2bYE8QluVvS6EEEJcgWpNXDhy5Agvvvgi48aNIzU1FYDly5ezZ8+ey7xSOJsDKdl8sVHbK+uVG1pj0JfzlTq9vfR4YLxtAhNCCHHVqHIys27dOtq2bcumTZtYvHgxOTk5AOzcuZNXXnmlxgMUddvUX/ZiMiuGtA7jmmbB1heVgnNHIOXCar93fg+RHWwdohBCCCdX5WTmueeeY+rUqSQkJODm5mY5379/f/78888aDU7UbWsPpPLboTQMeh2Th5Wzku9PT8D7nSD9mPZchpiEEELUgionM7t27WLkyJFlzoeEhHDu3LkaCUrUfcUmM9OX7gNgfFxDYoK8yxY6vFp7dPeDNqPBJ9SGEQohhLhaVHkCcEBAAMnJyTRq1Mjq/Pbt26lfv34FrxLO5putJzl4JocALwOPXdusbIGCTMg6qR1P3AWeATaNTwghxNWjyj0z48aNY9KkSaSkpKDT6TCbzfzxxx88/fTT3HXXXbURo6hjcgqLeXulti3B49c2K7v/0i9Pw6wLd7v5RkoiI4QQolZVOZmZNm0aDRo0oH79+uTk5NCqVSv69OlDz549efHFF2sjRlHHfLLuCGk5hTQM8uKOHpfcip1zFrZ8WrpAXsNrbB+gEEKIq0qVh5kMBgNffvkl//nPf9i+fTtms5mOHTvSrFk5Qw3C6SRn5vPJb9q+W88NbYGb6yX5cOpe7dE/GsbMhfB2tg1QCCHEVadai+YBNGnShCZNmtRkLMIBvLXiIAVGM10bBjKkdbj1xbMHYeE47Ti8HUR1sX2AQgghrjqVSmaefPLJSlf4zjvvVDsYUbftPpXJku3apN4XhrdCp7tkV+yVL0CRtu4QEdIjI4QQwjYqlcxs377d6vnWrVsxmUw0b65tKHjw4EH0ej2dO3eu+QhFnfH68v0oBTe2j6RDdEDZAsk7tcfmw6D7AzaNTQghxNWrUsnMmjVrLMfvvPMOvr6+zJs3j8DAQADS09O5++676d27d+1EKexuw+E0ywJ5z1y6K7ZSkPgb5KRoz0d+DB5+tg9SCCHEVanKdzO9/fbbzJgxw5LIAAQGBjJ16lTefvvtGg1O1A1KKV6/sCv2uG4NiK7nZV3g0EqYd4N27B8tiYwQQgibqnIyk5WVxZkzZ8qcT01NJTs7u0aCEnXLqn1n+TspAy83PY+Wt0De8Q2lx32esV1gQgghBNVIZkaOHMndd9/Nt99+y8mTJzl58iTffvst9957L6NGjaqNGIUdmRW8veoQAPde04gQX/eyhc7u1x6HvQWdx9swOiGEEKIat2b/97//5emnn+aOO+7AaDRqlbi6cu+99/Lmm2/WeIDCvrac1XHkbC4BXgbu69PY+qJSsOR+OLhcex7SwvYBCiGEuOpVOZnx8vLio48+4s033+TIkSMopWjatCne3uVsNCgcWmGxmWVJWufdw/2a4OdxybYFaYdg19fasbuf3I4thBDCLqq9aJ63tzft2skfL2f21ZYk0ot0hPm5c1dcw7IFSlb7RQePbQMPf1uGJ4QQQgDVmDMjrg45hcV8tFbbtuDx/k3wMOitCygFy5/XjjvcDj4hNo5QCCGE0EgyI8o1+7djpOcZCfVQjOoYWbbAqW2QfVo7jmhv2+CEEEKIi0gyI8rIzDPy2YXNJIdFm3HVl/M1SdlZetzxDhtFJoQQQpQlyYwoY/bvR8kuLKZ5mA/tg1TZAvnpsHGWdtzzMXDzKltGCCGEsBFJZoSVjLwi/vdHIgCP9W+Ci66cQvNuhDRtRWBCWtosNiGEEKI8kswIK5/9doycwmJaRvgxqGVo2QIFWaVDTPW7QIvhtg1QCCGEuES1b80Wzic9t4g5fxwDYOLAZriU1y1z9kKPjE843LfahtEJIYQQ5ZOeGWHx6W9HyS0y0TrSj8GtwsoW2PsDzB6oHYfK8JIQQoi6QZIZAcD53CLmbkgEYOLAWHS6cnpldn5dehx7nW0CE0IIIS5DhpkEAB+vP0JekYm29f0ZWN5cGSjdUHL0bGh7s+2CE0IIIf6BJDOCtJxCPt9wHNDmypTplTGbYO07cO6w9rzhNTaOUAghhKiYDDMJPl1/lHyjifZR/lzbomyvjO7Ialg7XXviHQo+5cynEUIIIexEkpmrXHpuEV9sLOmVKX+ujO7M7tInt86H8ubTCCGEEHYiycxVbs4fx8grMtGmvh/9mpfdLNLNmIXLlo+1JwPjoUF32wYohBBCXIbMmbmKZRcYLXcwPdKvadleGaXoezAeXdE57bms9iuEEKIOkp6Zq9j8jSfIKiimSYg3Q1qHly2QdQqvojTtOHYoNO5n0/iEEEKIypCematUgdHE7N+1nbEf7te03NV+dWf3AaBCWqIbt9Cm8QkhhBCVJT0zV6mFm0+QllNEVKAnN3aILFvAZMR10VgAVEgLG0cnhBBCVJ5dk5lZs2bRrl07/Pz88PPzIy4ujmXLllmuT5gwAZ1OZ/XTo0cPO0bsHIqKzXy8XuuVebBvEwz6cr4GZ/ZYDs3NBtsqNCGEEKLK7DrMFBUVxWuvvUbTpk0BmDdvHiNGjGD79u20bt0agOuuu445c+ZYXuPm5maXWJ3Jd9tPkpxZQKivOzd3jiq/UKo2xJTp2QCvNmNsGJ0QQghRNXZNZm644Qar59OmTWPWrFls3LjRksy4u7sTHl7O5FRRLcUmM7PWHgHgvt6N8TDoyxY6vBq+fxCAc96xeNkyQCGEEKKK6swEYJPJxDfffENubi5xcXGW82vXriU0NJSAgAD69u3LtGnTCA2tYO8goLCwkMLCQsvzrKwsAIxGI0ajsUZjLqmvpuutTT/vTCbxXB4BngbGdIooN3bXFZMpmQ6c7t2EcAdqX1U44udXVc7eRmmf43P2Nkr7rrzuytAppVSNR1AFu3btIi4ujoKCAnx8fFiwYAHDhg0DYNGiRfj4+BATE8OxY8d46aWXKC4uZuvWrbi7u5dbX3x8PFOmTClzfsGCBXh5Xd19DErBGzv1nM7TMSzaxJCosh+9zlzM9X/fhwsmdtcfy9GQwShdOb03QgghRC3Ky8tj3LhxZGZm4ufn949l7Z7MFBUVceLECTIyMli8eDGfffYZ69ato1WrVmXKJicnExMTw8KFCxk1alS59ZXXMxMdHU1aWtplfxlVZTQaSUhIYNCgQRgMhhqtuzb8diiNez7fhpebnvVP98Hfs2zMuuN/4Dp/BMrNh/wnDpKwapXDtK+qHO3zqw5nb6O0z/E5exulfdWXlZVFcHBwpZIZuw8zubm5WSYAd+nShS1btvDuu+/y8ccflykbERFBTEwMhw4dqrA+d3f3cnttDAZDrX2RarPumjT7ws7Yt3VtQLBfBb1Ui8YBoAtpjuHCZGtHaV91OXv7wPnbKO1zfM7eRmlf9eqsrDq3zoxSyqpn5WLnzp0jKSmJiIgIG0fl+HafyuSPw+fQu+i455qG5RfKOw/GXO242wM2i00IIYS4EnbtmZk8eTJDhw4lOjqa7OxsFi5cyNq1a1m+fDk5OTnEx8czevRoIiIiSExMZPLkyQQHBzNy5Eh7hu2QPv1NW1dmeNsIogIr6JU5u1979I+G9reCk05YE0II4VzsmsycOXOGO++8k+TkZPz9/WnXrh3Lly9n0KBB5Ofns2vXLj7//HMyMjKIiIigf//+LFq0CF9fX3uG7XBOpufx885kAO7v07hsgcIcmD3IsrYMobKhpBBCCMdh12Rm9uzZFV7z9PRkxYoVNozGef3v90RMZkWvpkG0qe9ftkDSJkjdW/o89jrbBSeEEEJcIbtPABa1KzPPyMItJwC4v0+T8guVDC/FXgc3zQKvejaKTgghhLhydW4CsKhZ8zcdJ6/IRItwX/o0Cy6/UEmvTER7SWSEEEI4HElmnFhhsYm5GxIBba6MTqcrv2DqhZ4ZmSsjhBDCAUky48S+336Ks9mFhPt5cEP7yPILKVU6zBQiyYwQQgjHI3NmnJRSik9/OwbAPdc0xKAvJ281GWHTx1CUAy4GCKpgTo0QQghRh0nPjJP67VAah1Nz8HF35bZuDcovtHMRrHxBOw6OBb3zrk4phBDCeUky46Tm/KH1ytzcOQo/jwqSlJN/lR4P/o8NohJCCCFqniQzTujo2RzWHDiLTgcTejYsv1BxERxdqx2P+gyaDrRVeEIIIUSNkjkzTmjehTuYrm0eSsNg77IFivLgw26QmaQ9D21hu+CEEEKIGiY9M04mq8DIt1tPAnB3r0blF0rZWZrIRHWFEElmhBBCOC7pmXEyX29JIrfIRGyYD72aBpVfqORW7KYD4Y7FtgtOCCGEqAXSM+NETGZlWSRvQs9G5S+SZzLCT09ox9IjI4QQwglIMuNEVu07w8n0fAK8DIzsWL/8QkfWlB5HdrRNYEIIIUQtkmTGiZTcjj22WwM83fTlF0rdoz26+0PrkTaKTAghhKg9ksw4iX3JWWw8eh69i447e8SUXyjtEKyK1457PQ4uFSQ8QgghhAORZMZJlPTKXNcmnMgAz7IFlILPR5Q+D2tto8iEEEKI2iXJjBNIzy3ihx2nAbinV8PyC2WnQNYp7bjTeFkkTwghhNOQW7OdwLdbT1JYbKZ1pB+dGgSWXyhll/YYHAs3vme74IQQQohaJj0zDs5sVszfdByAO3vEVHw79oIx2nFoSxtGJ4QQQtQ+SWYc3G+H0zh+Lg9fD1du7BBZfqG0g6XHbcfYJjAhhBDCRiSZcXBf/Kn1yozuFIWXWwWjhqn7tMfoHtDyBhtFJoQQQtiGJDMO7FRGPr/uPwPAHRXdjm0ywuJ7tWMZYhJCCOGEJJlxYF9tOoFZQc8mQTQN9Sm/0ImNpccxPW0TmBBCCGFDksw4qKJiMwu3nACoeJE8KN1U0icc2txsg8iEEEII25JkxkEt35NCWk4Rob7uDGwVVn6hc0dgxQvacYex4CIftxBCCOcjf90c1PyN2sTfsd0aYNBX8DF+NRZMhdpxaCsbRSaEEELYliQzDuhASjabj2n7MI3t1qD8QgVZkHZAO24zGlpcb7sAhRBCCBuSFYAdUEmvzOBWYYT7e5RfqGTir0843Pw/G0UmhBBC2J70zDiY3MJivtuu7bFU4e3Y2z6XFX+FEEJcNSSZcTA/7zxNTmExjYK96dkkqPxCB5aVHre/zTaBCSGEEHYiw0wOZuGWJABu7Rpd/j5MAKl7tcfxP0GjPjaKTAghhLAP6ZlxIAdSstl+IgNXFx2jO0WVX2j3YkhP1I7lDiYhhBBXAUlmHMhXm7VF8ga2DCPE1738Qps+1h71buAdbKPIhBBCCPuRZMZBFBhNlom/t3aLLr+QUpB6YcXfOxbbKDIhhBDCviSZcRAr9qSQmW+kfoAnfZqFlF/o0EoozASdHqK72zZAIYQQwk4kmXEQCzdrE3/HdIlC71LBxN+lT2uPAdHgWsEwlBBCCOFkJJlxAIlpufx59Bw6HYzpUsEQU3EhZGrDUAx61XbBCSGEEHYmyYwDWPSX1ivTNzaE+gGe5Rc6ewCUCdz9oeUNNoxOCCGEsC9JZuo4o8nMN3+dBOC2rhX0ygDMGao9hraAitafEUIIIZyQJDN13K/7U0nLKSTYx40BLcPKL5R3HopytOPWo2wXnBBCCFEHSDJTxy28sLbM6M5RGPQVfFyp+7THgAbQ40EbRSaEEELUDXZNZmbNmkW7du3w8/PDz8+PuLg4li0r3VdIKUV8fDyRkZF4enrSr18/9uzZY8eIbSsls4B1B88CcFvXBuUXOvIrzB2mHYfIppJCCCGuPnZNZqKionjttdf466+/+Ouvv7j22msZMWKEJWF54403eOedd/jggw/YsmUL4eHhDBo0iOzsbHuGbTNLtp/ErKBbw3o0CvYuv9CfH5Yex8TZJjAhhBCiDrFrMnPDDTcwbNgwYmNjiY2NZdq0afj4+LBx40aUUsycOZMXXniBUaNG0aZNG+bNm0deXh4LFiywZ9g2oZTi263axN+bO1ewDxOUDjENnAI9H7dBZEIIIUTdUmd2zTaZTHzzzTfk5uYSFxfHsWPHSElJYfDgwZYy7u7u9O3blw0bNvDAAw+UW09hYSGFhYWW51lZWQAYjUaMRmONxlxSX03XC7A9KYOjZ3PxNLgwqGVwue+hO/UXrlna2jLG9neAyaz91JDabF9d4OztA+dvo7TP8Tl7G6V9V153ZeiUUqrGI6iCXbt2ERcXR0FBAT4+PixYsIBhw4axYcMGevXqxalTp4iMjLSUv//++zl+/DgrVqwot774+HimTJlS5vyCBQvw8vKqtXbUtK+PuvDHGRe6Bpu5o1n5CUrf/S8RkH+cQr0Py9t9ZOMIhRBCiNqTl5fHuHHjyMzMxM/P7x/L2r1npnnz5uzYsYOMjAwWL17M+PHjWbduneW67pI1U5RSZc5d7Pnnn+fJJ5+0PM/KyiI6OprBgwdf9pdRVUajkYSEBAYNGoTBYKixeguNJl58Yx1QzKPXd6Vnk6CyhZQZ190PAaAf8h+GdRxWY+9forbaV1c4e/vA+dso7XN8zt5GaV/1lYysVIbdkxk3NzeaNm0KQJcuXdiyZQvvvvsukyZNAiAlJYWIiAhL+dTUVMLCKlhvBW0oyt297L5EBoOh1r5INV338r1nyS4oJtLfg96xYbiUtxfTmb1gzAW9G66dx4O+9j7K2vzd1QXO3j5w/jZK+xyfs7dR2le9Oiurzq0zo5SisLCQRo0aER4eTkJCguVaUVER69ato2fPnnaMsPYt3qZN/B3dOar8RAbg8xHaY3DzWk1khBBCiLrOrn8FJ0+ezNChQ4mOjiY7O5uFCxeydu1ali9fjk6nY+LEiUyfPp1mzZrRrFkzpk+fjpeXF+PGjbNn2LXqTFYB6y+sLTOqUwV3MRXlQq5Who632ygyIYQQom6yazJz5swZ7rzzTpKTk/H396ddu3YsX76cQYMGAfDss8+Sn5/Pww8/THp6Ot27d2flypX4+vraM+xa9d32U5gVdIkJrHhtmbP7AQXeodDjIZvGJ4QQQtQ1dk1mZs+e/Y/XdTod8fHxxMfH2yYgO6vU2jIHV8CCW7TjUFnxVwghhKhzc2auZjtPZnI4NQcPgwvD2kWUX2j7F6XHTa61TWBCCCFEHSYzR+uQkl6ZIa3D8fOoYBb32QPa4/UzocvdtglMCCGEqMOkZ6aOKCw28ePfp4F/GGJK3QdpB7Xj2CE2ikwIIYSo2ySZqSPW7E8lM99IuJ8HPZsEl19o6TPao94NfCsYhhJCCCGuMpLM1BHfb9d6ZUZ0iERf0doyJUNM/SfDP6yCLIQQQlxNJJmpAzLzjfy6PxWAER3qV1DoJORqZeh2v40iE0IIIeo+SWbqgOW7kykymYkN86FlRAVr6HwxUnsMiAG3CtafEUIIIa5CkszUAaVDTPXL30TTVAzpidpxu1tsF5gQQgjhACSZsbOUzAI2HjsHaPNlynX+KJiKwOAF/SbbMDohhBCi7pNkxs5+/PsUSkHXhoFEBXqVLXB0HXzYVTsOaQEu8pEJIYQQF5O/jHZ28RBTuf5eWHrcdKANIhJCCCEci6wAbEeHzmSzNzkLVxcdw9pWsG5M6l7tcfBUiHvUdsEJIYQQDkJ6Zuzohx1ar0zf2BDqebuVLZC8E5J3aMexQ2VtGSGEEKIckszYiVKKH/4+BcCIjhUMMf06tfS4XiMbRCWEEEI4Hklm7GTbiXSSzufj7aZnUMuw8gud3a89DnoVXPS2C04IIYRwIJLM2EnJxN8hrcPxdCsnUUn+GzKOa8cdxtkwMiGEEMKxSDJjB0aTmV92JQMVDDEl/gEf99GOvYLBu4KNJ4UQQgghyYw9/H4ojfO5RQT7uNGrSVDZAom/lR73fsp2gQkhhBAOSJIZO/h5p9YrM7xtBK76cj6C1H3a4+CpEPewDSMTQgghHI8kMzZWWGxi5d4UAIa3K2f7gqTNsPd77Ti0pe0CE0IIIRyUJDM29tvBNLILignzc6dLTGDZAru+KT2u39l2gQkhhBAOSpIZG/t5p3YX07C2Ebi4lLMIXskQ09A3wbOcZEcIIYQQViSZsaECo4mEvWcAuL68IaazB0sn/0Z1sWFkQgghhOOSZMaG1h44S26RifoBnnRqEFC2wPo3S49DmtssLiGEEMKRSTJjQ6VDTOHoyttnqWRTyd5PgZu3DSMTQgghHJckMzaSX2Ri9b5UoIIhpqPr4Mxu7bjTXTaMTAghhHBskszYyK/7U8k3moiu50m7KH/riyc2wuc3ascGb/BvYPsAhRBCCAclyYyN/LJLG2Ia3jay7BBT0ubS4+umg4t8LEIIIURlyV9NG8gtLObX/SVDTBFlCyT/rT32fwE6T7BdYEIIIYQTkGTGBlbvT6XAaKZhkBetI/2sL57YBLu/1Y5DW9k+OCGEEMLBSTJjAz//rQ0xXd+unCGmA0tLj2N62jAqIYQQwjlIMlPLsguMrD14FoDh5Q0xnT2gPV73OnjVs2FkQgghhHOQZKaWrd6XSlGxmSYh3rQI97W++Md7cHCZdhwmQ0xCCCFEdUgyU8uW79Z2yB7WNsJ6iCntECS8pB27GCCsjR2iE0IIIRyfJDO1KK+omLUHtbuYhrQOt75YskAewF0/yBCTEEIIUU2SzNSi9QfPUmA0E13P0/ouppxUWDNdO+54BzTsZZ8AhRBCCCcgyUwtKhliuq71JXsxfXsPpB3UjuV2bCGEEOKKSDJTSwqLS/diuq7NRUNMZhOc3KIdR7SHdrfaITohhBDCebjaOwBnteHIObILiwn1dadjdGDphbSDUFwArh5w3xpw0dsvSCGEEMIJSM9MLVlxYYhpSOtwXFwuDDEdXAEf9dCOg2MlkRFCCCFqgF2TmRkzZtC1a1d8fX0JDQ3lpptu4sCBA1ZlJkyYgE6ns/rp0aOHnSKunGKTmZV7zwCXDDHt+6n0uO3NNo5KCCGEcE52TWbWrVvHI488wsaNG0lISKC4uJjBgweTm5trVe66664jOTnZ8rN06dIKaqwbtiSmcz63iAAvA90bXXTLdeo+7XHUp9DrCfsEJ4QQQjgZu86ZWb58udXzOXPmEBoaytatW+nTp4/lvLu7O+Hh4Ze+vM5asUcbYhrUMgxX/YV8MWkznPpLOw5vZ6fIhBBCCOdTpyYAZ2ZmAlCvnvUCcmvXriU0NJSAgAD69u3LtGnTCA0NLbeOwsJCCgsLLc+zsrIAMBqNGI3GGo23pL6L6zWbFct2JwMwsGWI5Zr+95mWbjCjXwOo4VhqQ3ntcybO3j5w/jZK+xyfs7dR2nfldVeGTimlajyCalBKMWLECNLT0/ntt98s5xctWoSPjw8xMTEcO3aMl156ieLiYrZu3Yq7u3uZeuLj45kyZUqZ8wsWLMDLy6tW2wCQmA3/t9sVd71iWhcThgsZzIC9z+JTmMKO6Ls5Hty/1uMQQgghHFleXh7jxo0jMzMTPz+/fyxbZ5KZRx55hF9++YXff/+dqKioCsslJycTExPDwoULGTVqVJnr5fXMREdHk5aWdtlfRlUZjUYSEhIYNGgQBoMBgNdXHOSz3xMZ3jacmbe0g6zT6E78gf7HR9ApM8bHd4FvObtn10Hltc+ZOHv7wPnbKO1zfM7eRmlf9WVlZREcHFypZKZODDM99thj/Pjjj6xfv/4fExmAiIgIYmJiOHToULnX3d3dy+2xMRgMtfZFKqlbKUXChYXyhrWN1N5v0VhI3aMV9AjAEBgNF68G7ABq83dXFzh7+8D52yjtc3zO3kZpX/XqrCy7JjNKKR577DG+++471q5dS6NGjS77mnPnzpGUlERERN3r3difks3xc3m4u7rQr3kIFGaXJjKN+2ur/TpYIiOEEELUdXZNZh555BEWLFjADz/8gK+vLykp2l1A/v7+eHp6kpOTQ3x8PKNHjyYiIoLExEQmT55McHAwI0eOtGfo5Sq5i6l3sxC8DTpI3KZd8AmDu763X2BCCCGEE7NrMjNr1iwA+vXrZ3V+zpw5TJgwAb1ez65du/j888/JyMggIiKC/v37s2jRInx9fe0Q8T9btU9bKG9oc194vxOkJ2oXQlvaLyghhBDCydl9mOmfeHp6smLFChtFc2WSM/PZfSoLnQ4G+J8uTWRcXKHNaLvGJoQQQjizOjEB2BmsurB9QacGgQRkX5gn02wI3LYA9PJrFkIIIWqL/JWtIXt2bmGu4X2aF+jg97PaybDWksgIIYQQtUz+0taA7IJiWp/8mn76vyHzogvR3e0WkxBCCHG1kGSmBvx+OI1muiQAVI+H0TWIA68giOlp58iEEEII5yfJTHUlbcHl6HqantnPkaTfaaU7DoCu3a0Q2cG+sQkhhBBXEUlmqivxN/Rr/kNroDWADswuBlxCmts5MCGEEOLqIslMdYW1xtxuHHuPJrE3wwU3VxduGHE7GDztHZkQQghxVZFkprpih2BqdC1vfbSctcUujG4XxU3t29s7KiGEEOKq42LvAByZUord57W9lga1CrVzNEIIIcTVSZKZK3D4bC5phToMeh29m4XYOxwhhBDiqiTJzBVYvS8VgJ6Ng/B2lxE7IYQQwh4kmbkCqw9oK/0OaCm9MkIIIYS9SDJTTanZBfx9Ulvut39zSWaEEEIIe5FkpprW7E9FKYj2VoT7edg7HCGEEOKqJclMNaXlFOFpcKFtPbO9QxFCCCGuapLMVNMj/Zuy+fn+9AlX9g5FCCGEuKpJMnMFPAx6POUmJiGEEMKuJJkRQgghhEOTZEYIIYQQDk2SGSGEEEI4NElmhBBCCOHQJJkRQgghhEOTZEYIIYQQDk2SGSGEEEI4NElmhBBCCOHQJJkRQgghhEOTZEYIIYQQDk2SGSGEEEI4NElmhBBCCOHQJJkRQgghhENz+j2flVIAZGVl1XjdRqORvLw8srKyMBgMNV6/vUn7HJ+zt1Ha5/icvY3Svuor+btd8nf8nzh9MpOdnQ1AdHS0nSMRQgghRFVlZ2fj7+//j2V0qjIpjwMzm82cPn0aX19fdDpdjdadlZVFdHQ0SUlJ+Pn51WjddYG0z/E5exulfY7P2dso7as+pRTZ2dlERkbi4vLPs2KcvmfGxcWFqKioWn0PPz8/p/ySlpD2OT5nb6O0z/E5exulfdVzuR6ZEjIBWAghhBAOTZIZIYQQQjg0SWaugLu7O6+88gru7u72DqVWSPscn7O3Udrn+Jy9jdI+23D6CcBCCCGEcG7SMyOEEEIIhybJjBBCCCEcmiQzQgghhHBokswIIYQQwqFJMlNNH330EY0aNcLDw4POnTvz22+/2TukSlm/fj033HADkZGR6HQ6vv/+e6vrSini4+OJjIzE09OTfv36sWfPHqsyhYWFPPbYYwQHB+Pt7c2NN97IyZMnbdiKis2YMYOuXbvi6+tLaGgoN910EwcOHLAq48htnDVrFu3atbMsUBUXF8eyZcss1x25beWZMWMGOp2OiRMnWs45ehvj4+PR6XRWP+Hh4Zbrjt4+gFOnTnHHHXcQFBSEl5cXHTp0YOvWrZbrjt7Ghg0blvkMdTodjzzyCOD47SsuLubFF1+kUaNGeHp60rhxY/7zn/9gNpstZepcG5WosoULFyqDwaA+/fRTtXfvXvXEE08ob29vdfz4cXuHdllLly5VL7zwglq8eLEC1HfffWd1/bXXXlO+vr5q8eLFateuXerWW29VERERKisry1LmwQcfVPXr11cJCQlq27Ztqn///qp9+/aquLjYxq0pa8iQIWrOnDlq9+7daseOHWr48OGqQYMGKicnx1LGkdv4448/ql9++UUdOHBAHThwQE2ePFkZDAa1e/dupZRjt+1SmzdvVg0bNlTt2rVTTzzxhOW8o7fxlVdeUa1bt1bJycmWn9TUVMt1R2/f+fPnVUxMjJowYYLatGmTOnbsmFq1apU6fPiwpYyjtzE1NdXq80tISFCAWrNmjVLK8ds3depUFRQUpH7++Wd17Ngx9c033ygfHx81c+ZMS5m61kZJZqqhW7du6sEHH7Q616JFC/Xcc8/ZKaLquTSZMZvNKjw8XL322muWcwUFBcrf31/997//VUoplZGRoQwGg1q4cKGlzKlTp5SLi4tavny5zWKvrNTUVAWodevWKaWcs42BgYHqs88+c6q2ZWdnq2bNmqmEhATVt29fSzLjDG185ZVXVPv27cu95gztmzRpkrrmmmsqvO4MbbzUE088oZo0aaLMZrNTtG/48OHqnnvusTo3atQodccddyil6uZnKMNMVVRUVMTWrVsZPHiw1fnBgwezYcMGO0VVM44dO0ZKSopV29zd3enbt6+lbVu3bsVoNFqViYyMpE2bNnWy/ZmZmQDUq1cPcK42mkwmFi5cSG5uLnFxcU7VtkceeYThw4czcOBAq/PO0sZDhw4RGRlJo0aNuO222zh69CjgHO378ccf6dKlC2PGjCE0NJSOHTvy6aefWq47QxsvVlRUxPz587nnnnvQ6XRO0b5rrrmG1atXc/DgQQD+/vtvfv/9d4YNGwbUzc/Q6TearGlpaWmYTCbCwsKszoeFhZGSkmKnqGpGSfzlte348eOWMm5ubgQGBpYpU9far5TiySef5JprrqFNmzaAc7Rx165dxMXFUVBQgI+PD9999x2tWrWy/APhyG0DWLhwIdu2bWPLli1lrjnD59e9e3c+//xzYmNjOXPmDFOnTqVnz57s2bPHKdp39OhRZs2axZNPPsnkyZPZvHkzjz/+OO7u7tx1111O0caLff/992RkZDBhwgTAOb6jkyZNIjMzkxYtWqDX6zGZTEybNo2xY8cCdbONksxUk06ns3qulCpzzlFVp211sf2PPvooO3fu5Pfffy9zzZHb2Lx5c3bs2EFGRgaLFy9m/PjxrFu3znLdkduWlJTEE088wcqVK/Hw8KiwnCO3cejQoZbjtm3bEhcXR5MmTZg3bx49evQAHLt9ZrOZLl26MH36dAA6duzInj17mDVrFnfddZelnCO38WKzZ89m6NChREZGWp135PYtWrSI+fPns2DBAlq3bs2OHTuYOHEikZGRjB8/3lKuLrVRhpmqKDg4GL1eXyazTE1NLZOlOpqSOyr+qW3h4eEUFRWRnp5eYZm64LHHHuPHH39kzZo1REVFWc47Qxvd3Nxo2rQpXbp0YcaMGbRv3553333XKdq2detWUlNT6dy5M66urri6urJu3Tree+89XF1dLTE6chsv5e3tTdu2bTl06JBTfIYRERG0atXK6lzLli05ceIE4Bz/DZY4fvw4q1at4l//+pflnDO075lnnuG5557jtttuo23bttx55538+9//ZsaMGUDdbKMkM1Xk5uZG586dSUhIsDqfkJBAz5497RRVzWjUqBHh4eFWbSsqKmLdunWWtnXu3BmDwWBVJjk5md27d9eJ9iulePTRR1myZAm//vorjRo1srruDG28lFKKwsJCp2jbgAED2LVrFzt27LD8dOnShdtvv50dO3bQuHFjh2/jpQoLC9m3bx8RERFO8Rn26tWrzHIIBw8eJCYmBnCu/wbnzJlDaGgow4cPt5xzhvbl5eXh4mKdHuj1esut2XWyjTU+pfgqUHJr9uzZs9XevXvVxIkTlbe3t0pMTLR3aJeVnZ2ttm/frrZv364A9c4776jt27dbbit/7bXXlL+/v1qyZInatWuXGjt2bLm320VFRalVq1apbdu2qWuvvbbO3FL40EMPKX9/f7V27VqrWyfz8vIsZRy5jc8//7xav369OnbsmNq5c6eaPHmycnFxUStXrlRKOXbbKnLx3UxKOX4bn3rqKbV27Vp19OhRtXHjRnX99dcrX19fy78fjt6+zZs3K1dXVzVt2jR16NAh9eWXXyovLy81f/58SxlHb6NSSplMJtWgQQM1adKkMtccvX3jx49X9evXt9yavWTJEhUcHKyeffZZS5m61kZJZqrpww8/VDExMcrNzU116tTJcutvXbdmzRoFlPkZP368Ukq75e6VV15R4eHhyt3dXfXp00ft2rXLqo78/Hz16KOPqnr16ilPT091/fXXqxMnTtihNWWV1zZAzZkzx1LGkdt4zz33WL53ISEhasCAAZZERinHbltFLk1mHL2NJetxGAwGFRkZqUaNGqX27Nljue7o7VNKqZ9++km1adNGubu7qxYtWqhPPvnE6roztHHFihUKUAcOHChzzdHbl5WVpZ544gnVoEED5eHhoRo3bqxeeOEFVVhYaClT19qoU0qpmu/vEUIIIYSwDZkzI4QQQgiHJsmMEEIIIRyaJDNCCCGEcGiSzAghhBDCoUkyI4QQQgiHJsmMEEIIIRyaJDNCCCGEcGiSzAghrnpr165Fp9ORkZFh71CEENUgyYwQQgghHJokM0IIIYRwaJLMCCFq3Lfffkvbtm3x9PQkKCiIgQMHkpubC2g7Dbds2RIPDw9atGjBRx99ZPXakydPctttt1GvXj28vb3p0qULmzZtslyfNWsWTZo0wc3NjebNm/PFF19YvV6n0/HZZ58xcuRIvLy8aNasGT/++KNVmaVLlxIbG4unpyf9+/cnMTHR6vrx48e54YYbCAwMxNvbm9atW7N06dIa/A0JIWpUrez4JIS4ap0+fVq5urqqd955x7K794cffqiys7PVJ598oiIiItTixYvV0aNH1eLFi1W9evXU3LlzlVLaru6NGzdWvXv3Vr/99ps6dOiQWrRokdqwYYNSSqklS5Yog8GgPvzwQ3XgwAH19ttvK71er3799VfL+wMqKipKLViwQB06dEg9/vjjysfHR507d04ppdSJEyeUu7u7euKJJ9T+/fvV/PnzVVhYmAJUenq6Ukqp4cOHq0GDBqmdO3eqI0eOqJ9++slhNpMV4mokyYwQokZt3bpVASoxMbHMtejoaLVgwQKrc6+++qqKi4tTSin18ccfK19fX0vicamePXuq++67z+rcmDFj1LBhwyzPAfXiiy9anufk5CidTqeWLVumlFLq+eefVy1btlRms9lSZtKkSVbJTNu2bVV8fHwVWi2EsCcZZhJC1Kj27dszYMAA2rZty5gxY/j0009JT0/n7NmzJCUlce+99+Lj42P5mTp1KkeOHAFgx44ddOzYkXr16pVb9759++jVq5fVuV69erFv3z6rc+3atbMce3t74+vrS2pqqqWOHj16oNPpLGXi4uKsXv/4448zdepUevXqxSuvvMLOnTur/wsRQtQ6SWaEEDVKr9eTkJDAsmXLaNWqFe+//z7Nmzfn6NGjAHz66afs2LHD8rN79242btwIgKen52XrvzgJAVBKlTlnMBjKvMZsNlvKX86//vUvjh49yp133smuXbvo0qUL77///mVfJ4SwD0lmhBA1TqfT0atXL6ZMmcL27dtxc3Pjjz/+oH79+hw9epSmTZta/TRq1AjQelR27NjB+fPny623ZcuW/P7771bnNmzYQMuWLSsdW6tWrSzJU4lLnwNER0fz4IMPsmTJEp566ik+/fTTSr+HEMK2XO0dgBDCuWzatInVq1czePBgQkND2bRpE2fPnqVly5bEx8fz+OOP4+fnx9ChQyksLOSvv/4iPT2dJ598krFjxzJ9+nRuuukmZsyYQUREBNu3bycyMpK4uDieeeYZbrnlFjp16sSAAQP46aefWLJkCatWrap0fA8++CBvv/02Tz75JA888ABbt25l7ty5VmUmTpzI0KFDiY2NJT09nV9//bVKCZMQwsbsPWlHCOFc9u7dq4YMGaJCQkKUu7u7io2NVe+//77l+pdffqk6dOig3NzcVGBgoOrTp49asmSJ5XpiYqIaPXq08vPzU15eXqpLly5q06ZNlusfffSRaty4sTIYDCo2NlZ9/vnnVu8PqO+++87qnL+/v5ozZ47l+U8//aSaNm2q3N3dVe/evdX//vc/qwnAjz76qGrSpIlyd3dXISEh6s4771RpaWk190sSQtQonVKVGEAWQgghhKijZM6MEEIIIRyaJDNCCCGEcGiSzAghhBDCoUkyI4QQQgiHJsmMEEIIIRyaJDNCCCGEcGiSzAghhBDCoUkyI4QQQgiHJsmMEEIIIRyaJDNCCCGEcGiSzAghhBDCoUkyI4QQQgiH9v8s/j/BG3oWXAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# estimate parameter values\n",
    "T_amb = 23\n",
    "x0 = 0\n",
    "K = 0.66\n",
    "tau = 180\n",
    "\n",
    "# known input\n",
    "U1 = 50\n",
    "\n",
    "# compute analytical solution\n",
    "t = data.index\n",
    "x = x0*np.exp(-t/tau) + (1 - np.exp(-t/tau))*K*U1\n",
    "\n",
    "# plotting solution for T1\n",
    "T1 = x + T_amb\n",
    "plt.plot(t, T1, t, data[\"T1\"])\n",
    "plt.legend([\"T1 predicted\", \"T1 measured\"])\n",
    "\n",
    "# dress up the plot\n",
    "plt.title(f\"{x0=}, {K=}, {tau=}\")\n",
    "plt.xlabel(\"seconds\")\n",
    "plt.ylabel(\"deg C\")\n",
    "plt.grid(True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lab Assignment\n",
    "\n",
    "The lab assignment is to conduct a step test of the Temperature Control Lab, and then to fit the results to a first order model of a heater/sensor assembly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{admonition} Task 1.\n",
    "\n",
    "Create a new Jupyter notebook to document the results of your step test and model fitting experiment. \n",
    "\n",
    "* Begin the notebook with an appropriate title, description, and any information that would be required to reproduce the experiment.\n",
    "* Create a cell to read the data you saved from your step test experiment. Plot the data as outlined above.\n",
    "\n",
    "* Inspecting the plot for $T_1$, estimate the\n",
    "    * gain,\n",
    "    * time constant\n",
    "    * ambient temperature\n",
    "    \n",
    "Write your estimates in a clearly labeled markdown cell.\n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{admonition} Task 2.\n",
    "\n",
    "Following the starter code presented above, create a new cell to plot an analytical solution for the step response of a first-order model in gain/time constant form. Use your estimates of gain, time constant, initial condition, and the input. On the same plot, overlay a plot of the experimental data. Adjust parameter values until you get the a good fit of the model to the experimental data.\n",
    "\n",
    "Note that you may need to also adjust values of the ambient temperature and initial condition to fit the model. \n",
    "\n",
    "Report\n",
    "\n",
    "* gain\n",
    "* time constant\n",
    "* ambient temperature\n",
    "* initial condition\n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{admonition} Task 3.\n",
    "\n",
    "A first-order model in gain/time constant form is given by\n",
    "\n",
    "$$\\tau\\frac{dx}{dt} = - x + K u $$\n",
    "\n",
    "Where $x$ is the state variable. Again letting $x = T_1 - T_{amb}$ and $u = u_1$  Comparing this model of a first order system to the model given up for the heater/sensor assembly.\n",
    "\n",
    "* Derive expressions for the parameters $\\tau$ and $K$ in terms of $C_p$, $U_a$, $\\alpha$, and $P_1$. \n",
    "\n",
    "* Assume $\\alpha = 0.16$ milliwatts per unit of $P1$ per percent. Solve for estimates of $C_p$ and $U_a$. \n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{admonition} Task 4. \n",
    "\n",
    "In a new markdown cell, discuss issues you would face in writing a Python function to automatically fit the model of the heater/sensor assembly to step test data. Your discussion should include the following considerations: \n",
    "\n",
    "* How can you measure the quality of fit?\n",
    "* How should one handle bad measurements? \n",
    "* What parameters should be fit?\n",
    "* How can you estimate uncertainty in the estimates of $C_p$ and $U_a$?\n",
    "* Is it possible to estimate $U_a$ from a steady state experiment?\n",
    "* Is is possible to estimate $C_p$ from a steady state experiment?\n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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