{ "cells": [ { "cell_type": "markdown", "metadata": { "nbpages": { "level": 0, "link": "[](https://jckantor.github.io/CBE32338/04.01-Relay-Control.html)", "section": "" } }, "source": [ "\n", "*This notebook contains material from [CBE32338](https://jckantor.github.io/CBE32338);\n", "content is available [on Github](https://github.com/jckantor/CBE32338.git).*\n" ] }, { "cell_type": "markdown", "metadata": { "nbpages": { "level": 0, "link": "[](https://jckantor.github.io/CBE32338/04.01-Relay-Control.html)", "section": "" } }, "source": [ "\n", "< [4.0 Feedback Control](https://jckantor.github.io/CBE32338/04.00-Feedback-Control.html) | [Contents](toc.html) | [4.3 PID Control](https://jckantor.github.io/CBE32338/04.03-PID_Control.html) >
"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 1,
"link": "[4.1 Relay Control](https://jckantor.github.io/CBE32338/04.01-Relay-Control.html#4.1-Relay-Control)",
"section": "4.1 Relay Control"
}
},
"source": [
"# 4.1 Relay Control"
]
},
{
"cell_type": "markdown",
"metadata": {
"nbpages": {
"level": 2,
"link": "[4.1.1 Simple Relay Control](https://jckantor.github.io/CBE32338/04.01-Relay-Control.html#4.1.1-Simple-Relay-Control)",
"section": "4.1.1 Simple Relay Control"
}
},
"source": [
"## 4.1.1 Simple Relay Control\n",
"\n",
"The following code implements relay control for temperature T1 on the Temperature Control Lab.\n",
"\n",
"\\begin{align}\n",
"Q(t) & = \\begin{cases} \n",
" Q^{max} &\\text{if $T \\leq T_{setpoint}$}\\\\\n",
" 0 & \\text{if $T \\geq T_{setpoint}$}\n",
" \\end{cases}\n",
"\\end{align}\n",
"\n",
"This is simple to implement, in fact it is just one line of code in the following cell. Adjust `Tsetpoint` to a desired setpoint value, then run the cell."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"nbpages": {
"level": 2,
"link": "[4.1.1 Simple Relay Control](https://jckantor.github.io/CBE32338/04.01-Relay-Control.html#4.1.1-Simple-Relay-Control)",
"section": "4.1.1 Simple Relay Control"
}
},
"outputs": [
{
"data": {
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OXKT3SQAzmwW8E/i9mWUCSwgS5pfcPdqlUZ6EzMxMysvLyc3tXTMcuDvl5eVk\nZmYmOpSE2HPoCN99cgPRqHPVmWO5cs7YRIckIiIi/VSna5DdfR2wDvi+mQ0ELgKuA24H5rZ2XJhM\nLwMywvM/7O5fN7NfAxcCFeGuH3P3NScbV35+PiUlJezbl1SD2h2SmZlJfn5+osPoUY1R569rd/Lb\nl7ZR2xBl1tjBXH/exESHJSIiIv1Yl1yk5+7VwGPhrT21wGJ3rzKzNOA5M3syfO5f3f3heGJJS0tj\n0qRJ8TQhPaRobxW3L9lE8b5qAC6YNpzPFEwhRWUVIiIikkA9PouFB4W2VeHDtPDWv4tv+5maukYe\nWLGNv67dSdQhLyeDzxRM4eyJwxIdmoiIiAiWiAvDzCwFWAlMBe5w938LSyzOJRhhfgb4qrvXtnDs\njcCNAHl5efMeeuihHotbTk5VVRXZ2dlNtm060Mjjm+upqHXM4JzRqRSMSyUjRaPGPa2l/pHkof5J\nbuqf5Kb+SW6J7J9FixatdPez2tsvrgTZzPKBae7+rJllAKlhuUVHjx8C/AX4PFAO7AbSgZ8Dxe7+\nzbaOnz59um/cuLHT8Uv3KiwspKCgAICDh+v45fItLH0rqA2fnDeQzy+eytQROQmMsH+L7R9JPuqf\n5Kb+SW7qn+SWyP4xsw4lyJ0usTCzTwCfAwYDU4AJwM+AizvahrsfNLNC4FJ3/0G4udbMfgXc0tnY\nJHm4O0s27OWXy7dQVdtAemqEj5wznnefMVa1xiIiIpKU4qlB/gIwH1gB4O5vmdmI9g4yszygPkyO\nswgS6u+Z2Wh332XB3GzvIZghQ3qxA0eifO3RdazdEUxMMmfcEG5eNJVRg/vnVHYiIiLSO8STIB9x\n97qjcw2HdcUdGRIcDdwX7h8BHnL3x81sSZg8G7AG+HQcsUkCNUadR9eU8rM1tWQNrCA7I5VPLZzE\noukjetXc1CIiItI/xZMgP29mXwEyzWwRcDPweHsHuftrwJktbF8cRyySJIr3VfHTZ4Kp2xqiUDA9\nj09eMJnBA9ISHZqIiIhIh8STIH+FYDaJDcAXgb8Dd3dFUNL7HKlv5Pcvb+eR1aXHpm57d34tn7pk\neqJDExERETkpnUqQw/KIe939euDOrg1JepuKw/V89c+vUXKgBjO4cs4Yrl0wgRUvLE90aCIiIiIn\nrVMJsrs3mtloM0tz9/quDkp6j8ao879/30DJgRrGDcviixedwvRRmrpNREREeq94Siw2A8vN7FHg\n2NzH7v6TuKOSpLdpTyV7K2tZte0Ar5VUMGRAGt+8chbDszMSHZqIiIhIXOJJkPcBTwMDwpv0E397\nbRd3LS0+9jgSMf7t0hlKjkVAwOJeAAAgAElEQVRERKRP6HSC7O5f68pApHdYv+sQP1++GYCzJg4l\nIzWFi2aOYNbYwQmOTERERKRrxLOS3tPACetUu/slcUUkSWtLWTX/8+QGolHnyjlj+OTbJic6JBER\nEZEuF0+Jxf+LuZ8JXA3UxheOJKPahkb+8MoO/rSqlGjUmTV2EB87b2KiwxIRERHpFvGUWKxotmmp\nmS2NMx5JMmt3HOSOZ4vYVXEEM7j89NFcf+5EUlMiiQ5NREREpFvEU2IxKOZhBJhHsIy09AGVR+q5\n97mt/HP9HgDGDxvA5xZPZeboQe0cKSIiItK7xVNi8QZBDbIBDcAW4FNdEZQkjruzfFMZv1i+mYOH\n60lNMa45exzvnZtPmkaNRUREpB+IJ0Ge3HyREDOLpz1JsL2HjvCzwmJWbjsAwKyxg7h50VTyh2oW\nPxERkaRUUQKlK8GjkDEIJi2ElLTjz9cdhi3LoKEmcTE2k1v2FlCQ6DDaFE9CuwKY22zbyy1sa8LM\nMoFlQEZ4/ofd/etmNgl4EBgGrAKuc/e6OOKTDopGnb++tpPfvrSNI/VRBmak8PHzJ/H2mSOJRCzR\n4YmIiHRcNAp+wiRbwTaPQiTl+La6w8G23sij8OajsOo+aIwZr8ydAm/7MgyZAHvegOd+CJW7Exdn\nC8YeAfi3RIfRppNOkM1sBEGtcZaZzSYosQAYRMcWDKkFFrt7lZmlAc+Z2ZPAl4Db3P1BM7sLuAG4\n82Tjk5OzeV8Vty8pYtPeKgDOnzqcmxZOZujA9ARHJiIichLcoXgJvHgHp1VUw7RBkD8veG7vhiBR\nPLQT5n8Kxp4Fz/8YdjSfb6CXmvQ2yBoGJa9CeTE88tmmz+dOhZGnJSa2FpRvK2VYooNoR2dGkC8H\nPgHkAz+L2V4JtLt4iLs7UBU+TAtvDiwGPhxuvw+4FSXI3aa2oZEHX97Bn1eVEHXIzU7nMxdOYcHk\n3ESHJiIivdHeDbD6N1BX1f6+3aG2CsqLAMg8Ugl/+1KQFFokGEk9OlK8/IdgFiTUkVRI7cWrwGaP\ngHM/f/wPgfoj8Oq98NZTEG0IXtus98EZ1zQdOU+w0sZCpiU6iHaYt/Q1REcONPuAuz/UyWNTgJXA\nVOAO4PvAS+4+NXx+HPCku89q4dgbgRsB8vLy5j30UKdC6Nc2H2zkr5vrOXDEMeDs0SlcND6NjJSu\nLaeoqqoiOzu7S9uUrqP+SW7qn+TWmf5JaTjM4Io3OTRoOg1pOVi0nqEH1pLacLibouw5mUf2MLzs\nJayTOUVXaUzJoiT/Chqry5m4fxmRaAMAbhH2jljI4QH55Jc8Slp9JfuHncmOce+hIS0noTH3R4n8\n+bZo0aKV7n5We/t1OkEGMLN3AKcRLBQCgLt/5ySOHwL8Bfgv4FfNEuQn3H12W8dPnz7dN27c2JnQ\n+6VDR+q597ktPLN+LwDjcwfw+cVTmTGqe6ZuKywspKCgoFvalvipf5Kb+qcbVZdDtL79/drwwgsv\ncN5553X8gD1vwIu3w+H9kJETjOi99RQc3BFXHEnFInD6B2Hc/MTFkDsVMgcFn5+zZ8PBbcH2nNEw\nKJyJtu4wVO+FoRMTFmZ/l8ifb2bWoQQ5nnmQfwYMARYCvyJYSe+lk2nD3Q+aWSFwDjDEzFLdvYGg\nfGNnZ2OTE1UcrufLf1zDnkO1pKUY15w9nqvmjtXUbSLSfxzaCc/dBjtejrup2ZWVsLUTI48DhgVJ\n8su/CB4PGQ/5Z8cdT8KlpMHUt8PwqYmO5LiBucGtufQBkD6xx8OR3iWeWSwucPfTzWytu3/NzP4X\n+FN7B5lZHlAfJsdZwMXA94BngfcRzGRxPfBoHLFJjGjU+f4/NrDnUC2T8wbylUtnMHZIVqLDEhEJ\nZhzY8FfY+GTTK/G7w8Ht0FgHqZmQOTiupupqUyH7JK7ZSM2A2e+HGVdA8TPw2kMw4TyYcy2k6qJo\nkWQTT4J85Oi/ZjYKKAcmduC40cB9YR1yBHjI3R83szeBB83sW8Bq4J44YpOQu3Pfi1tZu6OCIQPS\n+NoVpzI8uxdfkCAi3WP/FijbBJMLgoStah9sWdr9Sev2F2HX2u49R6xpl8A5nwlGcuPwejxfEU97\ne3ATkaQVT4L8RFhD/ANgDdBIMPtEm9z9NeDMFrZvBhJYuNT37Kqo4Y5ni1i7o4KIwVfeMUPJsUhf\nU10G9XEuAPDWU7D29xBtDGYhmLI4GOGs76GLx7KGwjmfhWGTuvc86dnH61BFRNrQqQTZzCIEs0wc\nBP5oZo8DWe6+v0ujk05pjDqPrC7ldy9vp64hSnZGKjcvmsrs/Pi+UhSRJFJdDi/8BDYXdk17ZjAw\nLyhDWPnrYNv4c7r/Qqb0bDj13XGXPIiIdKVOJcjuHjWzHxNcXIe71wDJs4ZhP1a0t5KfPFPElrJq\nAAqm5/HJCyYzeEBaO0eKSLfa/Tq8+isYfgrMux6q98GKu4NlYltw6r59sPdXrbdXtTcY4U3NCBLb\neAzIhfk3BrGteQBKXoEzPhQsPiAi0g/FU2LxtJld6e66mC4JHKlv5LcvbeOva3cSdRg5KIPPFExh\n3oRkX6tGJIm5w5ZlUPZWfO1U7YFNTwf3S1dC0T/hyME263uzairhQHXb7Y4/Fy74F8gZFV98sc76\neHATEenH4kmQPwcMNrNagtFjI1goTxlZD1u5bT8/e7aYvZW1RAyunDOGj5wzgcy05Fk1R6RHRaNw\nqCSoqe2shlp49Z4umRIMCFaxOu29sGtNcDEcwPTLYNbVLa5w9caKFZyzYEHr7aVmBomxde0CPyIi\nEl+CPLzLopBOqThczy+Wb2bpW/sAmDR8IJ9fPJVpI7UqkPRju9fB8v+D/Zu7pr2MHDj1yiAh7SyL\nBFN6DZsUJO1FzwQXi41qfS2kI1nbuv+iNRERaVGnE2R3bzSza4DJ7v4dM8sHRhIsIS3dyN1ZsmEv\nv1y+haraBtJSjGsXTODKOWNI1cIf0hu5ByUIrz8U/4wMR2t6s4bEf+FX3kxYcFPcU4I1EUmBUy7p\nuvZERKTLxbOS3u1AGsFKet8BDgN3AX1gSaDkFTt1G8AZ4wZz86KpjB6shT8kgRob4K0noaK0c8eX\nbYTSVV0TSyQluMBs7keDC9hEREROUjwlFue5+1wzWw3g7vvNTMsBdZOGxiiPrtnZZOq2Ty2cxKLp\nIzDVIEpXizYGdbLRhvb3ra2EV34J5UXxnTMjJ5gLt42ygw7JHAyZg+JrQ0RE+rV4EuT6cD5kBzCz\nXCDaJVFJE5v2VPLTJZq6TXpI2SYo/O7JJ7w5o2HG5RDpxI+V1PRgcYqsoSd/rIiISBeLJ0G+A/gT\nkGdm3wA+AHyjS6ISAGrqGnlgxfGp20bkZPDZRZq6TeJUtQ9W3MmsN5fBzjtbeH4veDSYGzeng6uO\njT0T5nwE0uK4kE1ERCRJxHOR3v1mthK4ONz0fndf1zVhybrSCm57+i1N3Sbtq9oH6x/t2MVtjfXB\nxXD1h8morYTKFubhNQumHjv7k5A+oOvjFRERSXLxjCADpAD1BGUWHZo+wczGAfcDowhKMn7u7j82\ns1uBTwH7wl3/w92fiDO+XqnkwGG++fib1NQ1auq2/qyuOpwv11vfp6wIXr03WFHtZEw4nzejs1lw\nQcGJz6UPVA2viIj0a/HMYvGfwIeBvxAsEvI7M3vA3f+nnUMbgC+7+yozywFWmlm4xBS3ufsPOhtT\nX3C4roFv/209NXWNnDcll399x3RN3dbfHJ3y7MXb4UhFx46ZcD6MObNj+w6bBGPnUbN0aTAXr4iI\niDQRzwjyR4B57n4YwMy+TTAHcpsJsrvvAnaF9yvNbD0wNo44+ow9h47wo3++RcmBGsbnDuBfLj5F\nyXFft3cDvPBTOLD1+DaPHh8RHjYJMtoYzU3NgBlXwOQLuzVMERGR/sTc2/j6tq0DzZ4CPuDuh8LH\ng4Dfu/vlJ9HGRGAZMAv4EvAx4BDwKsEo84EWjrkRuBEgLy9v3kMPPdSp+JNJ1J2XdjXy7PZ66qMw\nIA1umJVBblbvTo6rqqrIzs5OdBgJlV67nxF7l5HacGJ9cCRay5CD6zA/cfKXhtSBlORfQXnu/G5b\nSlj9k9zUP8lN/ZPc1D/JLZH9s2jRopXuflZ7+8WTIP+ZYFGQvxMUSV4CPAfsAXD3L7VzfDawFPi2\nu//ZzEYCZWFb/w2MdvdPtNXG9OnTfePGjZ2KP1kU76vi9iVFFO2tAuBt04Zz48LJDBnQ+6eULiws\npKCgINFhdK+6w7BvfVAW0dz+Le3XB1sETv8gnP4BSImZti9tQLDgRTfqF/3Ti6l/kpv6J7mpf5Jb\nIvvHzDqUIMdTYvG38HbUSx090MzSCKaIe8Dd/wzg7ntinv8F8HgcsSW9I/WN/P7l7TyyupSoQ15O\nBp8pmMLZEzWFW6+xZTk8/2Oo3tf2fpMvhPHntvzciJkwdGKXhyYiIiKdF880b/d05jgLln27B1jv\n7j+M2T46rE8GuAros1PGrd5+gDueLWbPoSOYwbvPCKZwy0rXFG5JZe96eP4nsH9zC086NNQGd4dO\ngAHDT9wlJR1mXAaTFnZrmCIiItK14pnF4lKCUogJYTsGuLu3NwR6PnAd8LqZrQm3/QfwITObQ1Bi\nsRW4qbOxJauKmnrueW4Lz27YC8CE3AF84aJpnKIp3BKrugzWPgg1MSXv9TWw/YWWSyeOSs+Gs2+A\nU98Dkd5dLy4iIiLHxVNicTvB6nmvcxJLTLv7cwTJdHN9ds5jd6dw4z5++dxmDtU0kJZiXDN/PO89\nc6xmqegJdYdh56pgkYzmKnfD6t8Ecw43ZxE44xqY8+Gm9cFHpaR3e52wiIiI9Lx4EuQSYI17C5fg\nyzF7Dh3hZ88WsWr7QQBm5w/m5kVTGTskK8GR9RPbV8DyHwTLJ7dlwvkwuaDpjBF502HI+O6MTkRE\nRJJQPAnyV4C/mlkhUHt0o7v/JN6g+oLGqPPY2lIeeGk7tQ1RsjNS+cQFk7h45gism6bt6tcqSoJ6\n4dKVNFl5LtoY/DtsUsvJrqXAlMUw8YJum05NREREepd4EuRvECwzPYSTKLHoD4r2VnH7kk0U7wu+\ntu9LU7clTM0BWPM7qNpz4nMeDUaKG+tOfC5tAMz9aDCNmsohREREpAPiSZBHuPu8LoukFztc18Cq\nbQepj0Yp3lvFX9fuJOowPDudzy6aqqnbOqKhFnasOD4zRKyaA7DqfqitbLuNU94BCz7ddOU5i+gC\nOhERETkp8STIz5jZYndf0mXR9EIvFJdx99LN7K8+PnqpqdtiuLec9Mba8wYs/z84VNr2fmPnwYzL\ng6S3uUFjIe+UzscpIiIiEoonQf4UcIuZHQbq6Pg0b31CeVUtdy/bzIvF5QBMyRtI/tABpKVEeOfs\nUZq6DRhYtQ3+9EkoL+rYAUMnQO60E7dbBMYtgKkXqU5YREREul08CXILKyP0fdGo8/c3dvOrF7ZS\nU9dIVloKHz1vApfNGk0k0seTt7JNsPq3UFfV/r6N9Uzf9DxkZ0Mkte3639TMoEb49GsgJZ7/kiIi\nIiLxi2clvUYzuwaY7O7fMbN8YCSwssuiSzI79h/m9iVFvLnrEADzJw3j0xdOIS8nI8GRdVJFKex+\nnSazPrRm/xZ4/Y/BBXEdZsEcwnOvh7TMzkYpIiIi0qPiWUnvdiANWAh8BzgM3AWc3TWhJV406hyu\nbyTqzhOv7eIPr+6godEZMiCNmxZO4fypuT0zZVu0sekIbH0NRBvia++NP8PqB06uHTOYdTWMP7dD\nu697czvnLbi6k0GKiIiIJEY832ef5+5zzWw1gLvvN7M+M4/Z6u0HuLOwmF0VR5psf/upI/n4+RPJ\nyWxhZbWuVlECy38Ie9bBnGth+mXw8t1Q9M+2l0A+GRPOh4wO1EunpMEpl8KoWR1uuq64hdXpRERE\nRJJcPAlyvZlFCL+fN7Nceng+5PS6A1BdDgNzgw3RKKx/FHauCb7aH34KbFkGRU/DjHfB+AXttlmx\nfx+vPXIbG8tqOZjxDjLSs0mJGKNzUvnyqDWMq/4j/KOLktP27F1/fG7fV+8NbhBctJY+ML62B4+F\nc2+G0WfE146IiIhIH3PSCbKZpbp7A3AH8Ccgz8y+AXyAYPGQHpPWUAUPXB0sBJGeA8VLYO+bwZNb\nlgUJ8r4N4ePlwVLCI5uOgEbd2bSnisraeqJ1hxm48S+MaqxmtMG7BrzJ8PkfIiU1AzY+AZu29uTL\nC0y7JIj7pZ8FI8r5Z8HbvgyDxvR8LCIiIiL9QGdGkF8G5rr7/Wa2EriYYIq397v7uvYONrNxwP3A\nKIIR55+7+4/NbBjwB2AisBX4gLsfaDcad1h53/HHA4dD/nx466kgOU4bEEwPtulp2FwImwuJepAY\nN0advZW1ROobGRzT5P4hs5g9KosB+9fDq/ccf2JwPsz/FGTG7t2NsobC0InB/fyzoWIHDJusqc5E\nREREulFnEuRj2Zm7vwG8cZLHNwBfdvdVZpYDrDSzp4GPAc+4+3fN7KvAV4F/a6uh+tQcWPw12Lc+\n2JA1FE67Kig/OO0q2P5iULebnQdzrqXujb+yungnb+w8dHzehghk5aQwafhADBg4/kzmX/Cu4EUW\n/RPKNgb7ZY+CU6+E1ASVWaemQ+6UxJxbREREpB/pTIKcZ2Zfau1Jd/9hWwe7+y5gV3i/0szWA2OB\nK4GCcLf7gELaSZB3Ng7mX9fkAXnHNxbFLkoxBzbvBHYCsKdyDgeqTyUyALIzU4mYcc7kXD543kSy\nM1p4K065JLiJiIiISL9hfpKzIZjZLuBOYkaSY7l7h+uQzWwisAyYBWx39yExzx1w96EtHHMjcCNA\n1shJ8+Z/4Y6TCZ/RA413TUlnTHYLyxVLl6qqqiI7OzvRYUgr1D/JTf2T3NQ/yU39k9wS2T+LFi1a\n6e5ntbdfZxLkVe4+t9ORHW8nG1gKfNvd/2xmBzuSIMeaNHW6/23ZKx0+Z1qKMTkvmJVCul9hYSEF\nBQWJDkNaof5Jbuqf5Kb+SW7qn+SWyP4xsw4lyHHVIHeWmaURzIDxgLv/Ody8x8xGu/suMxsN7G2v\nnfQUOHXMoHjDERERERE5pjN1BhfFc0ILlp67B1jfrF75MeD68P71wKPxnEdEREREpDNOegTZ3ffH\nec7zgeuA181sTbjtP4DvAg+Z2Q3AduD9cZ5HREREROSkxbOSXqe4+3O0XqYR1+i0iIiIiEi8NJWD\niIiIiEgMJcgiIiIiIjGUIIuIiIiIxFCCLCIiIiISQwmyiIiIiEgMJcgiIiIiIjGUIIuIiIiIxFCC\nLCIiIiISQwmyiIiIiEgMJcgiIiIiIjGUIIuIiIiIxOjxBNnM7jWzvWa2LmbbrWZWamZrwttlPR2X\niIiIiAgkZgT518ClLWy/zd3nhLcnejgmEREREREgAQmyuy8D9vf0eUVEREREOiI10QHE+JyZfRR4\nFfiyux9oaSczuxG4MXxYG1uqIUlnOFCW6CCkVeqf5Kb+SW7qn+Sm/kluieyfCR3Zydy9uwM58aRm\nE4HH3X1W+HgkwRvlwH8Do939Ex1o51V3P6sbQ5U4qH+Sm/onual/kpv6J7mpf5Jbb+ifpJjFwt33\nuHuju0eBXwDzEx2TiIiIiPRPSZEgm9nomIdXASqbEBEREZGE6PEaZDP7PVAADDezEuDrQIGZzSEo\nsdgK3NTB5n7eHTFKl1H/JDf1T3JT/yQ39U9yU/8kt6Tvn4TUIIuIiIiIJKukKLEQEREREUkWSpBF\nRERERGL02gTZzC41s41mVmRmX010PAJmttXMXg+XC3813DbMzJ42s03hv0MTHWd/0cqy7i32hwV+\nEn6eXjOzuYmLvH9opX9uNbPS8DO0xswui3nu38P+2Whm70hM1P2DmY0zs2fNbL2ZvWFmXwy36/OT\nBNroH31+koCZZZrZy2a2Nuyfb4TbJ5nZivDz8wczSw+3Z4SPi8LnJyYy/qN6ZYJsZinAHcA7gVOB\nD5nZqYmNSkKLwuXCj85v+FXgGXefBjwTPpae8WtOXNa9tf54JzAtvN0I3NlDMfZnv+bE/gG4LfwM\nzXH3JwDCn2/XAKeFx/ws/Dko3aOBYMGqmcA5wM1hH+jzkxxa6x/Q5ycZ1AKL3f0MYA5wqZmdA3yP\noH+mAQeAG8L9bwAOuPtU4LZwv4TrlQkywTzJRe6+2d3rgAeBKxMck7TsSuC+8P59wHsSGEu/0sqy\n7q31x5XA/R54CRjSbPpF6WKt9E9rrgQedPdad98CFKH54ruNu+9y91Xh/UpgPTAWfX6SQhv90xp9\nfnpQ+DmoCh+mhTcHFgMPh9ubf36Ofq4eBi4yM+uhcFvVWxPkscCOmMcltP3hkJ7hwD/MbGW4JDjA\nSHffBcEPNWBEwqITaL0/9JlKHp8Lv6a/N6YkSf2TIOHXvWcCK9DnJ+k06x/Q5ycpmFmKma0B9gJP\nA8XAQXdvCHeJ7YNj/RM+XwHk9mzEJ+qtCXJLf1lovrrEO9/d5xJ83XizmS1MdEDSYfpMJYc7gSkE\nX0vuAv4v3K7+SQAzywb+BPyLux9qa9cWtql/ulkL/aPPT5IIV0eeA+QTjNbPbGm38N+k7J/emiCX\nAONiHucDOxMUi4TcfWf4717gLwQfij1Hv2oM/92buAiF1vtDn6kk4O57wl8sUeAXHP8aWP3Tw8ws\njSD5esDd/xxu1ucnSbTUP/r8JB93PwgUEtSKDzGzowvUxfbBsf4Jnx9Mx8vPuk1vTZBfAaaFV0Sm\nExTfP5bgmPo1MxtoZjlH7wOXECwZ/hhwfbjb9cCjiYlQQq31x2PAR8Or8c8BKo5+lSw9p1nd6lUE\nnyEI+uea8GrvSQQXg73c0/H1F2H94z3Aenf/YcxT+vwkgdb6R5+f5GBmeWY2JLyfBVxMUCf+LPC+\ncLfmn5+jn6v3AUs8CVax6/GlpruCuzeY2eeAvwMpwL3u/kaCw+rvRgJ/CevqU4HfuftTZvYK8JCZ\n3QBsB96fwBj7FWt5Wffv0nJ/PAFcRnDxymHg4z0ecD/TSv8UmNkcgq8XtwI3Abj7G2b2EPAmwRX8\nN7t7YyLi7ifOB64DXg/rKAH+A31+kkVr/fMhfX6SwmjgvnCmkAjwkLs/bmZvAg+a2beA1QR/5BD+\n+xszKyIYOb4mEUE3p6WmRURERERi9NYSCxERERGRbqEEWUREREQkhhJkEREREZEYSpBFRERERGIo\nQRYRERERiaEEWUSkk8ws18zWhLfdZlYa8/iFbjzvynAO+NhtV5jZajNba2ZvmtlN3XX+dmKrSsR5\nRUS6Uq+cB1lEJBm4eznBsraY2a1Albv/oDvPaWYTgVJ3r4vZlgb8HJjv7iVmlgFM7M44RET6Mo0g\ni4h0g6MjqWZWYGZLzewhM3vLzL5rZtea2ctm9rqZTQn3yzOzP5nZK+Ht/FaafifwVLNtOQQDHuUA\n7l7r7hvbatfMss3sV2EMr5nZ1eH2D4Xb1pnZ92Jfj5l9OxyhfsnMRobbJ5nZi2Hb/x2z/2gzWxaO\npq8zs7d1wdsqItIjlCCLiHS/M4AvArMJVgA7xd3nA78EPh/u82PgNnc/G7g6fK4ll9IsQXb3/QTL\ntW4zs9+HCfjRn++ttfs1giWRZ7v76cASMxsDfA9YTDAyfraZvSfcfyDwkrufASwDPhXT/p1h+7tj\nwvow8Hd3nxO+/jWIiPQSKrEQEel+r7j7LgAzKwb+EW5/HVgU3r8YODVcrh1gkJnluHvl0Q1h3XG+\nu29ufgJ3/6SZzQ7buQV4O/Cx1toNt18Tc/wBM1sIFLr7vvB8DwALgUeAOuDxcPeVYfsQLPt7dXj/\nNwQJNsArwL1h+ccj7q4EWUR6DSXIIiLdrzbmfjTmcZTjP4cjwLnuXtNGO28DnmvtSXd/HXjdzH4D\nbCFIkFts14KM2Zs1YbSu3t2P7t9I098fzdvB3ZeFCfflwG/M7Pvufn8b7YuIJA2VWIiIJId/AJ87\n+sDM5rSwz6XAk803hvXEBTGb5gDb2mm3+fahwArgQjMbbmYpwIeApe3E/TzHR6KvjWlvArDX3X8B\n3APMbacdEZGkoQRZRCQ5fAE4K7xg7k3g0y3sU0DLCasBXzGzjWa2BvgGwehxW+1+CxgaXkC3FlgU\nloH8O/AssBZY5e6PthP3F4GbzewVYHCzWNeY2WqCEowft9OOiEjSsOPfmImISLIys3zgF+7+zkTH\nIiLS1ylBFhERERGJoRILEREREZEYSpBFRERERGIoQRYRERERiaEEWUREREQkhhJkEREREZEYSpBF\nRERERGIoQRYRERERiaEEWUREREQkhhJkEREREZEYSpBFRERERGIoQRYRERERiaEEWUREREQkhhJk\nEREREZEYSpBFRERERGKkJjqAeAwZMsSnTp2a6DCkFdXV1QwcODDRYUgr1D/JTf2T3NQ/yU39k9wS\n2T8rV64sc/e89vbr1QnyyJEjefXVVxMdhrSisLCQgoKCRIchrVD/JDf1T3JT/yQ39U9yS2T/mNm2\njuynEgsRERERkRhKkEVEREREYihBFhERERGJ0atrkEVERESka9XX11NSUsKRI0e6pf3Bgwezfv36\nbmn7qMzMTPLz80lLS+vU8UqQRUREROSYkpIScnJymDhxImbW5e1XVlaSk5PT5e0e5e6U///t3X2U\nVPWd5/H3B0QbY+MDKkPAA+i0jKJRRB2fxrQSZzTOiA/JiZgoyzrBeMSHlURNMhNlGFGzGlaz6gZH\nI7CuGaNRMWOMDlg6rqMiSsKTCmNEWwm4jIbu8KA23/2jbmvZdldXV1fVvU1/Xuf0qbq/unV/X+vb\nv+brr3733g0baGpqYtSoUWUdo2pLLCTdJWm9pGUFbXtIekLSquRx96Rdkm6RtFrSbyUdVq24zMzM\nzKxzW7ZsYfDgwVUpjmtBEoMHD+7RDHjRAjkpXPcp89h3Aye3a7sKWBARDcCCZBvgFKAh+ZkC3F5m\nn2ZmZmbWQ721OG7T02F5WuwAABwESURBVPiLLrGIiJD0EDCuuweOiKcljWzXPAFoTJ7PAXLAlUn7\n3IgI4DlJu0kaGhFri/XxTss2/ubHz3Q3NKuR5ubN1C/NRn7Gjdida04bk3YY1kPXzF/O4jXvpda/\nf486Vuu8OA8eC71FWnlyfnqulDXIz0k6IiIWVaC/IW1Fb0SslbR30j4MeKtgv6ak7TMFsqQp5GeZ\nGThkFM3NzRUIy6qhdVtrZvKTW9ZMbtC7aYeRKS0tLeRyubTD6Jbcss0p91+736PelJ9a5yUL4znt\n/PSlsVCOtPPTJq089TQ/u+66a1X//W5t7bo+ePvtt5k2bRqvvPIK27Zt46STTmLmzJm0tLRw3nnn\n8dJLL3HOOedw0003dXqMLVu2lP17UEqBfALwLUlvAH8ERH5y+Qtl9dixjubBo6MdI2I2MBugflhD\n5L53SgXDsErKyp2M2r5laGw8LuVIsiUr+emOtm8kHrm49rms9e9Rb8pPLfOSlfGcdn760lgoR9r5\naZNGniqRn5UrV1b1JLquTtKLCM477zwuvPBCJk+eTGtrK1OmTGHGjBnMnDmTmTNnsmzZMpYtW1b0\nOHV1dYwdO7asGEspkCtZga5rWzohaSiwPmlvAgrXOg8H3qlgv2ZmZmbWTdVYytra2sqjl32x09cX\nLlxIXV0dkydPBqB///7MmjWLESNGcO2113LcccexevXqisdVqMurWETEGvLF64nJ802lvK8T84FJ\nyfNJwMMF7eclJwUeBfyhq/XHZmZmZrb9Wb58OePGffr0t0GDBjFy5MiqF8ZtupxBlnQ1cDgwGvgp\nMAD438CxXbzvXvIn5O0pqQm4GrgeuE/S+cCbwFeT3R8FvgysJl+ATy7jv8XMzMzMKqgay0O6Wn8c\nER1ehSJ/LYfaKGWJxRnAWOAlgIh4R1KXC1MiYmInL43vYN8ALiohFjMzMzPbjo0ZM4YHHnjgU20b\nN25k3bp1jB49uiYxlLJU4oOkgA0ASZ+rbkhmZmZm1leNHz+eTZs2MXfuXCC/ZnnatGlMnTqVgQMH\n1iSGUgrk+yT9BNhN0jeBfwXuqG5YZmZmZtYXSeLBBx/k/vvvp6GhgcGDB9OvXz++//3vAzBy5Egu\nv/xy7r77boYPH86KFSsqHkOXSywi4kZJJwEbya9D/kFEPFHxSMzMzMzMgH322Yf58+cD8OyzzzJx\n4kQWL17MuHHjeOONN6refykn6f1X4N8i4jtVj8bMzMzMrMAxxxzDmjVratpnKSfpjQS+IWkEsBj4\nN/IF85JqBmZmZmZmloZSroP8g4g4ETgIeAb4DvlC2czMzMxsu1PKEou/I3/N412Al4Fvk59FNjMz\nMzPb7pSyxOJM4CPgX4CngOciYktVozIzMzMzS0kpSywOI39zjxeAk4Clkip/Y24zMzMzswzoskCW\ndBDwDWAS8DWgCVhY5bjMzMzMrI9qampiwoQJNDQ0sO+++zJ16lS2bt3KE088wbhx4zj44IMZN24c\nCxdWpyQt5UYhNwCDgFuAAyLihIj4QVWiMTMzM7M+LSI488wzOf3001m1ahWrVq1i8+bNXHHFFey5\n55488sgjLF26lDlz5nDuuedWJYZSbhRyqqQdgf2B0ZJejYgPqxKNmZmZmWXHT75Y8UPuvG0bXNj5\n9R4WLlxIXV0dkydPBqB///7MmjWLESNGcO2117LLLrsAMGbMGLZs2cLWrVvZaaedKhpjKUssvgis\nAm4FbgNek3R8RaMwMzMzMwOWL1/OuHHjPtU2aNAgRo4cyerVqz9ue+CBBxg7dmzFi2Mo7SoWPwL+\nMiJeBZC0P3AvMK7ou4qQ9N+AvwUCWApMBoYCPwP2AF4Czo2ID8rtw8zMzMx66IKnKn7ITc3N1Bd5\nPSKQ1GF7m+XLl3PllVfy+OOPVzw+KG0N8oC24hggIl4DBpTboaRhwCXA4RFxENAfOJv8WudZEdEA\nvAecX24fZmZmZtY7jRkzhhdffPFTbRs3bmTdunWMHj2apqYmzjjjDObOnct+++1XlRhKKZBflHSn\npMbk5w56fie9HYCBknYAdgbWAicC9yevzwFO72EfZmZmZtbLjB8/nk2bNjF37lwAWltbmTZt2sdX\nsjj11FO57rrrOPbYY6sWQylLLC4ELiI/6yvgafJrkcsSEW9LuhF4E9gMPE6+4H4/Ij5KdmsChnX0\nfklTgCkAA4eMIpfLlRuKVVlLS0sm8tPcvBkgE7FkSVby0x1p5rLWffem/NTys8nKeE47P31pLJQj\n7fy0SeOzqkSfu+66K83NzRWK6LNaW1u7PP68efOYNm0a06dPZ8OGDZx55plccskl/PCHP2T16tVM\nnz6d6dOnA/DQQw+x1157feYYW7ZsKftzKFogSxoL7Af8KiJ+VFYPnz3m7sAEYBTwPvBz4JQOdo0O\n2oiI2cBsgPphDdHY2FiJsKwKcrkcWchP/dL8fW0aG49LOZJsyUp+uiPNXNa6796Un1p+NlkZz2nn\npy+NhXKknZ82aXxWlehz5cqV1NcXWyXcM83NzV0e/4ADDuDRRx8F4Nlnn2XixIm89tprzJgxgxkz\nZpTUT11dHWPHji0rxk4LZEk/IH+DkMXADyVdFxF3lNXLp30J+F1EvJv08wvgGGA3STsks8jDgXcq\n0JeZmZmZ9WLHHHMMa9asqWmfxdYgfw04NCImAkeQLGuogDeBoyTtrPwpiuOBFcCTwFeSfSYBD1eo\nPzMzMzOzkhUrkLdExCaAiNjQxb4li4jnyZ+M9xL5S7z1I79k4krgckmrgcHAnZXoz8zMzMy6p/CS\nar1RT+MvtgZ5P0nzk+dqt01EnFZupxFxNXB1u+bXgSPLPaaZmZmZ9VxdXR0bNmxg8ODBHV6POOsi\ngg0bNlBXV1f2MYoVyBPabd9Ydi9mZmZm1isMHz6cpqYm3n333aocf8uWLT0qXktRV1fH8OHDy35/\npwVyRFT+1ilmZmZmlmkDBgxg1KhRVTt+Lpcr++oStVKRdcVmZmZmZtsLF8hmZmZmZgW6LJAlfWaR\niKQ9qxOOmZmZmVm6SplBXiTpqLYNSWcBz1YvJDMzMzOz9BS91XTiHOAuSTng8+SvUXxiNYMyMzMz\nM0tLlwVyRCyVdC0wD2gGjo+IpqpHZmZmZmaWgi4LZEl3AvsBXwD2Bx6R9D8j4tZqB2dmZmZmVmul\nrEFeBpwQEb+LiF8DRwGHVTcsMzMzM7N0lLLEYla77T8A51ctIjMzMzOzFJWyxKIBuA44EPj4km8R\nsW8V4zIzMzMzS0UpSyx+CtwOfAScAMwlf8Je2STtJul+Sa9IWinpaEl7SHpC0qrkcfee9GFmZmZm\nVo5SCuSBEbEAUESsiYhr6Pll3m4GHouIPwMOAVYCVwELIqIBWJBsm5mZmZnVVCkF8hZJ/YBVkqZK\nOgPYu9wOJQ0CjgfuBIiIDyLifWACMCfZbQ5werl9mJmZmZmVq5QbhVwG7AxcAswgP3s8qQd97gu8\nC/xU0iHAYuBSYEhErAWIiLWSOizCJU0BpgAMHDKKXC7Xg1CsmlpaWjKRn+bmzQCZiCVLspKf7kgz\nl7Xuuzflp5afTVbGc9r56UtjoRxp56dNGp+V81MZpVzFYlHytAWYXKE+DwMujojnJd1MN5ZTRMRs\nYDZA/bCGaGxsrEBIVg25XI4s5Kd+6TMANDYel3Ik2ZKV/HRHmrmsdd+9KT+1/GyyMp7Tzk9fGgvl\nSDs/bdL4rJyfyui0QJY0v9gbI+K0MvtsApoi4vlk+37yBfI6SUOT2eOhwPoyj29mZmZmVrZiM8hH\nA28B9wLPA6pEhxHxe0lvSRodEa8C44EVyc8k4Prk8eFK9GdmZmZm1h3FCuQ/AU4CJgLnAP8C3BsR\nyyvQ78XAPZJ2BF4nv3SjH3CfpPOBN4GvVqAfMzMzM7Nu6bRAjohW4DHgMUk7kS+Uc5L+ISJ+3JNO\nI2IJcHgHL43vyXHNzMzMzHqq6El6SWF8KvnieCRwC/CL6odlZmZmZpaOYifpzQEOAn4FTI+IZTWL\nyszMzMwsJcVmkM8F/gjsD1wifXyOnoCIiEFVjs3MzMzMrOaKrUEu5S57ZmZmZmbbFRfBZmZmZmYF\nXCCbmZmZmRXotEBOrmBhZmZmZtanFJtB/ncASfNqFIuZmZmZWeqKXcViR0mTgGMkndn+xYjw9ZDN\nzMzMbLtTrED+FvB1YDfgb9q9FviGIWZmZma2HSp2mbdngGckvRgRd9YwJjMzMzOz1BS91XRinqRL\ngOOT7aeA/xURH1YvLDMzMzOzdJRymbfbgHHJ423AYcDtPe1YUn9JL0v6ZbI9StLzklZJ+mdJO/a0\nDzMzMzOz7iqlQD4iIiZFxMLkZzJwRAX6vhRYWbB9AzArIhqA94DzK9CHmZmZmVm3lFIgt0rar21D\n0r5Aa086lTQcOBX4p2RbwInA/ckuc4DTe9KHmZmZmVk5SlmD/B3gSUmvAwJGAJN72O//AK4A6pPt\nwcD7EfFRst0EDOthH2ZmZmZm3dZlgRwRCyQ1AKPJF8ivRMTWcjuU9NfA+ohYLKmxrbmjrjt5/xRg\nCsDAIaPI5XLlhmJV1tLSkon8NDdvBshELFmSlfx0R5q5rHXfvSk/tfxssjKe085PXxoL5Ug7P23S\n+Kycn8ooZQaZpCD+bYX6PBY4TdKXgTpgEPkZ5d0k7ZDMIg8H3ukkltnAbID6YQ3R2NhYobCs0nK5\nHFnIT/3SZwBobDwu5UiyJSv56Y40c1nrvntTfmr52WRlPKedn740FsqRdn7apPFZOT+VUcoa5IqK\niO9GxPCIGAmcDSyMiK8DTwJfSXabBDxc69jMzMzMzGpeIBdxJXC5pNXk1yT75iRmZmZmVnNdLrGQ\ntCAixnfVVo6IyAG55PnrwJE9PaaZmZmZWU90WiBLqgN2BvaUtDufnEg3CPh8DWIzMzMzM6u5YjPI\nFwCXkS+GF/NJgbwRuLXKcZmZmZmZpaLTAjkibgZulnRxRPy4hjGZmZmZmaWmlOsg/1jSMcDIwv0j\nYm4V4zIzMzMzS0UpJ+nNA/YDlvDJLaYDcIFsZmZmZtudUm4UcjhwYER0eGc7MzMzM7PtSSnXQV4G\n/Em1AzEzMzMzy4JSZpD3BFZIegHY2tYYEadVLSozMzMzs5SUUiBfU+0gzMzMzMyyopSrWDwlaQTQ\nEBH/KmlnoH/1QzMzMzMzq70u1yBL+iZwP/CTpGkY8FA1gzIzMzMzS0spJ+ldBBxL/g56RMQqYO9q\nBmVmZmZmlpZSCuStEfFB24akHchfB9nMzMzMbLtTSoH8lKTvAQMlnQT8HHik3A4l7SPpSUkrJS2X\ndGnSvoekJyStSh53L7cPMzMzM7NylVIgXwW8CywFLgAeBf6uB31+BEyLiAOAo4CLJB2Y9LMgIhqA\nBcm2mZmZmVlNlXKZt4HAXRFxB4Ck/knbpnI6jIi1wNrkebOkleRP/JsANCa7zQFywJXl9GFmZmZm\nVq5SCuQFwJeAlmR7IPA4cExPO5c0EhgLPA8MSYpnImKtpA5PBJQ0BZgCMHDIKHK5XE/DsCppaWnJ\nRH6amzcDZCKWLMlKfrojzVzWuu/elJ9afjZZGc9p56cvjYVypJ2fNml8Vs5PZZRSINdFRFtxTES0\nJNdC7hFJuwAPAJdFxEZJJb0vImYDswHqhzVEY2NjT0OxKsnlcmQhP/VLnwGgsfG4lCPJlqzkpzvS\nzGWt++5N+anlZ5OV8Zx2fvrSWChH2vlpk8Zn5fxURilrkP8o6bC2DUnjgM096VTSAPLF8T0R8Yuk\neZ2kocnrQ4H1PenDzMzMzKwcpcwgXwr8XNI7yfZQ4Gvldqj8VPGdwMqI+FHBS/OBScD1yePD5fZh\nZmZmZlauogWypH7AjsCfAaMBAa9ExIc96PNY4FxgqaQlSdv3yBfG90k6H3gT+GoP+jAzMzMzK0vR\nAjkitkm6KSKOBpZVosOIeIZ8od2R8ZXow8zMzMysXKWsQX5c0lkq9Sw6MzMzM7NerJQ1yJcDnwNa\nJW0mP/sbETGoqpGZmZmZmaWgywI5IuprEYiZmZmZWRZ0ucRCed+Q9PfJ9j6Sjqx+aGZmZmZmtVfK\nGuTbgKOBc5LtFuDWqkVkZmZmZpaiUtYg/3lEHCbpZYCIeE/SjlWOy8zMzMwsFaXMIH8oqT8QAJL2\nArZVNSozMzMzs5SUUiDfAjwI7C3pWuAZYGZVozIzMzMzS0kpV7G4R9Ji8jfxEHB6RKysemRmZmZm\nZinotECWVAd8C/hTYCnwk4j4qFaBmZmZmZmlodgSiznA4eSL41OAG2sSkZmZmZlZiootsTgwIg4G\nkHQn8EJtQjIzMzMzS0+xGeQP257UammFpJMlvSpptaSratGnmZmZmVmhYjPIh0jamDwXMDDZFhAR\nMaiSgSSXkrsVOAloAhZJmh8RKyrZj5mZmZlZMYqItGMAQNLRwDUR8VfJ9ncBIuK6zt5z0Od3jmVX\nH1GjCK27mpubqa+vTzsMVq1vSTuETNq2bRv9+pVypcfsadh7l5r3Wevfo96Yn1rkJSvjOSv56Qtj\noRxZyU+bWuapt+Rn9NUvp9K3pMURcXhX+5VyJ71aGQa8VbDdBPx5+50kTQGmABw4tI7m5ubaRGfd\n1rptWybyM0DB1ta0o8ieiGDbtt53z5+d+pPK71Wtf496W35qlZesjOcs5KevjIVyZCE/bWqdp96S\nn1wul3YYRWWpQFYHbZ+Z3o6I2cBsgNGjR0f9t1+qdlxWplwuR2NjY9phkP4cdjZlJT+9Ra1/j5yf\njmVlPPfl/GQlB8U4P9nWG/KTne8f8jPG+xRsDwfeSSkWMzMzM+ujslQgLwIaJI2StCNwNjA/5ZjM\nzMzMrI/JzBKLiPhI0lTg10B/4K6IWJ5yWGZmZmbWx2SmQAaIiEeBR9OOw8zMzMz6rsxc5q0ckpqB\nV9OOwzq1J/D/0g7COuX8ZJvzk23OT7Y5P9mWZn5GRMReXe2UqRnkMrxayrXsLB2SXnR+ssv5yTbn\nJ9ucn2xzfrKtN+QnSyfpmZmZmZmlzgWymZmZmVmB3l4gz047ACvK+ck25yfbnJ9sc36yzfnJtszn\np1efpGdmZmZmVmm9fQbZzMzMzKyiXCCbmZmZmRXotQWypJMlvSpptaSr0o7HQNIbkpZKWiLpxaRt\nD0lPSFqVPO6edpx9haS7JK2XtKygrcN8KO+WZDz9VtJh6UX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"text/plain": [
"
\n",
"\n",
"The furnance is turned on for temperatures below the range \n",
"\n",
"\\begin{align}\n",
"T_{Setpoint} - \\frac{d}{2} \\leq T \\leq T_{Setpoint} + \\frac{d}{2}\n",
"\\end{align}\n",
"\n",
"and is turned for temperatures above the range. Within the range, however, the furnance may be on or off depending on what happened at the last decision point.\n",
"\n",
"The following code implements relay control with hystersis. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"nbpages": {
"level": 2,
"link": "[4.1.2 Relay Control with Hysteresis](https://jckantor.github.io/CBE32338/04.01-Relay-Control.html#4.1.2-Relay-Control-with-Hysteresis)",
"section": "4.1.2 Relay Control with Hysteresis"
}
},
"outputs": [
{
"data": {
"image/png": 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ux8iBfeiXkcoHThrR4T1gvY3ZwXb/zLnjOXHkAF5Zs7tJ0rp0aynLtu7n5j+9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\nARwDrAM+BSyLiFZgWTJdlyKC888/n1mzZtHe3k5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"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
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"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
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}
},
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}