RC Tutorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bond Graph Tools Tutorial 1\n",
    "\n",
    "## Part 1: Installing BondGraphTools\n",
    "\n",
    "### Setup:\n",
    "Install BondGraphTools v0.3 from PyPI using `pip install BondGraphTools`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import:\n",
    "Import the BondGraphTools package. Initially, we will be using the new, draw and simulate functions.\n",
    "\n",
    "This may take a while on first import, as it will download and build the required Julia libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from BondGraphTools import new, draw, simulate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2: Basic modelling\n",
    "\n",
    "We're going to build and simulate a simple resistor-capacitor system.\n",
    "\n",
    "All models in BondGraphTools are 'components', and components are created with `new`.\n",
    "Create a new model and name it 'RC' using the following command:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = new(name='RC')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us also make a new capacitor with a capacitance of 1 Farad, a 1 Ohm resistor, and a conservation law which we want them to obey (ie; a common voltage). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "C = new(\"C\", value=1)\n",
    "R = new(\"R\", value=1)\n",
    "KCL = new(\"0\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to now add the components to our model, and then to wire them up."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from BondGraphTools import add, connect\n",
    "add(model, R,C,KCL)\n",
    "connect(R,KCL)\n",
    "connect(C,KCL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can display a basic visualisation of the model using the draw command."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig = draw(model)\n",
    "import matplotlib.pyplot as plt\n",
    "plt.savefig(\"RC_1.svg\", pad_inches=0, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to run a simulation, we need to know what the state variables of the system are, so as to select the initial conditions.\n",
    "\n",
    "We can find this out via:\n",
    "\n",
    "(Note that 'q_i' corresponds to position-like variables, and 'p_i' correspond to momentum-like variables)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'x_0': (C: C1, 'q_0')}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.state_vars"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we clearly have one state variable `x_0` which corresponds to the accumulated charge.\n",
    "\n",
    "Hence, our state space is one dimensional.\n",
    "Let us define intial values and an simulation window, then simulate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "timespan = [0, 5]\n",
    "x0 = {'x_0':1}\n",
    "t, x = simulate(model, timespan=timespan, x0=x0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and plot the results in a matplotlib figure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.pyplot import plot\n",
    "fig = plot(t,x)\n",
    "plt.savefig(\"RC_2.svg\", pad_inches=0, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Is this right?\n",
    "Try to derive this by hand and then verify that your derivation has the same constitutive relation as the model.\n",
    "\n",
    "The constitutive relaiton $\\Phi(x)=0$ can be produced via:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 3: Basic Control\n",
    "\n",
    "Now, let us add some additional components.\n",
    "In particular, we want to add a modulated current source."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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eDW2AUMRFKT1Wrafe26bskzvr//O3BuqXk4fJFRXu9GgAgDZSuL/xZK+PS8rVLTJM97mH6a6rB6lTKCd7dVSEIi7J5j1ezV9aoPzdXrmiOun+ycN055UDFcY3DQDoMMora/X0+9v02sbdsiXdMWagHpgyTLFdI5weDW2MUMQls21bb362T0++u1UHK2qU1Lub5s1I1dUJsU6PBgC4BHUNPv11wy49m7NdFdX1unJwjObOSNE3+kU7PRraCaGIVlNZU68XVxXr5TUlqq33adqI3ppzY7IGxEQ5PRoAoIXWFh3W/KUFKio9rr7RkZozLVk3Xd6HBxiDDKGIVre77IQef6dQywsOKiIsRBnXxevuCQmKCmerBADwd7vKKvXY21uUU9j4Pfzu8Qm6e3yCOoezJVowIhTRZtYVN/40uv3gcfWJjtRvbkzSzSP78tMoAPihypp6vbCyWK+sKVFtg0/TL++jOTcmqX937goFM0IRbaq+wae/fbxbz+Rs19GqOo0e1F0P35zK+hYA8BM+3z/WmZceq1Fyn8s0b0aKropnnTkIRbST8spaPZOzTf/348Yn5m4fPUAP3DBccTwxBwCO+ezkzhWf7vaqe1Qn3T9luO68cqBCOXYPJxGKaFdbDjTuwbXBU65uEWH6hXuo7rp6sMLD2E4HANpLaUW1Fi7fpiUn98L9/lWD9Ev3MEVHdXJ6NPgZQhHtzrZtvfflV3rs7cZd/eN7dNFDN6Vo4vCeTo8GAB1aTX2D/rhup55fUaTK2gaNS4zT3BkpGtaL07VgRijCMdV1Dcr60KMXVzWeEzopqaceuilFQzgnFABalW3b+mBrqR5dVqidZSc0MCZKD05P1uSUXjxgiHMiFOG4/d4qPfnuVr21eb86hVr60dghundSorpFcgsEAC5VcelxPbKsUB9uP6So8FDdOylRPx43RBFhbHeD8yMU4Tc+2Vmu+UsL9OW+CsV1jdDsqcOVntZfISyqBoAWO1pVp+dWFOlP63eq3mfr1rR+ypyapF6XRTo9GgIIoQi/0uCzlZ23R08t36ayylpd3j9a82akatSg7k6PBgABocFn6428PVp08vvoyP7RmndzqtIG8n0ULUcowi8drarT8yuK9OrJn4RvuaLxJ+He0fwkDABfZ2NJ452Zgv2Nd2Yypw7Xd7kzg0tAKMKvFZce16PLCrX65NqaeyY2rq2J7MTaGgBost9bpSfe3aqlTWu9xw3RvRNZ641LRyjC79m2rZXbSvXosi0qOVypATGd9btpKbohlaf1AAS36roGLV7t0UurG3ePcCf31O+ms3sEWg+hiIBRW+/Tq+tL9NyKYh2vqdfYxFjNm5HK/l8Ago5t23r3y6/0+Mn9aBN6dNHcGakaP6yH06OhgyEUEXBKj1Xrqfe2KfvkiQL//K2B+uXkYXJFhTs9GgC0udNOuIoM033uYbrr6kHqFMoJV2h9hCIC1uY9Xj18yhmlv5oyXHeOGaAwvlkC6IDKK2v19Pvb9NrG3bIl3TFmgB6YMlyxXSOcHg0dGKGIgObz2frfzfv05LtbdbCiRkm9u2nejFRdnRDr9GgA0CrqGnz624ZdeiZnuyqq6zVmcHfNm5Gqb/SLdno0BAFCER1CZU29XlxVrJc/LFFtg0/TRvTWnBuTNSAmyunRAOCirS06rPlLC1RUelx9oyM1Z1qybrq8Dw/yod0QiuhQdped0GNvF+r9woOKCAtRxnXxuntCgqLCw5weDQAu2O6yE3r07ULlNH0vG5+gn45PUOdwtgZD+yIU0SGtLTqsR5YVaPvB4+pz8qfwGfwUDsDPVdbU64WVxXplTePdkekj+mjOtCT1787dETiDUESHVd/g098+3q1ncrbraFUd63oA+C2fz9abnzWuty49VqPkPpdp3owUXRXPems4i1BEh1deWatncrbp/37c+KTg7aMH6IEbhiuOJwUB+IEzd3C4f8pw3XnlQIVy7B78AKGIoHHm3mO/uH6o7rp6sMLD2E4HQPsrPVathe9t05KTe8J+/6pB+qV7mKKjOHYP/oNQRFA58zSD+B5dNPemFE0Y3tPp0QAEiZr6Br26bqee/6DxlKlxiXGaOyOFU6bglwhFBKXqugZlfejRi6saz0edlNRTD93E+agA2o5t2/pga6keXVaonWUnNDAmSg9OT9bkFM6th/8iFBHU9nur9OS7W/XW5v3qFGrpR2OH6N5JieoWya0fAK2nuPS4HllWqA+3H1JUeKjumZioH48boshObHcD/0YoApI+2Vmuh98qUMH+CsV1jdDsqcOVntZfISwmB3AJjlbV6bkVRfrT+p2q99m69Yp+yrwxSb0ui3R6NOCCEIrASQ0+W9l5e/TU8m0qq6zVyP7RmndzqtIGdnd6NAABpsFn6428PVrE9xMEOEIROMOZVwBuuaKffsMVAAAX6Mw7FJlTh+u73KFAgCIUga9RXHpMjyzbwpoiABdkv7dKT7y7VUub1jyPG6J7J7LmGYGNUATOwfSU4u+mJ2sKTykCOKm6rkGLV3v00urGXRSuT+qpB9lFAR0EoQhcgDP3PRubGKt5M1LZ9wwIYmfuy5rQo4seYl9WdDCEItACpceq9dR725TNSQpAUDvzpKf73MN019WD1CmUk57QsRCKwEU482zWX00Zru9xNivQ4R2prNXTp5wdf8eYAbp/CmfHo+MiFIGL5PPZ+t/N+/Tku1t1sKJGSb27ad6MVF2dEOv0aABaWX2DT3/dsEvP5hbpaFWdxgzurnkzUvWNftFOjwa0KUIRuESVNfV6YWWxXllTotoGn6aN6K3fTktW/+5RTo8GoBWsLTqsR5YVaPvB4+oTHak505I14/I+PNCGoEAoAq1kV1mlHn97i94vPKiIsBBlXBevuyckKCo8zOnRAFyE3WUn9Njbhf/4Mz0+QXePj+fPNIIKoQi0srVFhzV/aYGKSrn6AASiM+8STB/RR7+5MUkDYrhLgOBDKAJtoGk90zM521VRXc96JiAA2LatNz9j3TFwKkIRaEPllbV65ownJB+YMlyxPCEJ+JXNe7yav7RA+Sd3Mrh/ynDdMWaAwtjuBkGOUATaQeH+xj3XPi5p3HPtF9cP1Q+uGcyea4DDTHuj3uceKldUuNOjAX6BUATaCac4AP6jtt6nP64raT5taVxinObOSOG0JeAMhCLQzjgXFnBO0/ntj729RSWHKzUgprMenJ7C+e3A1yAUAYfs91bpiXe3aunm/eoUaulHY4fo3kmJ6hbJcYBAWyguPa5HlxVq9fZDigoP1T0TE/XjcUMU2SnU6dEAv0UoAg7bWFKu+UsLVLC/QnFdI5Q5dbi+m9ZfIRwHqPLKWm3e49XEJG7P4+JVVNfp97lF+tP6nar32br1in6aPTVJvaMjnR4N8HuEIuAHGny23sjbo6eWb1N5Za1G9o/WvJtTlTawu9OjOeqXr3+m//l0nzb+7nr17MZ/1NEyDT5b2Sf/XJWd/HM1d0aqRg0K7j9XQEu0JBR5PBNoI6Ehlu68cqBWPjBBPx43RAX7K3Tri+v1q9c/08GKaqfHc8zYxDhJ0vriMocnQaD5ZGe5vv3CWv3m71/Isiw9lX65/udfxxKJQBvizCKgjUV37qSHbkrRnVcO0CPLtujvn+7TewVfBe1aqrGJjRsdry0+rO9c0c/haRAI9nur9OS7W/XWybW/GePjde9E1v4C7YFbz0A7ano689FlhdpZdkIDY6L0u+nJQfd05vVPr9KJ2gat/82koPr7RstU1zUo60OPXlq1Q1V1DewmALSSltx65ooi0I4sy9L1yb00bmic/rhup55fUaSMv2wKuv3exiXG6U8f7ZLncKUSenR1ehz4mTP3J43v0UVz2Z8UcARrFAEHRISF6u7xCVr56wlKH9Vfa4sP68bfr9HDbxXo6Ik6p8drc03rFNcVH3Z4EvibLQcqdOfLG/Svf8tXRVWdHpyerOX3XUckAg7h1jPgBzbv8erhpQX69OSZtL+aMlzfu3KgQjvodjoV1XX65vz35U7upay7Rjs9DvzAkcpaPX3GGer3TxmuOM5QB1od2+MAAcjns/XmZ/v05LtbVXqsRkm9u+nhm1N1VXys06O1iVteXKfi0uP6bO6UDhvEOL/6Bp/+9vFuPZOzXUer6jRmcHfNm5Gqb/SLdno0oMNijSIQgEJCLN2a1l83pPbWCyuL9cqaEt2RtUHTR/TRnGlJ6t89yukRW9W4xDh9uturL/Yd1TcHuJweBw5YV3xY85cWaPvB4+oTHalHv/MNzbi8Dw84AX6ENYqAn+kSEabZU5OU86vrNCWll97+4oCuf3q1nsnZrqraBqfHazXXJLBOMVjtLjuhjL/k6Z9e+Vi7yk7o59cP1Yr7x+vmkX2JRMDPcOsZ8HNrixqvuhSVNl51mTMtuUNcdampb9DI+e/rigHd9dqsq5weB+2gsqZeL64q1strSlRb79O0Eb0158ZkDYjpWFfLAX/HGkWgg6lr8OmvG3bp2Zztqqiu7zDruO76r43asKNMm+dNUefw4Np4PJjY9j/W3x6saFx/O3dGSvNVZQDtiyP8gA6mU2iI/s/YIVr164n6p28N1KZdRzTjP9Zqzt8/V9nxGqfHu2jjEmNV2+DTJzvLnR4FbeTzvV5996X1+uXrm1VT79Oj3/mGlv1sHJEIBAgeZgECSEyXcD1+ywj907cGaf7SAr22cY+WfX5A97mH6a6rB6lTaGD97HfqforXDevh8DRoTaXHqvXUe9u0JH+vQixLP7xmsO5zD5UrKtzp0QC0ALeegQBl27be+eIr/ds7jadXJPToorkzUjU+gILL57M1+vFc9YmO1Ns/v9bpcdAKaut9enV9iZ5bUazjNfUamxiruTelanjv4Dh1CAgEbI8DBAHLsjT98j66PrmnFq/26KXVxfrBf22UO7mnfjc9MM7DDQmxdE1CrJZ9fkDllbWK6cLVpkD2wdaDenTZFpUcrtSAmM56+raRQXeOOdDRBNZ9KgBniewUql+4h2rF/RN00+V9lLulVFOeXa0n3t2iY9X+fxzguJO3nz/aUebwJLhYxaXH9cM/btSPXs3TwYpq/fqG4cr55XjdkNqbSAQCHLeegQ5mY0m5Hn6rQIUHKtSjW4Rm3zBc303rrxA/Pf1kT/kJXbtwpe68cqCeuHWE0+OgBSqq6/RcbpFeXb9T9T5bt1zRT5lTk9Q7OtLp0QCcA9vjAEGuwWfrjbw9emr5NpVX1mpk/2jNuzlVaQO7Oz2a0finVsq2pQ9nT3R6FFyABp+t7JP/fpVV1ury/tGaNyNVowb5579fAE7H9jhAkAsNsXTnlQO18oEJ+tHYISrYX6FbX1yvX73+mQ5WVDs93lnGJsZpd/kJ7S474fQoOI+8neX69gtr9Zu/fyHLsrQw/XK9+a9jiUSggyIUgQ4sunMnzZ2Rovfuu1bXDeuhv3+6TxMXrdKLq4pVXec/xwE2rVNct4Pj/PzVgaNV+vlrnyr9Dx9p21fHlHFdvFY+MF63jR7gt8saAFw6bj0DQcK2bX2wtVSPLivUzrITGhgTpQenJ2uyHzyVeqSyVmmP5WjaiD564Xtpjs6C01XXNejlDz16cdUOVdU16Pqknvrd9GTF9+jq9GgALhLb4wA4i2VZuj65l8YNjdMf1+3U8yuKNOsvm3Tt0DjNvSlFQ3s5t89d9y7hSu17mdYXH5bPZ3OFyg/Ytq33vvxKj7+zRXuPVCm+RxfNvSlFE4b3dHo0AO2IW89AkIkIC9Xd4xO08tcTlD6qv9YUHdbU36/Rw28V6OgJ57bTGZsYpyMn6lR4oMKxGdBoy4EKfe/lj/XTv+Xr6Ik6PTg9Wcvvu45IBIIQoQgEqZ7dIrVo5ki9ec9YjegXrVfX79SERSv11w271OBr2ZKU1jDulOP84IwjlbV66M0vNf25NdpQUqY7xgzQyl9P0L9cGx9wx0MCaB2sUQQgn8/Wm5/t05PvblXpsRol9e6mh29O1VXxse02Q3Vdgy6f/76+NSRGf/nxt9rt60Kqb/Dpbx/v1jM523W0qk6jB3XXwzen6hv9op0eDUAbYI0igBYJCbF0a1p/TUntrRdXFuuVNSW6I2uDpo/ooznTktS/e1SbzxDZKVSjB3VMW1fCAAAVwUlEQVTXJzvLVVPfoIiw0Db/mmi8gjt/aYG2HzyuPtGReuTbqbp5ZF/HH3AC4B8IRQDNukaEafbUJN0+ZoAee3uL3v7igHK3HFTG+AT9dHyCOoe3bbyNTYzT+h1lyt/l1dUJ7Xc1MxjtKT+hx94u1PKCg4oIC9HPJyXq7gkJigrnPwsA/oFFJwDOMii2i16+a7T+8uMrNTAmSs+tKNL1T6/S0s371dLlKi3BOsW2V1lTr6eWb9X1z6zW8oKDmjait3J/NV6/mjKcSARwFtYoAjinugaf/rphl57N2a6K6npdOThGc2ektMn6tQafrSseeV/xPbrqzXvGtvrnD2a2bet/P9uvJ97dooMVjetQ585I0TUJcU6PBqCdcdYzgFZXdrxGz+Rs12sbd8uWdMeYgXpgyjDFdo1o1a9z91826f3Cr/Tp3CmK7typVT93sPp8r1cPv1Wg/N1euaI66f4pw3XnmAEK40lmIChx1jOAVhfbNUKP3zJCS382TmMGx+i1jbs1YdEq/efaEtU1+Frt64wdGiefLW3wlLXa5wxWpceq9evszfr2C+u0ee9R/eDqQVr1wAR9/6pBRCKAC8J3CgAtkto3Wq/PukovfC9Nl0V20qPLCjX13z/U6u2HWuXzs07x0tXW+5T14Q5NWrRa2Zv26pqEWL3z82s1/9vfkCsq3OnxAAQQVi4DaDHLsjT98j6alNRTWR969NLqYv3gvzbKndxTD05P0eC4Lhf9uQfHRqlvdKTWEooX5YOtB/Xosi0qOVypATGd9fRtIzXFD87zBhCYCEUAF61zeKh+4R6q9NH99cQ7W7Ts8wNavf2QfjRuiH42aai6RrT8W4xlWRqbGKfsTXt14GiV+kR3boPJO54dh47r0WWFWrXtkKLCQ/XrG4brx+OGKLIT+1ECuHjcegZwyfq5Ous/vpemNzKu1tCe3bR4tUcTF63Skk175buI4wDHDW26/cw6xfOpqK7TY8sKdcOzH2rVtkO65Yp++uD+CbpnYiKRCOCSEYoAWs2VQ2K09Gfj9G+3jFCDz9YD2Zt1y0vr9enuIy36PE1btrBO8es1+Gy9/sluTVq0Sq+sLVFK38v03z+9Rs/e/k31jo50ejwAHQTb4wBoE0dP1On3K4r05492qt5n69Yr+inzxiT1uuzCImbqv3+osspabfzt9ayvO0PeznI9vLRAX+6rUFzXCM2eOlzpaf0VEsI/JwDnx/Y4ABwXHdVJc2ek6L37rtW1Q+P090/3aeKiVXpxVbGq6xrO++vHJsbp0LEaFZUeb4dpA8OBo1X6+WufKv0PH2nbV8c067p4rXxgvG4bPYBIBNAmCEUAbSqxZzf9+UdX6pW7RqtHtwgtfG+bpjz7od4v+OqcxwE2bZOztojbz9V1DXp+RZEmLVqttzbv16Sknlp+33X67bRkdYtkU3IAbYdbzwDaTU19g/64bqeeX1GkytoGXTs0TnNvStHQXt3Oem9lTb1Gzn9f44f10H/+cIwD0zrPtm299+VXevydLdp7pErxPbrooZtSNHF4T6dHAxDAOMIPgF8rrajWwuXbtGTTXoWGWPr+VYP0S/cwRUedfnXstj98pIL9R/XZvCnqFGQniWz9qkLz3yrUR54ydYsI0y/cQ3XX1YMVHhZc/xwAtD7WKALwaz0vi9SimSP15j1jNaJftF5dv1MTFq3UXzfsUsMp2+mMTYxTZW2DNu/xOjht+zpSWauH3vxS036/RhtKynTHmAFa+esJ+pdr44lEAO2O7zoAHPPNAS79/afX6OmZIxUWGqIH3/xSNz2/tvmc53FDYyUpKE5pqW/w6U/rd2rColX6y4ZdShvYXW/dM05PfvdyxXWNcHo8AEGKW88A/MLxmnq9sLJY/7mmRLUNPk0f0Uezpw7X9OfWKrlPN2XffY3TI7aZ9cWHNX9pobYdPKbel0VqzrQk3TyyL9sCAWgTrFEEELB2Hq7U4+9sUU7hQUWEhSg8NERVdQ3aPG+KulzEkYD+bE/5CT32dqGWFxxUeFiI7r4uXndPSFBUeMf6+wTgX1oSinw3AuBXBsd10ct3jdaaokOav7RQxSf3UdxYUq6JSR3nad//3rRXc/7nC9XW+5Q20KXf33GFBsREOT0WAJyGUATgl64d2kPv/uJa/XXDLv1lw66znogOdAeOVqmuwSdJyt/t1fde2aBxiXEamxinaxLiFNMl3OEJAYBbzwDgmPLKWn20o0xriw9rXfFh7S4/0fyx1L6XNYfjmMEx6hwe6uCkADoS1igCQADaXXZC63Y0RuP6HWUqr6yVJIWHhmjUoO4aN7QxHEf0i1YoR/YBuEiEIgAEOJ/P1pavKrSu+LDWFpdpY0mZqusab1V3iwzT1fGxzeEYH9eFJ6QBXDBCEQA6mJr6BuXv8p4Mx8P6fK9XTXuT94mO1NjEOI1LjNM1ibHq2S3S2WEB+DVCEQA6uKNVdfrYU9YcjjsOVTZ/bHivbo3hODRWVw6JVdcOtq0QgEtDKAJAkDlwtErriv8RjoeO1UiSwkIsfXOA62Q4xumbA1xBd242gNMRigAQxGzbVlHpca07+TT1Bk+5jtfUS5K6hIfqW/Gxzbeqh/XqyvpGIMgQigCAZnUNPn2+16u1RY1XHPN3H1H9yQWOcV0jNC6xMRzHJsapr6uzw9MCaGuEIgC0UG5urrKzs+VyuSRJc+bMaf7rjqaypl4bS8qb92/c+tWx5o/F9+jSvH/jVfGxiu7csTY6B0AoAkCLLFmyRDNnztSRI0fkcrmUlZWlzMxMlZSUdNhYPNWhYzVaf3L/xrVFh7X/aLUkKcSSRvR3NV9xHDWouyLC2PgbCHSEIgC0QPfu3TV69Gjl5OQ0v2ZZlmbPnq0FCxY4OFn7s21bO8tONF5tLDqs9TsOq6K6cX1jZKcQjRkco3GJcZqc0kvxPbo6PC2Ai9GSUGTPBABBzePxyOv1Kj4+/qyP5ebmOjCRsyzL0pC4LhoS10Xfv2qQGny2vtx3VGuLG6Px45JyrSk6LMuSZhGKQIdHKAIIah6Px/i6y+VSfn5+O0/jf0JDLI0c4NLIAS7dMzFR1XUNytt5RPE9ujg9GoB2QCgCCGper1eSgmItYmuI7BSqcUPjnB4DQDth11UAQa0pEJuCEQDwD4QigKAWExMjSSovLz/t9a9btwgAwYRQBBDU0tLSvvZjbre7HScBAP9DKAIIerNnzz7tCeemv87IyHBqJADwCzzMAiDoNe2VOHnyZMXHxysvL085OTnnvNoIAMGADbcBAACCSEs23ObWMwAAAIwIRQAAABgRigAAADAiFAEAAGBEKAIAAMCIUAQAAIARoQgAAAAjQhEAAABGhCIAAACMCEUAAAAYEYoAAAAwIhQBAABgRCgCAADAiFAEAACAEaEIAAAAI0IRAAAARoQiAAAAjAhFAAAAGBGKAAAAMCIUAQAAYEQoAgAAwIhQBAAAgBGhCAAAACNCEQAAAEaEIgCc9M4XB/SD/9qoqtoGp0cBAL8Q5vQAAOAP3tq8X/f9v0/ls6WdZZVK7nOZ0yMBgOO4oggg6J0aiQCAfyAUAQS1pkjs2S1St6b1c3ocAPArhCKAoHVqJL426yoNie3i9EgA4FcIRQBB6axIjCMSAeBMhCKAoEMkAsCFIRQBBBUiEQAuHKEIIGgQiQDQMoQigKBAJAJAyxGKADo8IhEALg6hCKBDIxIB4OIRigA6LCIRAC4NoQigQyISAeDSEYoAOhwiEQBaB6EIoEMhEgGg9RCKADoMIhEAWhehCKBDIBIBoPURigACHpEIAG2DUAQQ0IhEAGg7hCKAgEUkAkDbIhQBBCQiEQDaHqEIIOAQiQDQPghFAAGFSASA9kMoAggYRCIAtC9CEUBAIBIBoP0RigD8HpEIAM4gFAH4NSIRAJxDKALwW0QiADiLUATgl4hEAHAeoQjA7xCJAOAfCEUAfoVIBAD/QSgC8BtEIgD4F0IRgF8gEgHA/xCKABxHJAKAfyIUAfiFPtGdiUQA8DNhTg8AADeP7KspKb0U2SnU6VEAAKfgiiIAv0AkAoD/IRQBAABgRCgCAADAiFAEAACAEaEIAAAAI0IRAAAARoQiAAAAjAhFAAAAGBGKAAAAMCIUAQAAYEQoAgAAwIhQBAAAgBGhCAAAACNCEQAAAEaEIgAAAIwIRQAAABgRigAAADAiFAEAAGBEKAIAAMCIUAQAAIARoQgAAAAjQhEAAABGhCIAAACMCEUAAAAYEYoAAAAwIhQBAABgRCgCAADAiFAEAACAEaEIAAAAI0IRAAAARoQiAAAAjAhFAAAAGBGKAAAAMCIUAQAAYEQoAgAAwIhQBAAAgBGhCAAAACNCEQAAAEaEIgAAAIwIRQAAABgRigAAADAiFAEAAGBEKAIAAMCIUAQAAIARoQgAAAAjQhEAAABGhCIAAACMCEUAAAAYEYoAAAAwIhQBAABgRCgCAADAiFAEAACAEaEIAAAAI0IRAAAARoQiAAAAjAhFAAAAGBGKAAAAMCIUAQAAYEQoAgAAwIhQBAAAgBGhCAAAACNCEQAAAEaEIgAAAIwIRQAAABgRigAAADAiFAEAAGBEKAIAAMCIUAQAAIARoQgAAAAjQhEAAABGhCIAAACMCEUAAAAYEYoAAAAwIhQBAABgRCgCAADAiFAEAACAEaEIAAAAI0IRAAAARoQiAAAAjAhFAAAAGBGKAAAAMCIUAQAAYEQoAgAAwIhQBAAAgBGhCAAAACNCEQAAAEaEIgAAAIwIRQAAABgRigAAADAiFAEAAGBEKAIAAMCIUAQAAIARoQgAAAAjQhEAAABGhCIAAACMCEUAAAAYEYoAAAAwIhQBAABgRCgCAADAiFAEAACAEaEIAAAAI0IRAAAARoQiAAAAjAhFAAAAGBGKAAAAMCIUAQAAYEQoAgAAwIhQBAAAgBGhCAAAACNCEQAAAEaEIgAAAIwIRQAAABgRigAAADAiFAEAAGBEKAIAAMCIUAQAAIARoQgAAAAjQhEAAABGhCIAAACMCEUAAAAYEYoAAAAwIhQBAABgRCgCAADAiFAEAACAEaEIAAAAI0IRAAAARoQiAAAAjAhFAAAAGBGKAAAAMCIUAQAAYEQoAgAAwIhQBAAAgBGhCAAAACNCEQAAAEaEIgAAAIwIRQAAABgRigAAADAiFAEAAGBEKAIAAMCIUAQAAIARoQgAAAAjQhEAAABGhCIAAACMCEUAAAAYEYoAAAAwIhQBAABgRCgCAADAiFAEAACAEaEIAAAAI0IRAAAARoQiAAAAjAhFAAAAGBGKAAAAMCIUAQAAYEQoAgAAwIhQBAAAgBGhCAAAACNCEQAAAEaEIgAAAIwIRQAAABgRigAAADAiFAEAAGBEKAIAAMCIUAQAAIARoQgAAAAjQhEAAABGhCIAAACMCEUAAAAYEYoAAAAwIhQBAABgRCgCAADAiFAEAACAEaEIAAAAI0IRAAAARoQiAAAAjAhFAAAAGBGKAAAAMCIUAQAAYEQoAgAAwIhQBAAAgBGhCAAAACNCEQAAAEaEIgAAAIwIRQAAABgRigAAADAiFAEAAGBEKAIAAMCIUAQAAIARoQgAAAAjQhEAAABGhCIAAACMCEUAAAAYEYoAAAAwIhQBAABgRCgCAADAiFAEAACAEaEIAAAAI0IRAAAARoQiAAAAjAhFAAAAGBGKAAAAMCIUAQAAYEQoAgAAwIhQBAAAgBGhCAAAAKMwpwcAAH/x3VH9dXVCrAbFRjk9CgD4BUIRAE7q6+qsvq7OTo8BAH6DW88AAAAwIhQBAABgRCgCAADAiFAEAACAEaEIAAAAI0IRAAAARoQiAAAAjAhFAAAAGBGKAAAAMCIUAQAAYEQoAgAAwIhQBAAAgBGhCAAAACNCEQAAAEaEIgAAAIwIRQAAABgRigAAADAiFAEAAGBEKAIAAMCIUAQAAIARoQgAAAAjQhEAAABGYU4PAADnkpmZKY/Ho5iYGEnS5MmTlZOTo8zMTMXHx7f4fRcrNzdX+fn5crlc8nq9crvdys3N1ezZsy/4fV6vV2+88YYkadOmTRo1apRmzZp1ybMBQFshFAH4rYyMDElSdnZ282sLFy5UVlaWMjMzW/y+i5WVlaWYmJjTonDmzJkaM2ZMi96XmZmpBQsWyOVySZK6d++u+Ph4ud3uS54RANoCt54B+K2srCyNGjXqtNdmz56ttLS0i3rfxcrOzlZ6evppr02ePPmswDvf+/Ly8pSXl9f8sZiYGOXn57fKjADQFghFAH5twYIF8ng8p702Z86c5lvMLX1fS+Xn56u8vPys1+Pj408L0Qt536ZNm06LS4/Hw9VEAH6NUATgt9LT0+XxeJSQkKCEhATNnDlTS5YsUXp6evPt25a871QLFy7UzJkzzztDfHy8PB6PJk+erCVLljS/fmbgXej7mmRkZGjx4sWtdtUTANoCoQjAb2VnZzc/7OHxeLRkyRLNnDlTkydPvqj3ncrtdjevbTwXl8ulkpISxcfH6yc/+YksyzKue7zQ93m9XmVlZcnlcl3y1U4AaGuWbdst+gX9+/e39+7d20bjAIBZbm6ucnJylJWVJa/Xq8WLFxufGL7Q913KHDNnztSmTZvO+TT1hbxv1KhRysjI4MlnAO3Ksqx9tm33v5D3ckURgN/Kyspq/mu3260FCxaopKREUuN6v5a+r6VMD5q43W653e7T1kNeyPuariSeavTo0VqwYMFFzwcAbY1QBOC3TBHlcrmUlpZ22trDC31fS73++uvG15v2R2zJ+/Ly8r72ljUA+CtCEYDf8ng8Z60j9Hg8ys/PP+31C33fmR/Pzc0959dfsmTJWe9pWv/Y0veNHj1ac+bMOe09ubm5Z70GAP6EDbcB+C23262ZM2eeFlxer/esdX8X+r5TLVmyRJ988snXPpXs9XqbrwA23TL2er1KS0s7ba/EC32fy+VSenq6Fi5cKJfLpU2bNikzM/OsfRcBwJ/wMAsAAEAQ4WEWAAAAXDJCEQAAAEaEIgAAAIwIRQAAABgRigAAADAiFAEAAGBEKAIAAMCIUAQAAIARoQgAAAAjQhEAAABGhCIAAACMCEUAAAAYEYoAAAAwIhQBAABgRCgCAADAiFAEAACAEaEIAAAAI0IRAAAARoQiAAAAjAhFAAAAGBGKAAAAMCIUAQAAYEQoAgAAwIhQBAAAgBGhCAAAACNCEQAAAEaEIgAAAIwIRQAAABgRigAAADAiFAEAAGBEKAIAAMCIUAQAAIARoQgAAAAjQhEAAABGhCIAAACMCEUAAAAYEYoAAAAwIhQBAABgRCgCAADAiFAEAACAkWXbdst+gWXVSDrUNuMAAACgjfWwbTviQt7Y4lAEAABAcODWMwAAAIwIRQAAABgRigAAADAiFAEAAGBEKAIAAMCIUAQAAIARoQgAAAAjQhEAAABGhCIAAACM/j/wXjgOPgehbAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 960x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Sf = new('Sf')\n",
    "add(model, Sf)\n",
    "connect(Sf, KCL)\n",
    "draw(model)\n",
    "plt.savefig(\"RC_3.svg\", pad_inches=0, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since we've not specified the value of the `Sf` component, it has been added to the control variables:\n",
    "\n",
    "`u_0` "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'u_0': (SS: SS3, 'f')}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.control_vars"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets also check the new system relation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[dx_0 - u_0 + x_0]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.constitutive_relations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First; lets suppose a constant current:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAHhBJREFUeJzt3Xl8XXWd//HXJ/ueJk2atqRJ6E5LKW3TQgGhINiKLA6ggIqAaB1FRgcd8Dc+FJ3RGR0dZXyoYEV2KCCLrLIUCwVsKd1XWkqXNE2apE2zb3f5/v64AQu2TWjvzck99/18PO7jbqf3vG9J3j18z/I15xwiIuIvSV4HEBGR6FO5i4j4kMpdRMSHVO4iIj6kchcR8SGVu4iID6ncRUR8SOUuIuJDKncRER9K8WrFRUVFrqKiwqvVi4jEpZUrV+5zzhX3tZxn5V5RUcGKFSu8Wr2ISFwys139WU7DMiIiPqRyFxHxIZW7iIgP9VnuZjbKzBab2SYz22hm3zzEMmZmvzazbWa2zsymxyauiIj0R392qAaBbzvnVplZLrDSzF5yzm06aJlPAuN6b6cAt/Xei4iIB/rccnfO1TrnVvU+bgU2A8d9aLGLgXtdxDJgiJmNiHpaERHpl4805m5mFcA04M0PvXUcsPug59X84z8AIiIyQPp9nLuZ5QCPAd9yzrUczcrMbD4wH6CsrOxoPkJEZEA55wiEHN3BED3BMD2hcOQ+GKb7oOeBUOQWWcYROPi1kCN40OPK8gLOHN/neUjHpF/lbmapRIr9Aefc44dYZA8w6qDnpb2vfYBzbgGwAKCyslKTt4rIUQuHHZ2BEO09QTq6I/ddgRAdPZHbe487e0J0BiLPuwKRx509YbqCIboDIboC4ch7wcjj7mCI7kCkuLuDIbqDYaI91fTX5ozxvtzNzIA/Apudc788zGJPAd8ws4eI7Ehtds7VRi+miPhFOOxo7Q7S0hmgpStAa1ew9xZ53NYdpKUrQFvv4/buyH3kcYi27iAd3UE6AqGPVLpmkJmaTEZqMpmpyaSnJpGRkkxGahIZqcnkZaaSkZpEeu9r6SnJpKUkkd57izyOvJaWHHn+3i09OYnU3tdTe99LTbbe+yRSk5JITTFSk5NISTIitRpb/dlyPx24ClhvZmt6X/t3oAzAOXc78BxwPrAN6ACujX5UERlMwmFHa1eQxo4eGtt7ONDeQ2NHD00dPTR1BGjqDNDcEaCps4cD7ZEib+kM0Nod7LOU01KSyE1PIScjhey0FHLSUxiWm0F2UQrZaclkp//9Pqv3cVZaMplpKZH71MjzrLSUSKGnRYp3IEp1sOiz3J1zrwNH/Btxzjng+miFEhFvBENh9rX10NDaTUNbF/Ut3exv72FfWzf723rY397NvtbI/YGOAKHwoVs6OckYkpnKkKxUhmSlMTw/g4nDc8nLTCUvIyVy/97jjFRyM1LJzUghNyNS6OkpyQP8zf3HswuHicjAcc7R1BGgprmTupYu9jZ3s7eli7rmrsh9SxcNrd00dvQccqs6Jz2FoTlpDM1Oo3xoFtPLh1CYnUZBVhqF2X+/FWSlMSQrlZz0lITaSh6MVO4iPhAKO2qbO6k+0Mnuxg72NHVS09RJbXPX+4+7AuEP/BkzKMpJZ3heBqUFmUwvL6A4J53i3HSG5Ubui3qfZ6RqSzreqNxF4kRbd5Bd+9up2t/Bzv0dkceNHew+0EFtUxfBg4ZIzKA4J52RQzKZODyXcyYMY+SQTEbkZzC891aUk05qsi4v5Vcqd5FBJBAKU9XYwfaGdrY3tEXu97WxY18H+9q6P7BsUU4aZYVZTC8roHRqJqMKsigtyGJUYSYj8jNJS1FxJzKVu4gHAqEwO/e1s7Wuja11re/fdu3v+MAWeFFOGqOLcjhnYjEVRdlUDM2mfGgW5UOzyUnXr68cnn46RGKsqaOHTbUtbKppef/+3YY2AqFIiZtBeWEW40tymTt5OKOLcxhTnM3oohzys1I9Ti/xSuUuEkXNHQHW7WliXXUza3c3sbGmhT1Nne+/X5KXzqQRecyZMIwJw3MYNyyXscNytMNSok7lLnKUAqEwG2taWLnrAGt3N7Guuomd+zvef390UTbTywu4anY5k0bkccKIPIpz0z1MLIlE5S7ST80dAVZWNbJi54FIoVc3vX944Yj8DKaWDuGzM0cxtXQIJx6XT36mhlTEOyp3kcNo7gywfEcjS9/dz9Lt+3l7bwvOQUqSMXlkHp+bVc6M8gJmlBcwPD/D67giH6ByF+nVFQixYucBXnungb+9u5+NNc2EHaSnJDGjvIB/PXc8s44vZGrpEDLTNEYug5vKXRKWc44d+9pZsrWBV7c2sGx7I52BEKnJxrSyAm44Zxyzxwzl5FFDtMNT4o7KXRJKIBTmrR2NvLipjpffrmN3Y+RIluOLsvlsZSlnTSjm1NFDyUrTr4bEN/0Ei++1dQd5dUsDL23ay+ItDTR3BkhPSeKMsUXMP3MMZ40rpmxoltcxRaJK5S6+1NETZNHmep5eW8OrWxroCYUpyErl3BNKOG9SCWeOL9LWufiafrrFN7oCIV7Z0sDT62p4eXMdXYEwJXnpfOHUcuZOLmFGeQEpulCWJAiVu8Q15xwrdx3gTyuqeXZ9LW3dQYZmp/GZGaO44KQRzKwoJClJ1xWXxKNyl7i0t7mLx1ZV89jKarbvaycrLZnzp4zg4pNHMnv0UG2hS8JTuUvcCIbCvPx2PQuXV7FkawNhB7OOL+Rrc8Zw/pQRZOsqiSLv02+DDHr727p56K3dPLBsFzXNXYzIz+Drc8Zy2YxSKoqyvY4nMiip3GXQWrO7iXuX7uSZtbX0hMKcPnYot1w0mY9PHKZhF5E+qNxlUAmHHS+/Xc9tr2xjVVUT2WnJXDFrFFedWs64klyv44nEDZW7DAo9wTBPra3h96++yzv1bZQWZPLDCydx6YxScjN0dUWRj0rlLp7q6AmycPlu/vjadmqau5g4PJf/u+JkPjVlhIZeRI6Byl080RUIcf+yXdz2yrvsb+9h1vGF/OSSKcwZX4yZjksXOVYqdxlQPcEwD6/YzW/++g51Ld2cMbaIfz1vHDPKC72OJuIrKncZEMFQmMdX7+H/Fr3DnqZOKssLuPXyacweM9TraCK+pHKXmHLO8cqWBn787CbebWjnpNJ8/uuSKZw5rkjDLyIxpHKXmNla18qPn93Mkq0NHF+Uze1fmMHcySUqdZEBoHKXqGts7+FXL23lweVVZKcl8/0LJnHVqeWkpejoF5GBonKXqAmGwtyzdBe3LtpKR0+Iz59SxrfOHU9hdprX0UQSTp/lbmZ3AhcA9c65Ew/xfj5wP1DW+3m/cM7dFe2gMrht2NPMdx9fx4Y9LXxsXBHfv2AS43VGqYhn+rPlfjfwG+Dew7x/PbDJOXehmRUDW8zsAedcT5QyyiDW3h3kVy9t5c43dlCYnc5vPjeNT00ZoXF1EY/1We7OuSVmVnGkRYBci/w25wCNQDAq6WRQ++vbdXz/zxvZ09TJ504p4+Z5E8nP1KUCRAaDaIy5/wZ4CqgBcoHLnXPhKHyuDFIH2nv4/pMbeGZdLeOG5fDoP8+mskInIYkMJtEo97nAGuAcYAzwkpm95pxr+fCCZjYfmA9QVlYWhVXLQFu8pZ6bH13HgY4evn3eeL561hgdBSMyCEWj3K8Ffuqcc8A2M9sBTASWf3hB59wCYAFAZWWli8K6ZYB09AT5ybObeeDNKiaU5HLXtTOZPDLf61gichjRKPcq4OPAa2ZWAkwAtkfhc2WQWFV1gBsfXsOuxg7mnzmaG88bT0ZqstexROQI+nMo5EJgDlBkZtXALUAqgHPuduA/gbvNbD1gwM3OuX0xSywDJhgK8+uX3+E3i7cxIj+ThV85lVNH61owIvGgP0fLXNnH+zXAJ6KWSAaF+tYu/mXhapZtb+TS6aX88KJJmjRDJI7oDFX5B29u3883Fq6mtSvA/35mKpfOKPU6koh8RCp3eZ9zjt8v2c7PX9hCeWEW9103i4nD87yOJSJHQeUuADR3Bvj2I2tZtLmOT00ZwU8vnaJhGJE4pnIXtta18uV7VlDb3MktF07imtMqdPkAkTinck9wr2yp5xsPriYzLZmH5s9mRnmB15FEJApU7gnKOcc9f9vJfzyziYnD87jj6kpGDsn0OpaIRInKPQEFQmF+9PRG7l9WxXmTSrj18pPJTtePgoif6Dc6wTR3BvjGg6t47Z19fPWs0dw8dyJJSRpfF/EblXsCqT7QwTV3vcXOfe38z6Un8dmZo7yOJCIxonJPENvq27jqj2/S1h3kvutOYfYYXUZAxM9U7glgfXUzV9+1nCQzHp4/m0kjdWKSiN+p3H1u6bv7+cq9K8jPTOX+L5/C8UXZXkcSkQGgcvexRZvq+PqDqygrzOL+605heH6G15FEZICo3H3qidXVfOdP6zhxZB53XTuLwuw0ryOJyABSufvQw29VcfNj6zltzFAWfLGSHB3DLpJw9FvvM4+trOa7j6/nrPHF/P6qGZoxSSRBaWZjH3l6bQ3/9uhaThszVMUukuBU7j7x/IZavvXwGirLC/nDFytV7CIJTuXuAy9vruOGhauZWprPndfOJCtNo20iiU7lHude3drA1+5fxQkj8rj7S7O081REAJV7XHtz+37m37uCscNyuPdLs8jTzEki0kvlHqfeqWvlK/eu4LiCTO67bhZDsnQcu4j8nco9DtW3dHHNXW+RlpLMPdfOYmhOuteRRGSQUbnHmbbuINfe/RYHOnq465qZjCrM8jqSiAxC2vsWRwKhMNc/sIq397Zyx9WVTCnN9zqSiAxS2nKPE845vvfEel7d2sBPPn0iZ08Y5nUkERnEVO5x4tcvb+ORFdXccM5YrphV5nUcERnkVO5x4InV1fxq0VYumX4cN5433us4IhIHVO6D3IY9zXz3sfWccnwhP73kJMw0mbWI9E3lPog1tvfw1ftWUpidxm8/P520FP3nEpH+0dEyg1QwFOaGhatoaOvmT1+dTZGOZReRj6DPTUEzu9PM6s1swxGWmWNma8xso5m9Gt2IiennL2zhjW37+fHFJzJ11BCv44hInOnP/+ffDcw73JtmNgT4HXCRc24y8JnoREtcz6yr4fdLtvOFU8v47MxRXscRkTjUZ7k755YAjUdY5HPA4865qt7l66OULSFt2dvKTY+uY0Z5AT+4YLLXcUQkTkVjD914oMDMXjGzlWb2xSh8ZkJq7gzw1ftWkJOewm3agSoixyAaO1RTgBnAx4FMYKmZLXPObf3wgmY2H5gPUFamE3EO5pzjpkfXsqepk4fmn8qwvAyvI4lIHIvGpmE18IJzrt05tw9YAkw91ILOuQXOuUrnXGVxcXEUVu0fD721mxc21nHT3InMKC/0Oo6IxLlolPuTwBlmlmJmWcApwOYofG7C2Fbfxo+e3sjHxhVx3RnHex1HRHygz2EZM1sIzAGKzKwauAVIBXDO3e6c22xmzwPrgDBwh3PusIdNygd1B0N886HVZKYm84vPTCUpSWegisix67PcnXNX9mOZnwM/j0qiBPO/L25lY00Lf/hiJSUaZxeRKNHhGB56/Z19LOg9nv28SSVexxERH1G5e6SxvYcbH1nD2GE5fO/8SV7HERGfUbl7IHLY4zqaOgL8+oppZKYlex1JRHxG5e6BB5dXsWhzHTfNm8CkkXlexxERH1K5D7A9TZ3817ObOWNsEV86XYc9ikhsqNwH0HvzoIYd/PclU3TYo4jEjMp9AD25poZXtjTwb3MnMKowy+s4IuJjKvcBsr+tmx89vZGTRw3h6tMqvI4jIj6nch8gP3p6E23dQf7nspNI1nCMiMSYyn0A/PXtOp5aW8P1Z49lfEmu13FEJAGo3GOstSvA957YwPiSHL4+Z6zXcUQkQajcY+xnz7/N3pYufnbpSZp8Q0QGjNomhpbvaOT+ZVVce9rxTCsr8DqOiCQQlXuMBEJh/v2J9ZQWZPKdueO9jiMiCUblHiP3Lt3Ftvo2brlwMllp0ZjNUESk/1TuMbCvrZtbF23lzPHFnHvCMK/jiEgCUrnHwC9e2EJnT4gfXDAJMx3TLiIDT+UeZeurm3l4xW6uOa2CscNyvI4jIglK5R5Fzjl++PRGhman8S/njvM6jogkMJV7FD25poaVuw5w09yJ5GWkeh1HRBKYyj1K2ruD/PdfNnNSaT6XzSj1Oo6IJDiVe5T8dvE26lq6ueXCybpOu4h4TuUeBTv3tXPHazu4ZNpxzCjXmagi4j2VexT85LnNpCYbN39yotdRREQAlfsxW7mrkZc21fG1OWMoycvwOo6ICKByPybOOX72/BaKctL50hma7FpEBg+V+zF4dWsDy3c0csM5Y3X9GBEZVFTuRykcdvz8hS2UFmRy5awyr+OIiHyAyv0oPbehlo01Ldx43nhNwiEig45a6SgEQ2F++eJWxpfkcPHJx3kdR0TkH6jcj8KjK6vZvq+d73xiAsk6YUlEBqE+y93M7jSzejPb0MdyM80saGaXRS/e4NMVCHHroneYVjaE8yaVeB1HROSQ+rPlfjcw70gLmFky8DPgxShkGtTuW7qLvS1d3DR3oq7VLiKDVp/l7pxbAjT2sdgNwGNAfTRCDVatXQF+98o2PjauiNljhnodR0TksI55zN3MjgP+CbitH8vON7MVZraioaHhWFc94P7w2g4OdAS4aa4uMyAig1s0dqjeCtzsnAv3taBzboFzrtI5V1lcXByFVQ+c5o4Ad76+g/OnDGdKab7XcUREjigap1VWAg/1jj8XAeebWdA59+cofPagcc/SnbR1B7nhHM2wJCKD3zGXu3Pu/YuqmNndwDN+K/b27iB3vrGDc08Yxgkj8ryOIyLSpz7L3cwWAnOAIjOrBm4BUgGcc7fHNN0gsXB5FU0dAb5+9livo4iI9Euf5e6cu7K/H+acu+aY0gxC3cEQC5Zs57QxQ5lepok4RCQ+6AzVPjy2cg/1rd1cr612EYkjKvcjCIbC3P7qu0wdNYTTdFy7iMQRlfsRPLOulqrGDq6fM0Zno4pIXFG5H0Y47PjdK9uYUJLLuSfoGjIiEl9U7oexaHMdW+va+PrZY0jSlR9FJM6o3A/BOcdvF2+jrDCLT00Z4XUcEZGPTOV+CG9s28/a6ma+NmcMKcn6KxKR+KPmOoTfLt5GSV46l0zXLEsiEp9U7h+yYU8zS7fv58tnjCY9JdnrOCIiR0Xl/iF3vbGTrLRkLp81yusoIiJHTeV+kIbWbp5eW8NlM0rJy0j1Oo6IyFFTuR9k4fIqekJhrj6twusoIiLHROXeqycY5r5luzhrfDFjinO8jiMickxU7r2eW19LQ2s3155e4XUUEZFjpnInctLSXW/sYHRxNmeOi6/p/0REDkXlDqze3cTa6mauOa1ClxoQEV9QuRM5/DE3PYVLp5d6HUVEJCoSvtz3Nnfxl/W1fHbmKLLTozFfuIiI9xK+3O9ftouQc1w9u8LrKCIiUZPQ5d4VCPHg8irOPaGEsqFZXscREYmahC73p9bU0Njew7U6aUlEfCZhy905x11/28mEklxma35UEfGZhC33VVVNbK5t4erTKjQ/qoj4TsKW+8NvVZGVlsxFJ4/0OoqISNQlZLm3dgV4em0tF540khwd/igiPpSQ5f7Mulo6AyFds11EfCshy/2h5VVMKMll2qghXkcREYmJhCv3TTUtrK1u5vKZo7QjVUR8K+HK/ZEVu0lLTuKfpmnyaxHxr4Qq965AiMdXVTP3xOEUZKd5HUdEJGb6LHczu9PM6s1sw2He/7yZrTOz9Wb2NzObGv2Y0fHCxr20dAW5YqZ2pIqIv/Vny/1uYN4R3t8BnOWcmwL8J7AgCrli4qHluxlVmMns0TojVUT8rc9yd84tARqP8P7fnHMHep8uAwblRdF37mtn6fb9XF45ShNyiIjvRXvM/TrgL1H+zKh4ZMVukgwum6EhGRHxv6idnmlmZxMp9zOOsMx8YD5AWVlZtFbdp2AozJ9WVnP2hGEMz88YsPWKiHglKlvuZnYScAdwsXNu/+GWc84tcM5VOucqi4sHbiLqxVsaaGjt5opZA/cPioiIl4653M2sDHgcuMo5t/XYI0Xfw29VMSw3nbMnDNw/KCIiXupzWMbMFgJzgCIzqwZuAVIBnHO3Az8AhgK/6z3jM+icq4xV4I+qvqWLv75dzz+fNYaU5IQ6rF9EElif5e6cu7KP978MfDlqiaLsqbU1hB1cOmNQHsQjIhITvt+U/fOaPZxUms+Y4hyvo4iIDBhfl/u2+jY27GnhoqmakENEEouvy/3JNXtIMlTuIpJwfFvuzjmeXFPDaWOKGJanY9tFJLH4ttxXVTVR1djBxZojVUQSkG/L/ck1e0hPSWLeicO9jiIiMuB8We6BUJhn1tVy7gkl5Gakeh1HRGTA+bLcX9+2j8b2Hg3JiEjC8mW5P7l6D/mZqcyZMMzrKCIinvBduXf0BHlxUx3nTxlBWorvvp6ISL/4rv1e2lRHR0+IT2tIRkQSmO/K/c+r9zAyP4OZFYVeRxER8Yyvyn1/WzdL3tnHhSeP1FR6IpLQfFXuz66vJRR2fPrk47yOIiLiKV+V+59X72FCSS4njMjzOoqIiKd8U+67GztYVdXExdO0I1VExDfl/tz6WgAuPEnlLiLim3J/fuNeTjwuj1GFWV5HERHxnC/KfW9zF6urmpg3WRcJExEBn5T7i5v2AjDvxBEeJxERGRx8Ue7Pb9jL2GE5jB2meVJFRMAH5d7Y3sObOxo1JCMicpC4L/dFm+oIhZ0m5RAROUjcl/vzG/dSWpDJ5JE6cUlE5D1xXe6tXQFef2cf8yYPx0zXkhEReU9cl/viLQ30hMIakhER+ZC4LvfnN9RSnJvO9LICr6OIiAwqcVvuXYEQi99uYO7kEl3eV0TkQ+K23JdsbaAzEGLeZJ24JCLyYXFb7s9v3Et+ZiqnjNaMSyIiHxaX5d4TDLNoUx3nnlBCanJcfgURkZjqsxnN7E4zqzezDYd538zs12a2zczWmdn06Mf8oGXb99PSFeSTOkpGROSQ+rPZezcw7wjvfxIY13ubD9x27LGO7PmNe8lKS+aMcUWxXpWISFzqs9ydc0uAxiMscjFwr4tYBgwxs5jt5QyFHS9urOPsicPISE2O1WpEROJaNAasjwN2H/S8uve1mFhVdYB9bd0akhEROYIB3RtpZvPNbIWZrWhoaDi6zwDOGl/MnAnDohtORMRHolHue4BRBz0v7X3tHzjnFjjnKp1zlcXFxUe1ssqKQu750ixy0lOO6s+LiCSCaJT7U8AXe4+aORVods7VRuFzRUTkKPW5+WtmC4E5QJGZVQO3AKkAzrnbgeeA84FtQAdwbazCiohI//RZ7s65K/t43wHXRy2RiIgcM53eKSLiQyp3EREfUrmLiPiQyl1ExIdU7iIiPmSRg108WLFZA7DrKP94EbAvinHigb5zYtB3TgzH8p3LnXN9ngXqWbkfCzNb4Zyr9DrHQNJ3Tgz6zolhIL6zhmVERHxI5S4i4kPxWu4LvA7gAX3nxKDvnBhi/p3jcsxdRESOLF633EVE5AjirtzNbJ6ZbemdkPu7XueJtb4mKPcjMxtlZovNbJOZbTSzb3qdKdbMLMPMlpvZ2t7v/COvMw0EM0s2s9Vm9ozXWQaCme00s/VmtsbMVsR0XfE0LGNmycBW4Dwi0/m9BVzpnNvkabAYMrMzgTYi89Se6HWegdA7B+8I59wqM8sFVgKf9vl/ZwOynXNtZpYKvA58s3deYt8ysxuBSiDPOXeB13lizcx2ApXOuZgf1x9vW+6zgG3Oue3OuR7gISITdPtWPyYo9x3nXK1zblXv41ZgMzGcl3cw6J1gvq33aWrvLX62vI6CmZUCnwLu8DqLH8VbuQ/oZNziPTOrAKYBb3qbJPZ6hyjWAPXAS845v3/nW4GbgLDXQQaQA140s5VmNj+WK4q3cpcEYmY5wGPAt5xzLV7niTXnXMg5dzKReYhnmZlvh+HM7AKg3jm30ussA+wM59x04JPA9b3DrjERb+Xe78m4Jb71jjs/BjzgnHvc6zwDyTnXBCwG5nmdJYZOBy7qHYN+CDjHzO73NlLsOef29N7XA08QGWqOiXgr97eAcWZ2vJmlAVcQmaBbfKR35+Ifgc3OuV96nWcgmFmxmQ3pfZxJ5KCBt71NFTvOuf/nnCt1zlUQ+T3+q3PuCx7Hiikzy+49QAAzywY+AcTsKLi4KnfnXBD4BvACkZ1sjzjnNnqbKrZ6JyhfCkwws2ozu87rTAPgdOAqIltza3pv53sdKsZGAIvNbB2RjZiXnHMJcXhgAikBXjeztcBy4Fnn3POxWllcHQopIiL9E1db7iIi0j8qdxERH1K5i4j4kMpdRMSHVO4iIj6kchcR8SGVu4iID6ncRUR86P8DqZTKaVzRXmsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t, x = simulate(model, timespan=timespan, x0=x0, control_vars={'u_0':2})\n",
    "plot(t,x)\n",
    "plt.savefig(\"RC_4.svg\", pad_inches=0, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let's suppose we drive it with a sinusional function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t, x = simulate(model, timespan=timespan, x0=x0, control_vars={'u_0':'sin(2*t)'})\n",
    "plot(t,x)\n",
    "plt.savefig(\"RC_5.svg\", pad_inches=0, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A step function?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "step_fn = 't < 1 ? 1 : 0' # if t < 0 then 1 else 0\n",
    "t, x = simulate(model, timespan=timespan, x0=x0, control_vars={'u_0':step_fn})\n",
    "plot(t,x)\n",
    "plt.savefig(\"RC_6.svg\", pad_inches=0, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One can also use loops to do parameter sweeps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "fig = plt.figure()\n",
    "\n",
    "for i in range(4):\n",
    "    func_text = \"cos({i}t)\".format(i=i)\n",
    "    t_i, x_i = simulate(model, timespan=timespan, x0=x0, control_vars={'u_0':func_text})\n",
    "    plot(t_i,x_i)\n",
    "\n",
    "plt.savefig(\"RC_7.svg\", pad_inches=0, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Part 4: ...and when it breaks.\n",
    "\n",
    "### What to do!\n",
    "1. Restart your kernal and try again.\n",
    "2. Come talk to me in my office or via email peter.cudmore@unimelb.edu.au\n",
    "3. If it is a bug: Add an issue to the github issue list, or email me. Please inculde all your code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}