{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# discrete_tf - Pythonize\n", "\n", "[`discretetf.py`](discretetf.py) - Use Python's syntactic sugar to 'pythonize' the Simulink Model. This class wraps the Simulink Model with some Python concepts. In addition to wrapping all of the functions with Python, it builds in a data-logger and plotting and pandas datadframes.\n", "\n", "This has been tested on both Windows and Linux. All of the python logic stays the same, the only difference is how the shared library is loaded.\n", "\n", "![](discrete_tf.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Python Setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import sys\n", "\n", "from discretetf import DiscreteTF\n", "\n", "mdl = DiscreteTF()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "discrete_tf<0.0, 0.0, 0.0>" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mdl.initialize()\n", "mdl" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "discrete_tf<0.0, 0.0, 0.0>" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mdl.step()\n", "mdl" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "discrete_tf<0.001, 0.0, 0.0>" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mdl.step()\n", "mdl" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0.0, 0.0014996250624921886]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mdl.num" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1.0, -0.9995001249791693]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mdl.den" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Validate against `control` toolbox." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "import control\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$$\\frac{0.0015}{z - 0.9995}\\quad dt = 0.001$$" ], "text/plain": [ "TransferFunction(array([0.00149963]), array([ 1. , -0.99950012]), 0.001)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# How fast the simulink model is running.\n", "Ts = 1e-3\n", "# Static Gain\n", "K = 3\n", "# Time Constant.\n", "tau = 2\n", "sys = control.TransferFunction([K], [tau, 1])\n", "sysd = control.c2d(sys, Ts)\n", "sysd" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[[array([0.00149963])]]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sysd.num" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0.0, 0.0014996250624921886]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mdl.num" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[[False, True]]])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.isclose(sysd.num, mdl.num)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[[array([ 1. , -0.99950012])]]" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sysd.den" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1.0, -0.9995001249791693]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mdl.den" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[[ True, True]]])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.isclose(sysd.den, mdl.den)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Pythonic Interactions" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "15.0" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mdl.initialize()\n", "for step in range(int(15 / Ts) + 1):\n", " mdl.step()\n", "mdl.time" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using the Datalogger" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "data = dict()\n", "mdl.init_log()\n", "for step in range(int(15 / Ts) + 1):\n", " mdl.step_log()\n", "mdl.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Step Response\n", "\n", "- Plot step response for a first order system with $\\tau=1s,2s,3s$ for K=1. Make the step at 2s.\n", "- The model is compiled with K=3, $\\tau=2s$\n", "- The simulink model is running at 0.001s." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEGCAYAAAB1iW6ZAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAAhOUlEQVR4nO3deXxV5b3v8c8vAwlCRAUEJGBQqKLIZABFPVqnolVRi1ZrrViH2qNWO5xb7bm1tuf2XHvrsZ7Wth60Dq04jzi1otUqCmiCzEMZZAiDhDCDQIbf/WMtIISE7MBeWXv4vl+v/Vprr72y9o9Avnl49rOex9wdERFJfzlxFyAiIsmhQBcRyRAKdBGRDKFAFxHJEAp0EZEMkRfXG3fq1MlLSkriensRkbRUXl6+xt07N/ZabIFeUlJCWVlZXG8vIpKWzGxJU6+py0VEJEMo0EVEMoQCXUQkQyjQRUQyhAJdRCRDNBvoZlZoZh+b2TQzm2VmP2/knAIze8bMFpjZZDMriaRaERFpUiIt9O3Ame4+ABgIjDCzkxqccx2wzt17A78BfpXUKkVEpFnNjkP3YH7dzeHT/PDRcM7dkcDd4f7zwANmZp6lc/POW7WJ16eviLsMEUkGd4w6zOvI8VrAyfFaDMe8FvM6jDpywq3V33odOdRiu64R7Pc+6iiGDRqQ9FITurHIzHKBcqA38Ht3n9zglO7AMgB3rzGzDUBHYE2D69wI3AjQs2fPA6s8hT38wSKeK6/ALO5KRFJLHjW0ZQdtqKaAatpYsC2gut6xmj2fU02BVdOGGgrYQQHV5FNDvtWSx56PfGrIpS7Yt2A/n1ryqAnPqSOPGvKpJdd2fk2wzaWWXOrIwcmhbve+Jb9dOqnqWzDod0m/bkKB7u61wEAzOwR4ycz6ufvMlr6Zu48BxgCUlpZmbOu91p3iQ9sy4cdnxl2KyP6rq4Mdm2H7Rti2cfd22wbYvgG2b4bqrbBjS7jdCtVbwm0Tx+uqD7yu3DbBIycPcvMhJz/cz2uwXxC+nlfv3Lx9f11OLlhO8Ni1nxvuW7398Pge5+3cb+r47q856bCjDvz70IgW3frv7uvN7F1gBFA/0JcDPYAKM8sDOgBVSatSRPafexDCW6tg69pw2/CxFr5YVy+8NwTbvXpXG5HXFtocBPntwu1B0KYdFHVr/Hh+W8grhLyCYJvbJnwebnMLdr+261i9bY4G5zWl2UA3s85AdRjmbYFz2PtDz3HANcBEYBTw92ztPxdpNbU1sGU1bFoJmz4PtpvD7aZVwWPz50Fg19U0fo2cfDioY/Boeygc0hMKO0DBwVB4cCPbDsHrhQdDm/ZBSCtgU0YiLfRuwONhP3oO8Ky7v2ZmvwDK3H0c8CfgL2a2AFgLXBFZxSLZomY7bKiA9Utg/VJYvyzcho9NK9m7BW3Q/nBo3wWKukK3AdCu8+7Q3vU4LNgWFKEPezJHIqNcpgODGjl+V739bcBlyS1NJAvU1QaBvWYBVM2HqgWwZj5ULYRNDUZKWS506A6HHAlHfxk6FAehXdQtDPBuQXjnxjaJqsRMf/NRUGeTNOQetKo/nxU+ZsDqubDuM6jdsfu8wg7QsQ8cdToc2ivoAtn5KOqmsJZ90r8OkWSrq4U1/4SKMlg5DT6fGYT49o27zzm0Fxx+HBwzIgjwjr2hU5+gG0RdILKfFOgR0c9kFtn0OSwvCwJ8eRks/xR2bApea1MEXY6HEy6Drv2gSz84vG/Qdy2SZAp0kZbauBKWfAiLP4DFE4J+bwjGMXfpBwO+Dt1LofuJQctbo0CklSjQRZqzfRMseg8WvBOE+M4ALzgYjhwOg6+BHsOgW/9gjLVITBToIg25Q+U8WDAe5r8FSyYGdzi2KYKSU+DE0VByKnTtH9wBKJIiFOgR0CCXNOQOK6bA7FeCx7rFwfHDj4OT/xX6nBu0wnPzYy1TZF8U6JK93GH5FJj9UhDi65cG/eC9Tofh3wtC/JAecVcpkjAFekQMDXNJWRtXwLSnYeqTwc08Oflw1Blw+o/hmPODuyhF0pACXbJDzQ6Y+2oQ4gv/Dl4HPU+G4bfCcRcF85iIpDkFumS2jSuh/FEoezSYyKpDDzjtRzDgCuh4dNzViSSVAl0y09JJMPlBmPNqcOfml74CQ26Ao8/UuHDJWAp0yRzusOBt+OC/YOnEYF6UYTfBkOvhsF5xVycSOQV6BDQVfCurqw1GqUy4D1bNgIOL4bxfw6CrggUVRLKEAl3SlzvMewPe+Q+onBNMcjXyD8G8KXlt4q5OpNUp0COiybki9tkH8M7PoeKTYL6UUY/CcSN156ZkNQW6pJfKf8Lf7gz6yg/uDhf9DgZ8Q/OEi6BAl3SxbSO8//9g0h+DRYfP+Q8YeoMmwxKpR4Euqc0dpj8L438aLHg86Jtw1t3QvnPclYmkHAV6BDTGJUnWLYFXb4NF78IRg+GKp6D4xLirEklZCnRJPXV18MnD8PbdwafL598LpdfphiCRZijQI6JBLvtp3WJ46buw9KPgrs4L/ztYIFlEmqVAl9Qx/Tl4/QfB/sg/wMBvaPynSAso0CV+2zfB6z+C6U8Hi0hc+hAcemTcVYmknWY7Jc2sh5m9a2azzWyWmd3WyDlnmNkGM5saPu6KplzJOKtmwIOnwYxn4fQ7YPQbCnOR/ZRIC70G+KG7TzGzIqDczMa7++wG533g7hckv0TJWNOfg3G3QttDYPTrwYLLIrLfmg10d18JrAz3N5nZHKA70DDQJaS5uZpRWw3j74JJf4Cew+Gyx6CoS9xViaS9Fo0DM7MSYBAwuZGXTzazaWb2ppkd38TX32hmZWZWVllZ2fJq04jpw7zGfbEO/nJJEOZDvwPXjFOYiyRJwh+Kmll74AXgdnff2ODlKcCR7r7ZzM4HXgb6NLyGu48BxgCUlpaqHZtt1i2GsZcF24sfhIFXxl2RSEZJqIVuZvkEYT7W3V9s+Lq7b3T3zeH+G0C+mXVKaqWS3irK4eGzYfNquPplhblIBBIZ5WLAn4A57n5fE+d0Dc/DzIaG161KZqGSxua9CY99NZhI67rxUHJK3BWJZKREulxOAa4GZpjZ1PDYT4CeAO7+IDAK+K6Z1QBfAFe4lu0RgBnPw4s3Qrf+8I1nof3hcVckkrESGeUygWbuZHf3B4AHklVUutNvslD548HkWkeeAt94GgqK4q5IJKNptiOJxsQ/wKvfg95nwVXPKcxFWoECPSJZPWjxoweCVYX6XghXPAltDoq7IpGsoLlcJLk+fgje+vdgfc+vPaKl4URakVrokjyfjoU3fgRfOg8ufVhhLtLKFOiSHDNfgHG3wFFfDm7lz2sTd0UiWUeBHoGsG7G56D148TvQ46Sgzzy/MO6KRLKSAl0OzOez4JmroWNvuPIpfQAqEiMFelSyYZjLhuXwxCho0w6++XwwDa6IxEafWsn+2bYBxo4KVhv69l+hQ3HcFYlkPQW6tFxdLbxwA6z5Z3DTUNd+cVckIijQZX+8+0uY/zc4/144+sy4qxGRkPrQpWVmvggf/BcM/hYMuT7uakSkHgV6BDJ20OLK6fDKzVA8NGida1UmkZSiQI9IxkXdtg3w7NVQ2AG+/hfIK4i7IhFpQH3o0jx3GHcrrF8G174JRV3jrkhEGqEWujSv7BGY/Qqc9VPoOSzuakSkCQp02beV0+Gvd0Lvs2H4bXFXIyL7oECXpm3fDM9fCwcdBpf8D+Ton4tIKlMfehQyZZjL+LugaiFc8yq06xR3NSLSDDW5pHEL3oayP8HJN0Ov0+KuRkQSoECPiKXzGO2ta+GVW6DzsXDmT+OuRkQSpC4X2dsb/wZbKuHKpzW3uUgaUQtd9jTrZZj5PJz+YzhiYNzViEgLKNBlty/WBa3zbgPg1B/EXY2ItFCzgW5mPczsXTObbWazzGyvwcgW+K2ZLTCz6WY2OJpy04On6zCXt++GrWvgwt9qgWeRNJTIT20N8EN3n2JmRUC5mY1399n1zjkP6BM+hgF/DLeSLpZ8BOWPwcm3qKtFJE0120J395XuPiXc3wTMAbo3OG0k8GcPTAIOMbNuSa82jaTVGJea7fDq7dChJ3z5J3FXIyL7qUV96GZWAgwCJjd4qTuwrN7zCvYOfczsRjMrM7OyysrKFpYqkZlwP6yZBxfcF6wPKiJpKeFAN7P2wAvA7e6+cX/ezN3HuHupu5d27tx5fy4hybZ+KUy4D46/BPqcE3c1InIAEgp0M8snCPOx7v5iI6csB3rUe14cHpNU99b/BsuBc/9P3JWIyAFKZJSLAX8C5rj7fU2cNg74Vjja5SRgg7uvTGKdEoXP3g+mxT31B9ChOO5qROQAJTLK5RTgamCGmU0Nj/0E6Ang7g8CbwDnAwuArcC1Sa80jXg6jFqsrYE3fwyH9ITht8RdjYgkQbOB7u4TaGbQhrs7cHOyisoEKT+VS/mjsHo2XP4XyG8bdzUikgS6UzQbfbEO3v0l9PoX6Hth3NWISJIo0LPRhPvhi/Xwlf9Mg/9KiEiiFOjZZsNymPwg9P86dD0h7mpEJIkU6Nnmvf8LXqc7QkUykAI9Aik7yqVyHkwdC0Ouh0OPjLsaEUkyBXo2eecXkN8OTvtR3JWISAQU6BGxVJuea9knMPc1OPU2aNcx7mpEJAIK9Gzxj3ug7WEw7LtxVyIiEVGgZ4OKcljwNgy/FQrax12NiEREgZ4NdrbOh94QdyUiEiEFegRSagm65eUw/61gvpaCorirEZEIKdAz3Xu/graHwtAb465ERCKmQI9IStxRv+JTmP83OPlmtc5FsoACPZNN+A0UdoCh34m7EhFpBQr0TFW1EGaPg9LroPDguKsRkVagQM9UEx+A3HwYdlPclYhIK1GgZ6LNlTD1SRhwBRR1ibsaEWklCvQIxD4518djoGY7DP9ezIWISGtSoGeaHVvgk4fg2K9Cpz5xVyMirUiBnmk+fSJYYk6tc5Gso0DPJHV1wWpExUOg57C4qxGRVqZAzyQL34G1izSyRSRLKdAzyeT/gfZdoO9FcVciIjFQoEcglkEuVQthwXgo/TbktYmjAhGJWbOBbmaPmNlqM5vZxOtnmNkGM5saPu5KfpnSrI8fgpx8OPHauCsRkZjkJXDOY8ADwJ/3cc4H7n5BUirKENaas3Nt3xws/nzcSN1IJJLFmm2hu/v7wNpWqEX21/SnYftGGKZJuESyWbL60E82s2lm9qaZHd/USWZ2o5mVmVlZZWVlkt46y7nDxw9Dt4HBcEURyVrJCPQpwJHuPgD4HfByUye6+xh3L3X30s6dOyfhrYWKT6ByDpRemyKTsItIXA440N19o7tvDvffAPLNrNMBV5bGWnUulymPQ3476Pe1VnxTEUlFBxzoZtbVwk8AzWxoeM2qA72uJGDbRpj5IvS7VCsSiUjzo1zM7CngDKCTmVUAPwPyAdz9QWAU8F0zqwG+AK5wj32+wdi1SufHzOeheiucOLo13k1EUlyzge7uVzbz+gMEwxqltU35Mxx+HHQ/Me5KRCQF6E7RdLVyerAI9OBr9GGoiAAK9PQ15XHILYD+l8ddiYikCAV6OqreBtOfg74XwkGHxV2NiKQIBXokIv5M+J9vwvYNMOiqaN9HRNKKAj0ikXZrT3sGirpBr9MjfBMRSTcK9HSzZU0wTe4JoyAnN+5qRCSFKNDTzcwXoa4G+l8RdyUikmIU6Olm+tPQpR907Rd3JSKSYhTo6WTNfFheDgPUOheRvSnQIxDZxAfTnwHLgRMui+gNRCSdKdDTRV1dEOhHnQFFXeOuRkRSkAI9Ikkftri8DNYvhf5fT/KFRSRTKNDTxayXglv9jzk/7kpEJEUp0NNBXR3Mehl6nw2FB8ddjYikKAV6Olg2GTatgOMvibsSEUlhCvQIJH2Qy6yXIK8QjhmR7CuLSAZRoKe6ulqY/Qr0OUfLzInIPinQI2LJWoRu6UTYvErdLSLSLAV6qpv1EuS1hT5fibsSEUlxCvRUtrO75UvnQkH7uKsRkRSnQE9lSyfClkp1t4hIQhToqWzu68HNRL3PibsSEUkDCvQIeDJm53KHua8Fc7eou0VEEqBAT1Wfzwzmbjn2q3FXIiJpotlAN7NHzGy1mc1s4nUzs9+a2QIzm25mg5NfZvo54Mm55r4OGBxzXjLKEZEskEgL/TFgX7congf0CR83An888LKEua9Bj2HQ/vC4KxGRNNFsoLv7+8DafZwyEvizByYBh5hZt2QVmJXWLYFVM9TdIiItkow+9O7AsnrPK8JjezGzG82szMzKKisrk/DWGWreG8FWgS4iLdCqH4q6+xh3L3X30s6dO7fmW7eqAx7jMvd16NwXOh6djHJEJEskI9CXAz3qPS8Oj8n+2LoWlnyk1rmItFgyAn0c8K1wtMtJwAZ3X5mE66a1/R7kMn88eK1WJhKRFstr7gQzewo4A+hkZhXAz4B8AHd/EHgDOB9YAGwFro2q2Kww/y1o1xmOGBR3JSKSZpoNdHe/spnXHbg5aRVls7paWPB20DrP0T1fItIySo1UUlEG29YHi1mIiLSQAj0C+z2Vy/y3wHLh6C8ntR4RyQ4K9FQy/63g7tC2h8ZdiYikIQV6VFo6mcvGlbBqurpbRGS/KdBTxYK3g22fc+OtQ0TSlgI9Vcx/C4qOgC7Hx12JiKQpBXoqqK2Ghe8G3S0HPO+uiGQrBXoqWDoJdmxSd4uIHBAFegRaPGpx4TuQkwdHnR5FOSKSJRToqWDRe1A8BAqK4q5ERNKYAj0iCfeEb10LK6bCUbqZSEQOjAI9bp+9DzgcdUbclYhImlOgx23Ru9CmCLqfGHclIpLmFOhxW/gu9DoNcpud+FJEZJ8U6BHwRGfnWvsZrF+i/nMRSQoFepwWvRts1X8uIkmgQI9IQjd8LnoPDu4OnfpEXY6IZAEFelzqamHRP4LWuW73F5EkUKDHZeW0YHUi9Z+LSJIo0OOy6L1gq9v9RSRJFOhxWTwBOh8L7Q+PuxIRyRAK9DjUVsOyyVByatyViEgGUaBHZJ8fc66cBjs2K9BFJKkU6HFY/EGwPfKUeOsQkYySUKCb2Qgzm2dmC8zsjkZeH21mlWY2NXxcn/xSM8jiD6HTMeo/F5GkanYCETPLBX4PnANUAJ+Y2Th3n93g1Gfc/ZYIaswstTWwdCL0vzzuSkQkwyTSQh8KLHD3Re6+A3gaGBltWRlslfrPRSQaiQR6d2BZvecV4bGGvmZm083seTPr0diFzOxGMyszs7LKysr9KDc97HNursUTgu2RCnQRSa5kfSj6KlDi7v2B8cDjjZ3k7mPcvdTdSzt37pykt04ziydAxz5Q1CXuSkQkwyQS6MuB+i3u4vDYLu5e5e7bw6cPA1m/WoM1Nj9LbQ0snaTuFhGJRCKB/gnQx8x6mVkb4ApgXP0TzKxbvacXAXOSV2IGWTUdtm9UoItIJJod5eLuNWZ2C/A3IBd4xN1nmdkvgDJ3Hwd8z8wuAmqAtcDoCGtOX0s+DLYafy4iEUho3TN3fwN4o8Gxu+rt3wncmdzSMtCSiXDYUXBwt+bPFcky1dXVVFRUsG3btrhLSQmFhYUUFxeTn5+f8NdoIcsIOI0Mc3EP5m/pc27rFySSBioqKigqKqKkpKTxz6CyiLtTVVVFRUUFvXr1SvjrdOt/a6laCFvXQM9hcVcikpK2bdtGx44dsz7MIRhU0bFjxxb/b0WBHpG9/kkumxRse5zU2qWIpA2F+W77871QoLeWpZOgsAN0+lLclYhIhlKgt5ZlH0OPYZCjb7lIqho+fHjSr7l48WKefPLJpF+3MUqX1rB1LayZFwS6iKSsjz76KOnXbM1A1yiX1rDs42DbU/3nIon4+auzmL1iY1KvedwRB/OzC4/f5znt27dn8+bNvPfee9x999106tSJmTNncuKJJ/LEE09gZpSUlHD55Zfz5ptv0rZtW5588kl69+7N6NGjueCCCxg1atQe17rjjjuYM2cOAwcO5JprruH73/9+Uv9c9amFHoG9JudaNgly8uCIwbHUIyIt9+mnn3L//fcze/ZsFi1axIcffrjrtQ4dOjBjxgxuueUWbr/99n1e55577uG0005j6tSpkYY5qIUemT0+oF46GboNgDYHxVaPSDppriXdGoYOHUpxcTEAAwcOZPHixZx6ajBtx5VXXrlrG3VIt4Ra6FGr2QErpmi4okiaKSgo2LWfm5tLTU3Nruf1hxTu3M/Ly6Ourg6Auro6duzY0UqV7qZAj9rKaVCzTTcUiWSQZ555Ztf25JNPBqCkpITy8nIAxo0bR3V1NQBFRUVs2rSpVepSl0vUlk0OthrhIpIx1q1bR//+/SkoKOCpp54C4IYbbmDkyJEMGDCAESNG0K5dOwD69+9Pbm4uAwYMYPTo0ZF20Zjvc3md6JSWlnpZWVks7x21bzw0ieraOp67aTg8c3XQSr99etxliaS0OXPm0Ldv37jLaFZJSQllZWV06tQp8vdq7HtiZuXuXtrY+epyicAevyOXl0PxkNhqEZHsoS6XKG1cCRuXQ/esX8BJJGMsXrw47hKapBZ6RAwLWucAxY3+70hEJKkU6FFaXhbcUNT1hLgrEZEsoECP0vJy6NIP8tvGXYmIZAEFekTMa2H5p+puEZFWo0CPgOMcUVsBOzbpA1GRDPbYY4+xYsWK/f76ZM/EqECPSJ8d84Kd7mqhi2SqVAt0DVuMSO+aeVDQATr2jrsUkfTz5h2wakZyr9n1BDjvnmZPu++++3jkkUcAuP7667n44ou54IILmDlzJgD33nsvmzdvpl+/fpSVlXHVVVfRtm1bJk6cSN++fWOdWlct9Ij03jEXug/SCkUiaaS8vJxHH32UyZMnM2nSJB566CHWrVvX6LmjRo2itLSUsWPHMnXqVNq2DQY/xDm1rlroEWhTt40jaz6D7pfEXYpIekqgJR2FCRMmcMkll+yah+XSSy/lgw8+aNE14pxaN6Hmo5mNMLN5ZrbAzO5o5PUCM3smfH2ymZUkvdI0UlK9kFzq9IGoSAZYv379rmlxAbZt27bP8+OcWrfZQDezXOD3wHnAccCVZnZcg9OuA9a5e2/gN8Cvkl1oOuldPTfYUaCLpJXTTjuNl19+ma1bt7JlyxZeeuklzjvvPFavXk1VVRXbt2/ntdde23V+Y1Pjxjm1biJdLkOBBe6+CMDMngZGArPrnTMSuDvcfx54wMzMI5jKcfp7L9Dh/Z9hOBBcfufvQ8PD4+yaIcvC4+HBPc5lj9f2PLb7d2z9Y42fu6uG8D2v8G1U5h1O56IuB/aHFZFWNXjwYEaPHs3QoUOB4EPRIUOGcNdddzF06FC6d+/Oscceu+v80aNHc9NNN+36UBTinVq32elzzWwUMMLdrw+fXw0Mc/db6p0zMzynIny+MDxnTYNr3QjcCNCzZ88TlyxZ0uKC537yNlv+8dudV9wVvXtErTWM7Ybn1otrs0Ze3/trguvuPr7zOo2ea0a7Y89i6IhvtvjPJ5Kt0mX63H1J9tS6LZ0+t1U/FHX3McAYCOZD359rHDvkbBhydlLrEhHJBIkE+nKgR73nxeGxxs6pMLM8oANQlZQKRUTSRNxT6yYyyuUToI+Z9TKzNsAVwLgG54wDrgn3RwF/j6L/XEQym2Jjt/35XjQb6O5eA9wC/A2YAzzr7rPM7BdmdlF42p+Ajma2APgBsNfQRhGRfSksLKSqqkqhThDmVVVVFBYWtujrtKaoiKSE6upqKioqmh3nnS0KCwspLi4mPz9/j+Mp86GoiEhT8vPz6dWrV9xlpDVNNCIikiEU6CIiGUKBLiKSIWL7UNTMKoGW3yoa6ASsafaseKnGA5fq9UHq15jq9YFqbKkj3b1zYy/EFugHwszKmvqUN1WoxgOX6vVB6teY6vWBakwmdbmIiGQIBbqISIZI10AfE3cBCVCNBy7V64PUrzHV6wPVmDRp2YcuIiJ7S9cWuoiINKBAFxHJEGkX6M0tWB03M+thZu+a2Wwzm2Vmt8VdU2PMLNfMPjWz15o/u/WZ2SFm9ryZzTWzOWZ2ctw11Wdm3w//fmea2VNm1rJp8aKp6REzWx2uILbz2GFmNt7M5ofbQ1Owxl+Hf8/TzewlMzskleqr99oPzczNLDnLEUUgrQI9wQWr41YD/NDdjwNOAm5OwRoBbiOYDjlV/TfwV3c/FhhACtVqZt2B7wGl7t4PyCVYJyBujwEjGhy7A3jH3fsA7xD/1NaPsXeN44F+7t4f+CdwZ2sXVc9j7F0fZtYDOBdY2toFtURaBTr1Fqx29x3AzgWrU4a7r3T3KeH+JoIg6h5vVXsys2Lgq8DDcdfSGDPrAPwLwTz7uPsOd18fa1F7ywPahit0HQSsiLke3P19YG2DwyOBx8P9x4GLW7Omhhqr0d3fCtddAJhEsCpaLJr4HgL8Bvhf1F9yOAWlW6B3B5bVe15BioVlfWZWAgwCJsdcSkP3E/zjrIu5jqb0AiqBR8NuoYfNrF3cRe3k7suBewlaayuBDe7+VrxVNamLu68M91cBXeIsJgHfBt6Mu4j6zGwksNzdp8VdS3PSLdDThpm1B14Abnf3jXHXs5OZXQCsdvfyuGvZhzxgMPBHdx8EbCH+roJdwn7okQS/eI4A2pnZN+OtqnnhspAp28I0s38n6LIcG3ctO5nZQcBPgLviriUR6RboiSxYHTszyycI87Hu/mLc9TRwCnCRmS0m6LI608yeiLekvVQAFe6+8382zxMEfKo4G/jM3SvdvRp4ERgec01N+dzMugGE29Ux19MoMxsNXABclWLrER9N8It7WvgzUwxMMbOusVbVhHQL9EQWrI6VmRlB3+8cd78v7noacvc73b3Y3UsIvn9/d/eUal26+ypgmZkdEx46C5gdY0kNLQVOMrODwr/vs0ihD20bqL+A+zXAKzHW0igzG0HQBXiRu2+Nu5763H2Gux/u7iXhz0wFMDj8N5py0irQm1qwOt6q9nIKcDVBy3dq+Dg/7qLS0K3AWDObDgwE/jPecnYL/+fwPDAFmEHwcxT7reFm9hQwETjGzCrM7DrgHuAcM5tP8D+Le1KwxgeAImB8+PPyYIrVlzZ067+ISIZIqxa6iIg0TYEuIpIhFOgiIhlCgS4ikiEU6CIiGUKBLlkjnMHxX8P9I8zs+bhrEkkmDVuUrBHOrfNaOEOiSMbJi7sAkVZ0D3C0mU0F5gN93b1feNv5xUA7oA/BxFttCG4Q2w6c7+5rzexogumbOwNbgRvcfW5r/yFEmqIuF8kmdwAL3X0g8G8NXusHXAoMAX4JbA0nBpsIfCs8Zwxwq7ufCPwI+ENrFC2SKLXQRQLvhvPXbzKzDcCr4fEZQP9w9szhwHPB9C0AFLR+mSJNU6CLBLbX26+r97yO4OckB1gftu5FUpK6XCSbbCKYBKrFwjntPzOzyyCYVdPMBiSzOJEDpUCXrOHuVcCH4QLAv96PS1wFXGdm04BZpNjyhyIatigikiHUQhcRyRAKdBGRDKFAFxHJEAp0EZEMoUAXEckQCnQRkQyhQBcRyRD/H9WvLJSwN0gSAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Ts = 0.001\n", "K = 1\n", "dataframes = list()\n", "for tau in [1, 2, 3]:\n", " sys = control.TransferFunction([K], [tau, 1])\n", " sysd = control.c2d(sys, Ts)\n", " mdl.num = sysd.num[0][0]\n", " mdl.den = sysd.den[0][0]\n", " mdl.init_log()\n", " for step in range(int(15 / Ts)):\n", " mdl.input_signal = 3 if mdl.time >= 2 else 0\n", " mdl.step_log()\n", " mdl.plot()\n", " dataframes.append(mdl.dataframe)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- Rename the data columns with their respective timeconstants\n", "- Merge into a single dataframe.\n", "- Plot all of the step responses on top of each other." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "dataframes[0].rename(columns={\"output\": \"output_tau1\"}, inplace=True)\n", "dataframes[1].rename(columns={\"output\": \"output_tau2\"}, inplace=True)\n", "dataframes[2].rename(columns={\"output\": \"output_tau3\"}, inplace=True)\n", "\n", "df = dataframes[0].append(dataframes[1]).append(dataframes[2])\n", "\n", "df.plot(x=\"time\", y=[\"output_tau1\", \"output_tau2\", \"output_tau3\"]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Sine Response\n", "\n", "- Input a sine-wave to the system. Estimate the mag/phase and compare to the ```control.bode``` function." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "import random" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "# Generate an unknown first order transfer function.\n", "K = random.randint(1, 10)\n", "tau = random.randint(1, 10)\n", "sys = control.TransferFunction([K], [tau, 1])\n", "sysd = control.c2d(sys, Ts)\n", "mdl.num = sysd.num[0][0]\n", "mdl.den = sysd.den[0][0]" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "def input_fcn(step, freq):\n", " \"\"\"Function to simplify calculate sine response given step and frequency (hz).\"\"\"\n", " return np.sin(2 * np.pi * freq * step / 1000)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mdl.init_log()\n", "for step in range(int(2 / Ts)):\n", " mdl.input_signal = input_fcn(step, 1)\n", " mdl.step_log()\n", "mdl.plot()\n", "dataframes.append(mdl.dataframe)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "f = 0.1\n", "cycles = 10\n", "mdl.init_log()\n", "for step in range(int((cycles * 1 / f) / Ts)):\n", " mdl.input_signal = input_fcn(step, f)\n", " mdl.step_log()\n", "mdl.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Select the last half of the data after it has 'setttled'." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "df = mdl.dataframe[int(len(mdl.dataframe) / 2) :]\n", "df.plot(x=\"time\", y=[\"input\", \"output\"])" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.input.max()" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.3077727333628815" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.output.max()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "from scipy.optimize import minimize\n", "from sklearn.metrics import mean_squared_error" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ " fun: 1.2575742218969943e-08\n", " hess_inv: array([[ 1.1534359 , -0.00529581, 0.16281604],\n", " [-0.00529581, 0.16905652, -0.0042234 ],\n", " [ 0.16281604, -0.0042234 , 0.67266656]])\n", " jac: array([-2.07334194e-06, -4.32183696e-07, -4.37765321e-06])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 40\n", " nit: 8\n", " njev: 10\n", " status: 0\n", " success: True\n", " x: array([ 2.30752107e+00, -1.31180928e+00, 6.21330875e-05])" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def minfunc(*args):\n", " \"\"\"Function to calculate error between estimate function and output.\"\"\"\n", " # Amplitude\n", " A = args[0][0]\n", " # Phase in Radians/s\n", " phi = args[0][1]\n", " # DC Offset\n", " dc = args[0][2]\n", "\n", " output_p = A * np.sin(2 * np.pi * f * df.time + phi) + dc\n", " # Return the mean squared between estimate function and actual output.\n", " return mean_squared_error(output_p, df.output)\n", "\n", "\n", "# Initial conditions\n", "x0 = [df.output.max(), 0, 0]\n", "results = minimize(minfunc, x0)\n", "results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Calculate the bode function at a given frequency f and return the magnitude and phase." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "mag=[2.30752317]@[0.1]Hz\n", "phase=[-1.31182349]@[0.1]Hz\n" ] } ], "source": [ "mag, phase, omega = control.bode(sysd, omega=[2 * np.pi * f], plot=False)\n", "print(f\"mag={mag}@{omega/(2*np.pi)}Hz\")\n", "print(f\"phase={phase}@{omega/(2*np.pi)}Hz\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The magnitude and phase of the output signal match the bode analysis results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Magnitude difference between `control.bode` function results and estimated function. " ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([2.10128312e-06])" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mag - results.x[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Phase difference between `control.bode` function results and estimated function. " ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-1.42067947e-05])" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "phase - results.x[1]" ] } ], "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }