{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "76a6ed14",
   "metadata": {},
   "source": [
    "# Interconnect Tutorial\n",
    "\n",
    "Sawyer B. Fuller 2023.04"
   ]
  },
  {
   "attachments": {
    "abea3596-e68b-445a-a86f-943dfcbde669.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "3cfc972b",
   "metadata": {},
   "source": [
    "### Goal: Create a single dynamic system that implements a complicated interconnected (ie, realistic) system such as the following:![image.png](attachment:abea3596-e68b-445a-a86f-943dfcbde669.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c56846b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np # numerical library\n",
    "import matplotlib.pyplot as plt # plotting library\n",
    "import control as ct # control systems library"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "9a123aa4",
   "metadata": {},
   "source": [
    "## preliminaries\n",
    "\n",
    "The representation of all systems in the interconnected system will be a linear, time-invariant system in state-space form given by\n",
    "\n",
    "$\\dot x = Ax + Bu$, <br>$y = Cx + Du$      \n",
    "\n",
    "for continuous-time systems, and \n",
    "\n",
    "$x[k+1] = Ax[k]+Bu[k]$<br> $~~~~~~~y[k]=Cx[k]+Du[k]$ \n",
    "\n",
    "for discrete-time systems. $x$ is the *state*, $u$ is the *input*, and $y$ is the *output*. All of which are possibly vector-valued. "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "c015dcd3",
   "metadata": {},
   "source": [
    "## auto-splitting\n",
    "\n",
    "A signal is automatically routed into every system that has an input of the same name\n",
    "\n",
    "```\n",
    "     u        y1\n",
    "u  +--> sys1 --->\n",
    "---|          \n",
    "   +--> sys2 --->\n",
    "     u        y2\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cbc685f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "\\left(\\begin{array}{rllrll|rll}\n",
       "-0.&\\hspace{-1em}1&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "\\hline\n",
       "0.&\\hspace{-1em}1&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "\\end{array}\\right)\n",
       "$$"
      ],
      "text/plain": [
       "StateSpace(array([[-0.1,  0. ],\n",
       "       [ 0. ,  0. ]]), array([[1.],\n",
       "       [1.]]), array([[0.1, 0. ],\n",
       "       [0. , 1. ]]), array([[0.],\n",
       "       [0.]]))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# arbitrary example systems\n",
    "sys1 = ct.tf(1, [10, 1], inputs='u', outputs='y1')\n",
    "sys2 = ct.tf(1, [1, 0], inputs='u', outputs='y2')\n",
    "\n",
    "# create interconnected system\n",
    "interconnected = ct.interconnect([sys1, sys2], inputs='u', outputs=['y1', 'y2'])\n",
    "display(interconnected) # 1-input, 2-output system"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "8d80cc7c",
   "metadata": {},
   "source": [
    "For this system, the input has a single value $[u]$, while the output is a two-element vector $y=[y1, y2]^T$."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "002e7111",
   "metadata": {},
   "source": [
    "## auto-summing\n",
    "\n",
    "Systems with output signals of the same name are automatically added.\n",
    "\n",
    "```\n",
    "  u1        y\n",
    "---> sys1 ---+ \n",
    "             |\n",
    "           + V    y\n",
    "             O----->\n",
    "           + ^\n",
    "             |\n",
    "---> sys2 ---+\n",
    "  u1        y\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6f932077",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "\\left(\\begin{array}{rllrll|rllrll}\n",
       "-0.&\\hspace{-1em}1&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "\\hline\n",
       "0.&\\hspace{-1em}1&\\hspace{-1em}\\phantom{\\cdot}&1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "\\end{array}\\right)\n",
       "$$"
      ],
      "text/plain": [
       "StateSpace(array([[-0.1,  0. ],\n",
       "       [ 0. ,  0. ]]), array([[1., 0.],\n",
       "       [0., 1.]]), array([[0.1, 1. ]]), array([[0., 0.]]))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sys1 = ct.tf(1, [10, 1], inputs='u1', outputs='y')\n",
    "sys2 = ct.tf(1, [1, 0], inputs='u2', outputs='y')\n",
    "\n",
    "# create interconnected system\n",
    "interconnected = ct.interconnect([sys1, sys2], inplist=['u1', 'u2'], outlist='y')\n",
    "display(interconnected) #  2-input, 1-output system"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "aa2b727c",
   "metadata": {},
   "source": [
    "## summing junctions\n",
    "\n",
    "Use a summing junction to interconnect signals of different names, or to change the sign of a signal. \n",
    "\n",
    "```\n",
    " u      w  \n",
    "---> O --->    \n",
    "     ^\n",
    "     | -v\n",
    "     |\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8d374ea0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "\\left(\\begin{array}{rllrll}\n",
       "1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&-1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "\\end{array}\\right)\n",
       "$$"
      ],
      "text/plain": [
       "StateSpace(array([], shape=(0, 0), dtype=float64), array([], shape=(0, 2), dtype=float64), array([], shape=(1, 0), dtype=float64), array([[ 1., -1.]]))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summer = ct.summing_junction(['u', '-v'], 'w') # w = u - v\n",
    "display(summer)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "aa2f9097",
   "metadata": {},
   "source": [
    "## constructing the goal system depicted above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b62a1549",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\n",
       "\\left(\\begin{array}{rllrllrllrll|rllrll}\n",
       "-2\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&-10\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&10\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "-2\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&-1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&-10\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&10\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0.&\\hspace{-1em}1&\\hspace{-1em}\\phantom{\\cdot}&-0.&\\hspace{-1em}01&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0.&\\hspace{-1em}1&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0.&\\hspace{-1em}1&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "\\hline\n",
       "0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&1\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}&0\\phantom{.}&\\hspace{-1em}&\\hspace{-1em}\\phantom{\\cdot}\\\\\n",
       "\\end{array}\\right)\n",
       "$$"
      ],
      "text/plain": [
       "StateSpace(array([[ -2.   ,   0.   ,   0.   , -10.   ],\n",
       "       [ -1.999,  -1.   ,   0.   , -10.   ],\n",
       "       [  0.   ,   0.1  ,  -0.01 ,   0.   ],\n",
       "       [  0.   ,   0.   ,   0.1  ,   0.   ]]), array([[10. ,  0. ],\n",
       "       [10. ,  0. ],\n",
       "       [ 0. ,  0.1],\n",
       "       [ 0. ,  0. ]]), array([[0., 0., 0., 1.]]), array([[0., 0.]]))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# constants\n",
    "K = 10\n",
    "zc = 0.001 # controller zero location\n",
    "pc = 2 # controller pole location\n",
    "tau = 1\n",
    "J = 100\n",
    "b = 1\n",
    "\n",
    "# systems\n",
    "C = ct.tf([K, K*zc],[1, pc], inputs='e', outputs='u')\n",
    "lopass = ct.tf(1, [tau, 1], inputs='u', outputs='v')\n",
    "P = ct.tf(1, [J, b], inputs='w', outputs='thetadot')\n",
    "integrator = ct.tf(1, [1, 0], inputs='thetadot', outputs='theta')\n",
    "error = ct.summing_junction(['thetaref', '-theta'], 'e') # e = thetaref-theta\n",
    "disturbance = ct.summing_junction(['d', 'v'], 'w') # w = d+v\n",
    "\n",
    "# interconnect everything based on signal names\n",
    "sys = ct.interconnect([C, lopass, P, integrator, error, disturbance], \n",
    "                       inputs=['thetaref', 'd'], outputs='theta')\n",
    "display(sys)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "897a9264",
   "metadata": {},
   "source": [
    "Finally, we can use the interconnected system just like we would use any other system object, such as computing step and frequency responses. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7a773597",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# extract system input-output pairs\n",
    "# index order is [output, input]\n",
    "plt.figure(figsize=(7,3))\n",
    "sys_thetaref_to_theta = sys[0, 0] \n",
    "sys_d_to_theta = sys[0, 1]\n",
    "t, y = ct.step_response(sys_thetaref_to_theta) # step response\n",
    "plt.plot(t,y)\n",
    "plt.figure(figsize=(7,3))\n",
    "t, yd = ct.step_response(sys_d_to_theta) # disturbance response\n",
    "plt.plot(t,yd);\n",
    "plt.figure(figsize=(7,5))\n",
    "ct.bode_plot(sys_thetaref_to_theta, plot=True);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}