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     "link": "[](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html)",
     "section": ""
    }
   },
   "source": [
    "<!--NOTEBOOK_HEADER-->\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/A.03-Modular-Simulation-using-Python-Generators.html)",
     "section": ""
    }
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [A.2 Modular Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.02-Modular-Approach-to-Simulation-using-Python-Generators.html) | [Contents](toc.html) | [A.4 Animation in Jupyter Notebooks](https://jckantor.github.io/CBE32338/A.04-Animation-in-Jupyter-Notebooks.html) ><p><a href=\"https://colab.research.google.com/github/jckantor/CBE32338/blob/master/docs/A.03-Modular-Simulation-using-Python-Generators.ipynb\"> <img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open in Google Colaboratory\"></a><p><a href=\"https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.ipynb\"> <img align=\"left\" src=\"https://img.shields.io/badge/Github-Download-blue.svg\" alt=\"Download\" title=\"Download Notebook\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "# A.3 A Modular Approach to Simulation using Python Generators\n",
    "\n",
    "by Jeffrey Kantor  (jeff at nd.edu). The latest version of this notebook is available at [https://github.com/jckantor/CBE30338](https://github.com/jckantor/CBE30338). \n",
    "\n",
    "### Summary\n",
    "\n",
    "This notebook demonstrates shows how to use the Python generators for simulation. This technique implements simulation blocks as Python generators, and shows how to piece blocks together to simulate more complex systems. This is an advanced technique that may be useful in certain projects and a convenient alternative to block diagram simulators.\n",
    "\n",
    "### Table of Contents\n",
    "\n",
    "1. [Simulation using scipy.integrate.odeint()](#section1)\n",
    "    1. [Typical Usage](#section1-1)\n",
    "    2. [What's Wrong with That? ](#section1-2)<br><br>\n",
    "2. [Python Generators](#section2)\n",
    "    1. [Yield Statement](#section2-1)\n",
    "    2. [Iterators](#section2-2)\n",
    "    3. [Two-way communcation with Generators using Send](#section2-3)<br><br>\n",
    "3. [Example Application: Modeling Gravity-Drained Tanks with Python Generators](#section3)\n",
    "    1. [Generator for a Gravity-Drained Tank](#section3-1)\n",
    "    2. [Simulation of a Single Tank with Constant Inflow](#section3-2)\n",
    "    3. [Simulation of Two Tanks in Series](#section3-3)\n",
    "    4. [Simulation of Two Tanks in Series with PI Level Control on the Second Tank](#section3-4)\n",
    "    5. [Adding a PI Control Generator](#section3-5)\n",
    "    6. [Implementing Cascade Control for Two Tanks in Series with Unmeasured Disturbance](#section3-6)<br><br>\n",
    "4. [Enhancing Modularity with Class Definitions for Process Units](#section4)\n",
    "    1. [Gravity-Drained Tank Class](#section4-1)\n",
    "    2. [PI Controller Class](#section4-2)\n",
    "    3. [Modular Simulation of Cascade Control for Two Tanks in Series](#section4-3)<br><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<a id='section1'></a>\n",
    "## Simulation using scipy.integrate.odeint()\n",
    "\n",
    "<a id='section1-1'></a>\n",
    "### Typical Usage\n",
    "\n",
    "The SciPy library provides a convenient and familiar means of simulating systems modeled by systems of ordinary differential equations.  As demonstrated in other notebooks, the straightforward approach consists of several common steps\n",
    "\n",
    "1. Initialize graphics and import libraries\n",
    "2. Fix parameter values\n",
    "3. Write a function to evaluate RHS of the differential equations\n",
    "4. Choose initial conditions and time grid\n",
    "5. Perform the simulation by numerical solution of the differential equations\n",
    "6. Prepare visualizations and post-processing\n",
    "\n",
    "Here we demonstrate this approach for a two gravity-drained tanks connected in series with constant inflow."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [
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XmWM8um9BTSm8/AOn2WjGt7xZhjEmKVlSiLJ1e4+xrqiMa84einh1aOg/fgTV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\nScEYY0yT/w/LWN3tD38gFwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x104aa5940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1. Initialize graphics and import libraries\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "\n",
    "# 2. Fix parameter values\n",
    "A = 0.2\n",
    "Cv = 0.5\n",
    "qin = 0.4\n",
    "\n",
    "# 3. Write a function to evaluate RHS of the differential equations\n",
    "def deriv(X,t,qin=0):\n",
    "    h1,h2 = X\n",
    "    dh1 = (qin - Cv*np.sqrt(h1))/A\n",
    "    dh2 =  (Cv*np.sqrt(h1) - Cv*np.sqrt(h2))/A \n",
    "    return [dh1,dh2]\n",
    "\n",
    "# 4. Choose initial conditions and time grid\n",
    "IC = [0,0]\n",
    "t = np.linspace(0,8,500)\n",
    "\n",
    "# 5. Perform the simulation by numerical solution of the differential equations\n",
    "sol = odeint(deriv,IC,t,args=(qin,))\n",
    "\n",
    "# 6. Prepare visualizations and post-processing\n",
    "plt.plot(t,sol)\n",
    "plt.legend(['Tank 1','Tank 2'])\n",
    "plt.xlabel('Time')\n",
    "plt.ylabel('Height [m]')\n",
    "plt.title('Simulation of Two Gravity-Drained Tanks in Series')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<a id='section1-2'></a>\n",
    "## What's Wrong with That?\n",
    "\n",
    "If direct simulation as outlined above meets the needs of your project, then be satisfied and move on. This is how these tools are intended to be used.\n",
    "\n",
    "However, as written above, simulation with scipy.integrate.odeint requires you to write a function that calculates the right hand side of a system of differential equations. This can be challenging for complex system. For example, you may have multiple PID controllers, each implementing logic for anti-reset windup. Or you may have components in the process that exhibit hysterisis, time-delay, or other difficult-to-model dynamics. These cases call for a more modular approach to modeling and simulation.\n",
    "\n",
    "In these cases we'd like to combine the continous time dynamics modeled by differential equations with more complex logic executed at discrete points in the time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<a id='section2'></a>\n",
    "## Python Generators\n",
    "\n",
    "<a id='section2-1'></a>\n",
    "### Yield Statement\n",
    "\n",
    "One of the more advanced and often overlooked features of Python is the use of [generators and iterators](http://nvie.com/posts/iterators-vs-generators/) for performing operations on sequences of information. In particular, a generator is a function that returns information to via the `yield` statement rather then the more commonly encountered return statement. When called again, the generator picks right up at the point of the yield statement.\n",
    "\n",
    "Let's demonsrate this by writing a generator of Fibonacci numbers. This generator returns all Fibonacci numbers less or equal to a given number $n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [],
   "source": [
    "def fib(n):\n",
    "    i = 0\n",
    "    j = 1\n",
    "    while j <= n:\n",
    "        yield j\n",
    "        i,j = j,i+j"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "Here's a typical usage.  What are the Fibonacci numbers less than or equal to 100?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "1\n",
      "2\n",
      "3\n",
      "5\n",
      "8\n",
      "13\n",
      "21\n",
      "34\n",
      "55\n",
      "89\n"
     ]
    }
   ],
   "source": [
    "for k in fib(100):\n",
    "    print(k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "The generator can also be used inside list comprehensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[k for k in fib(1000)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<a id='section2-2'></a>\n",
    "### Iterators\n",
    "\n",
    "When called, a generator function creates an intermediate function called an iterator. Here we construct the iterator  and use it within a loop to find the first 10 Fibonacci numbers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "1\n",
      "2\n",
      "3\n",
      "5\n",
      "8\n",
      "13\n",
      "21\n",
      "34\n",
      "55\n"
     ]
    }
   ],
   "source": [
    "f = fib(500)\n",
    "for k in range(0,10):\n",
    "    print(next(f))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "Using `next` on an iterator returns the next value. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<a id='section2-3'></a>\n",
    "### Two-way communcation with Generators using Send\n",
    "\n",
    "So far we have demonstrated the use of `yield` as a way to communicate information from the generator to the calling program. Which is fine if all you need is one-way communication. But for the modular simulation of processes, we need to be able to send information both ways.  A feedback control module, for example, will need to obtain current values of the process variable in order to update its internal state to provide an update of the manipulated variable to calling programm.\n",
    "\n",
    "Here's the definition of a generator for negative feedback proportional control where the control gain $K_p$ and setpoint $SP$ are specified constants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [],
   "source": [
    "def proportionalControl(Kp,SP):\n",
    "    MV = None\n",
    "    while True:\n",
    "        PV = yield MV\n",
    "        MV = Kp*(SP-PV)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "The `yield` statement is now doing double duty.  When first called it sends the value of MV back to the calling program, then stops and waits. It is waiting for the calling program to send a value of PV using the `.send()` method. Execution resumes until the yield statement is encountered again and the new value of MV returned to the calling program.\n",
    "\n",
    "With this behavior in mind, gettting the generator ready for use is a two step process. The first step is to create an instance (i.e., an iterator).  The second step is to initialize the instance by issuing `.send(None)` command.  This is will halt execution at the first `yield` statement. At that point the generator instance will be ready to go for subsequent simulation.\n",
    "\n",
    "Here's the initialization of a new instance of proportional control with $K_p = 2.5$ and $SP = 2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [],
   "source": [
    "pc = proportionalControl(2.5,2)\n",
    "pc.send(None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "This shows it in use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 5.0\n",
      "1 2.5\n",
      "2 0.0\n",
      "3 -2.5\n",
      "4 -5.0\n"
     ]
    }
   ],
   "source": [
    "for PV in range(0,5):\n",
    "    print(PV, pc.send(PV))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "You can verify that these results satisfy the proportional control relationship."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<a id='section3'></a>\n",
    "## Example Application: Modeling Gravity-Drained Tanks with Python Generators"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "The first step in using a Python generator for simulation is to write the generator. It will be used to create instances of the dynamical process being modeled by the generator. Parameters should include a sample time `dt` and any other model parameters you choose to specify a particular instance of the process. The yield statement should provide time plus any other relevant process data. The yield statement will produce new values of process inputs valid for the next time step.\n",
    "\n",
    "<a id='section3-1'></a>\n",
    "### Generator for a Gravity-Drained Tank"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [],
   "source": [
    "# generator for a gravity-drained tank model\n",
    "\n",
    "def gravtank_generator(dt, A=1, Cv=1, IC=0):\n",
    "    \n",
    "    def qout(h):\n",
    "        return Cv*np.sqrt(float(h))\n",
    "    \n",
    "    def deriv(h,t):\n",
    "        dh = (qin - qout(h))/A\n",
    "        return dh\n",
    "    \n",
    "    h = IC\n",
    "    t = 0\n",
    "    while True:\n",
    "        qin = yield t,qout(h),float(h)\n",
    "        h = odeint(deriv,h,[t,t+dt])[-1]\n",
    "        t += dt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<a id='section3-2'></a>\n",
    "### Simulation of a Single Tank with Constant Inflow\n",
    "\n",
    "Next we show how to use the generator to create a simulation consisting of a single gravity drained tank with constant inflow.\n",
    "\n",
    "1. Choose a sample time for the simulation.\n",
    "2. Create instances of the processes to be used in your simulation.\n",
    "3. The first call to an instance is f.send(None). This will return the initial condition.\n",
    "4. Subsequent calls to the instance should be f.send(u) where u is variable, tuple, or other data time being passed to the process. The return value will be a tuple contaning the next value of time plus other process data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [
    {
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83Olhmc68/PLLPP744wBcddVVVFVVUVtby6JFi1i3bh35+fl89rOfZeXKlVRU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\niA8p3EVEfEjhLiLiQ/8f0QpgsygntOMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x104aa5828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 1. select sample time\n",
    "dt = 0.02\n",
    "\n",
    "# 2. create a process instance\n",
    "tank = gravtank_generator(dt, A=0.2, Cv=.5)\n",
    "\n",
    "# 3. get initial condition\n",
    "y = [tank.send(None)]\n",
    "\n",
    "# 4. append subsequent states \n",
    "y += [tank.send(0.5) for t in np.arange(0,10,dt)]\n",
    "\n",
    "# 5. extract information into numpy arrays for plotting\n",
    "t,q,h = np.asarray(y).transpose()\n",
    "plt.plot(t,q,t,h)\n",
    "plt.xlabel('Time')\n",
    "plt.legend(['Outlet Flow','Level'])\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<a id='section3-3'></a>\n",
    "### Simulation of Two Tanks in Series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x111f5a7f0>,\n",
       " <matplotlib.lines.Line2D at 0x11213bf28>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XsH7Dz7oD61i0exEfFn9Iq9HK8LTh/HDyD5kzeA5DU4daNpYQIrpFb7h76qFu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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111f5a7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dt = 0.02\n",
    "\n",
    "tank1 = gravtank_generator(dt, A=0.2, Cv=.5)\n",
    "tank2 = gravtank_generator(dt, A=0.2, Cv=.5)\n",
    "\n",
    "y1 = [tank1.send(None)]\n",
    "y2 = [tank2.send(None)]\n",
    "\n",
    "for t in np.arange(dt,10,dt):\n",
    "    t1,q1,h1 = tank1.send(0.5)\n",
    "    t2,q2,h2 = tank2.send(q1)\n",
    "    \n",
    "    y1.append([t1,q1,h1])\n",
    "    y2.append([t2,q2,h2])\n",
    "    \n",
    "t1,q1,h1 = np.asarray(y1).transpose()\n",
    "t2,q2,h2 = np.asarray(y2).transpose()\n",
    "plt.plot(t1,q1,t1,h1)\n",
    "plt.plot(t2,q2,t2,h2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<a id='section3-4'></a>\n",
    "### Simulation of Two Tanks in Series with PI Level Control on the Second Tank"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1123d0240>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hQ3Gc7l6hiqIoUTQwgnv1fuOcMjyqxQaLimjYsIHESy/tG9voKYqiNBsYwb2q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\nM7MMubibmWXIxd3MLEMu7mZmGfoXWDNaEUx1pSwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111f54518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dt = 0.02\n",
    "\n",
    "tank1 = gravtank_generator(dt, A=0.2, Cv=.5)\n",
    "tank2 = gravtank_generator(dt, A=0.2, Cv=.5)\n",
    "\n",
    "y1 = [tank1.send(None)]\n",
    "y2 = [tank2.send(None)]\n",
    "\n",
    "u = 0.0\n",
    "r2 = 1.5\n",
    "Kp = .6\n",
    "Ki = .6\n",
    "ecurr = 0\n",
    "ulog = [u]\n",
    "\n",
    "for t in np.arange(dt,10,dt):\n",
    "    t1,q1,h1 = tank1.send(u)\n",
    "    t2,q2,h2 = tank2.send(q1)\n",
    "    \n",
    "    eprev,ecurr = ecurr,r2-h2\n",
    "    u += Kp*(ecurr-eprev) + Ki*ecurr*dt\n",
    "    u = max(0,min(1,u))\n",
    "    \n",
    "    y1.append([t1,q1,h1])\n",
    "    y2.append([t2,q2,h2])\n",
    "    ulog.append(u)\n",
    "    \n",
    "t1,q1,h1 = np.asarray(y1).transpose()\n",
    "t2,q2,h2 = np.asarray(y2).transpose()\n",
    "plt.plot(t1,q1,t1,h1)\n",
    "plt.plot(t2,q2,t2,h2)\n",
    "plt.plot(t1,ulog)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<a id='section3-5'></a>\n",
    "### Adding a PI Control Generator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [],
   "source": [
    "def PI_generator(dt, Kp, Ki, MVmin = 0, MVmax = np.Inf):\n",
    "\n",
    "    ecurr = 0\n",
    "    eprev = 0\n",
    "    t = 0\n",
    "    u = MVmin\n",
    "    \n",
    "    while True:\n",
    "        r,y,u = yield t,u\n",
    "        eprev,ecurr = ecurr,r-y\n",
    "        u += Kp*(ecurr - eprev) + Ki*ecurr*dt\n",
    "        u = max(MVmin,min(MVmax,u))\n",
    "        t += dt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1124d7c50>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hQ3Gc7l6hiqIoUTQwgnv1fuOcMjyqxQaLimjYsIHESy/tG9voKYqiNBsYwb2q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\nM7MMubibmWXIxd3MLEMu7mZmGfoXWDNaEUx1pSwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112380f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dt = 0.02\n",
    "\n",
    "tank1 = gravtank_generator(dt, A=0.2, Cv=.5)\n",
    "tank2 = gravtank_generator(dt, A=0.2, Cv=.5)\n",
    "pi = PI_generator(dt, Kp = 0.6, Ki = 0.6, MVmin = 0, MVmax = 1)\n",
    "\n",
    "y1 = [tank1.send(None)]\n",
    "y2 = [tank2.send(None)]\n",
    "ulog = [pi.send(None)[1]]\n",
    "\n",
    "u = 0\n",
    "\n",
    "for t in np.arange(dt,10,dt):\n",
    "    t1,q1,h1 = tank1.send(u)\n",
    "    t2,q2,h2 = tank2.send(q1)\n",
    "    t3,u = pi.send((r2,h2,u))\n",
    "    \n",
    "    y1.append([t,q1,h1])\n",
    "    y2.append([t,q2,h2])\n",
    "    ulog.append(u)\n",
    "    \n",
    "t1,q1,h1 = np.asarray(y1).transpose()\n",
    "t2,q2,h2 = np.asarray(y2).transpose()\n",
    "\n",
    "plt.plot(t1,q1,t1,h1)\n",
    "plt.plot(t2,q2,t2,h2)\n",
    "plt.plot(t1,ulog)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<a id='section3-6'></a>\n",
    "\n",
    "### Implementing Cascade Control for Two Tanks in Series with Unmeasured Disturbance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1125c0710>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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FnXsDjxPWzzESe0z73Rlr5i/AV1wsbe1CiKgSTnLPBfaFvC4M7gv1JDAK2A+s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\n7o7jOF3IL+F3WjNQRyOLAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112489b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# disturbance function\n",
    "def d(t):\n",
    "    if t > 10:\n",
    "        return 0.1\n",
    "    else:\n",
    "        return 0\n",
    "\n",
    "# simulation\n",
    "dt = 0.02\n",
    "\n",
    "tank1 = gravtank_generator(dt, A=0.2, Cv=.5)\n",
    "tank2 = gravtank_generator(dt, A=0.2, Cv=.5)\n",
    "\n",
    "# level control for tank 1.  \n",
    "pi1 = PI_generator(dt, Kp = 1, Ki = 0.6, MVmin = 0, MVmax = 1)\n",
    "\n",
    "# cascade level control for tank 2. Manipulated variable is the setpoint to pi1\n",
    "pi2 = PI_generator(dt, Kp = 0.6, Ki = 0.6, MVmin = 0, MVmax = 2)\n",
    "\n",
    "y1 = [tank1.send(None)]\n",
    "y2 = [tank2.send(None)]\n",
    "ulog = [pi1.send(None)[1]]\n",
    "pi2.send(None)\n",
    "\n",
    "u = 0\n",
    "r1 = 0\n",
    "r2 = 1.3\n",
    "\n",
    "for t in np.arange(dt,20,dt):\n",
    "    t1,q1,h1 = tank1.send(u)\n",
    "    t2,q2,h2 = tank2.send(q1 + d(t))\n",
    "    t3,r1 = pi2.send((r2,h2,r1))\n",
    "    t4,u = pi1.send((r1,h1,u))\n",
    "    \n",
    "    y1.append([t,q1,h1])\n",
    "    y2.append([t,q2,h2])\n",
    "    ulog.append(u)\n",
    "    \n",
    "t1,q1,h1 = np.asarray(y1).transpose()\n",
    "t2,q2,h2 = np.asarray(y2).transpose()\n",
    "plt.plot(t1,q1,t1,h1)\n",
    "plt.plot(t2,q2,t2,h2)\n",
    "plt.plot(t1,ulog)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<a id='section4'></a>\n",
    "## Enhancing Modularity with Class Definitions for Process Units\n",
    "\n",
    "One of the key goals of a modular approach to simulation is to implement process specific behavior within the definitions of the process, and separate from the organization of information flow among units that takes place in the main simulation loop.\n",
    "\n",
    "Below we define two examples of class definitions demonstrating how this can be done. The class definitions add features for defining names and parameters for instances of each class, and functions to log and plot data gathered in the course of simulations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<a id='section4-1'></a>\n",
    "### Gravity-Drained Tank Class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [],
   "source": [
    "class gravtank():\n",
    "    \n",
    "    def __init__(self, name='', A=1, Cv=1):\n",
    "        self.name = name\n",
    "        self.A = A\n",
    "        self.Cv = Cv\n",
    "        self._log = []\n",
    "        self.qin = 0\n",
    "    \n",
    "    def qout(self,h):\n",
    "        return self.Cv*np.sqrt(float(h))\n",
    "    \n",
    "    def deriv(self,h,t):\n",
    "        dh = (self.qin - self.qout(h))/self.A\n",
    "        return dh\n",
    "    \n",
    "    def plot(self):\n",
    "        t,qout,h = np.asarray(self._log).transpose()\n",
    "        plt.plot(t,qout,label=self.name + ' qout')\n",
    "        plt.plot(t,h,label=self.name + ' h')\n",
    "        plt.legend()\n",
    "    \n",
    "    def generator(self,dt,IC = 0):\n",
    "        h = IC\n",
    "        while True:\n",
    "            t,self.qin = yield self.qout(h),float(h)\n",
    "            h = odeint(self.deriv,h,[t,t+dt])[-1]\n",
    "            self._log.append([t,self.qout(h),float(h)])\n",
    "            t += dt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<a id='section4-2'></a>\n",
    "### PI Controller Class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [],
   "source": [
    "class PI():\n",
    "    \n",
    "    def __init__(self, name='', Kp = 0, Ki = 0, MVmin = 0, MVmax = np.Inf):\n",
    "        self.name = name\n",
    "        self.Kp = Kp\n",
    "        self.Ki = Ki\n",
    "        self.MVmin = MVmin\n",
    "        self.MVmax = MVmax\n",
    "        self._log = []\n",
    "        \n",
    "    def plot(self):\n",
    "        t,r,y,u = np.asarray(self._log).transpose()\n",
    "        plt.subplot(1,2,1)\n",
    "        p = plt.plot(t,y,label=self.name + ' PV')\n",
    "        plt.plot(t,r,'--',color=p[-1].get_color(),label=self.name + ' SP')\n",
    "        plt.legend()\n",
    "        plt.title('Process Variable and Setpoint')\n",
    "        plt.subplot(1,2,2)\n",
    "        plt.plot(t,u,label=self.name + ' MV')\n",
    "        plt.title('Manipulated Variable')\n",
    "        plt.legend()\n",
    "        plt.tight_layout()\n",
    "        \n",
    "    def generator(self,dt):\n",
    "        ecurr = 0\n",
    "        eprev = 0\n",
    "        u = self.MVmin\n",
    "        while True:\n",
    "            t,r,y,u = yield u\n",
    "            self._log.append([t,r,y,u]) \n",
    "            eprev,ecurr = ecurr,r-y\n",
    "            u += Kp*(ecurr - eprev) + Ki*ecurr*dt\n",
    "            u = max(self.MVmin,min(self.MVmax,u))\n",
    "            t += dt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<a id='section4-3'></a>\n",
    "### Modular Simulation of Cascade Control for Two Tanks in Series\n",
    "\n",
    "The following simulation shows how to use the class definitions in a simulation.  Each process instance used in the simulation requires three actions:\n",
    "\n",
    "1. Create an instance of the process. This is the step at which you can provide an instance name, parameters specific to the process and instance. Methods associated with the instance will be used to examine simulation logs and plot simulation results.\n",
    "\n",
    "2. Create a generator. A call to the generator function for each process instance creates an associated iterator. A sample time must be specified.\n",
    "\n",
    "3. An initial call to the iterator with an argument of `None` is needed to advance execution to the first `yield` statement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "outputs": [
    {
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3AX2UUj1rbpJOAz48o002cDmAUioB6Afs82WgPrFnJUR0a7z6HVC+cSOuo0eJ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\nZu6GYRh1iJm7YRhGHfILRAxaAVwadSAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1123990f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ovsIojgQiHpgsItuAwcCbIpJrPQ5jzARjTLwxJr5GjRrFsGulyoDUw7B9Qfmu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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1127efa90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# disturbance function\n",
    "def d(t):\n",
    "    if t > 10:\n",
    "        return 0.1\n",
    "    else:\n",
    "        return 0\n",
    "\n",
    "# sample time\n",
    "dt = 0.1\n",
    "\n",
    "# create and initialize tank1\n",
    "tank1_obj = gravtank(name='Tank 1',A=0.2, Cv=.5)\n",
    "tank1 = tank1_obj.generator(dt)\n",
    "tank1.send(None)\n",
    "\n",
    "# create and initailize tank2\n",
    "tank2_obj = gravtank(name='Tank 2',A=0.2, Cv=0.5)\n",
    "tank2 = tank2_obj.generator(dt)\n",
    "tank2.send(None)\n",
    "\n",
    "# level control for tank 1. \n",
    "pi1_obj = PI('Tank 1',Kp = 1, Ki = 0.6, MVmin = 0, MVmax = 1)\n",
    "pi1 = pi1_obj.generator(dt)\n",
    "pi1.send(None)\n",
    "\n",
    "# cascade level control for tank 2. Manipulated variable is the setpoint to for pi1\n",
    "pi2_obj = PI('Tank 2',Kp = 0.6, Ki = 0.6, MVmin = 0, MVmax = 2)\n",
    "pi2 = pi2_obj.generator(dt)\n",
    "pi2.send(None)\n",
    "\n",
    "# initial signals\n",
    "u, r1 = 0, 0\n",
    "\n",
    "# setpoint for tank 2 level\n",
    "r2 = 1.3\n",
    "\n",
    "for t in np.arange(0,20,dt):\n",
    "    qout1,h1 = tank1.send((t,u))\n",
    "    qout2,h2 = tank2.send((t,qout1 + d(t)))\n",
    "    r1 = pi2.send((t,r2,h2,r1))\n",
    "    u = pi1.send((t,r1,h1,u))    \n",
    "\n",
    "plt.figure()\n",
    "tank1_obj.plot()\n",
    "tank2_obj.plot()\n",
    "\n",
    "plt.figure(figsize=(11,4))\n",
    "pi1_obj.plot()\n",
    "pi2_obj.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbpages": {
     "level": 1,
     "link": "[A.3 A Modular Approach to Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.html#A.3-A-Modular-Approach-to-Simulation-using-Python-Generators)",
     "section": "A.3 A Modular Approach to Simulation using Python Generators"
    }
   },
   "source": [
    "<!--NAVIGATION-->\n",
    "< [A.2 Modular Simulation using Python Generators](https://jckantor.github.io/CBE32338/A.02-Modular-Approach-to-Simulation-using-Python-Generators.html) | [Contents](toc.html) | [A.4 Animation in Jupyter Notebooks](https://jckantor.github.io/CBE32338/A.04-Animation-in-Jupyter-Notebooks.html) ><p><a href=\"https://colab.research.google.com/github/jckantor/CBE32338/blob/master/docs/A.03-Modular-Simulation-using-Python-Generators.ipynb\"> <img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open in Google Colaboratory\"></a><p><a href=\"https://jckantor.github.io/CBE32338/A.03-Modular-Simulation-using-Python-Generators.ipynb\"> <img align=\"left\" src=\"https://img.shields.io/badge/Github-Download-blue.svg\" alt=\"Download\" title=\"Download Notebook\"></a>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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