{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A discrete controller class\n",
    "---------------------------\n",
    "\n",
    "Let's extend the example from our previous object-oriented simulation notebook to discrete controllers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy\n",
    "import scipy.signal\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by defining a `class` for the tank system again:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class TankSystem:\n",
    "    def __init__(self, A, alpha, K, V, Fi):\n",
    "        \"\"\" This special function gets called when an object of this class is created\"\"\"\n",
    "        self.A = A\n",
    "        self.alpha = alpha\n",
    "        self.K = K\n",
    "        self.Fi = Fi\n",
    "        self.change_state(V)\n",
    "    \n",
    "    def f(self, x):\n",
    "        return self.alpha**(x - 1)\n",
    "    \n",
    "    def change_input(self, x):\n",
    "        self.Fo = self.K*self.f(x)*numpy.sqrt(self.h)\n",
    "        \n",
    "    def change_state(self, V):\n",
    "        self.state = self.V = V\n",
    "        self.output = self.h = self.V/self.A\n",
    "\n",
    "    def derivative(self, x):\n",
    "        self.change_input(x)\n",
    "        dVdt = self.Fi - self.Fo\n",
    "        return dVdt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But this time we'll do a discrete controller:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class DiscreteController:\n",
    "    def __init__(self, DeltaT, Kc, tau_i, bias):\n",
    "        self.DeltaT = DeltaT\n",
    "        self.Kc = Kc\n",
    "        self.tau_i = tau_i\n",
    "        self.next_sample_time = 0\n",
    "        self.error_sum = 0\n",
    "        self.bias = self.output = bias\n",
    "        \n",
    "    def update(self, u, t):\n",
    "        if t >= self.next_sample_time:\n",
    "            self.error_sum += u\n",
    "            self.output = self.Kc*(u + 1/self.tau_i*self.error_sum)\n",
    "            self.next_sample_time += self.DeltaT"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I've changed the way we update the controller here to accomodate the fact that discrete controllers don't have states to integrate, so we don't need the `derivative` method. The way I've built this class requires that the `update` method be called with strictly ascending times in `t`. Note that this class corresponds very closely to a physical box. All the sampling is taking place inside the class and it is designed to be updated in a \"normal\" Euler integration loop. See how using classes makes the calculations which are about a particular physical object (the controller) stay together in the code rather than being spread out in lots of places?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course, we still have to test that this works:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ts = numpy.linspace(0, 100, 1000)\n",
    "dt = ts[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sp = 1.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I've changed this function to use the new `update` methods, but otherwise it is similar to the previous one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def control_simulation_discrete(system, controller):\n",
    "    outputs = []\n",
    "    for t in ts:\n",
    "        system.change_input(controller.output)\n",
    "\n",
    "        e = sp - system.output\n",
    "\n",
    "        controller.update(e, t)\n",
    "\n",
    "        system.change_state(system.state + system.derivative(controller.output)*dt)\n",
    "\n",
    "        outputs.append(system.output)\n",
    "    return outputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "system = TankSystem(A=2, alpha=20, K=2, V=2, Fi=1)\n",
    "controller = DiscreteController(DeltaT=1, Kc=-1, tau_i=5, bias=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "outputs = control_simulation_discrete(system, controller)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10cf877f0>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mTYMXX2zaboflxRdh/nw491z4m79Jbm1sZtZMo65G34ozbmo55JDk7pZHH508qOSCC/zc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\n8TJIPgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b2fdd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(ts, outputs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can still simulate different situations easily."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cf514e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "outputs = control_simulation_discrete(system=TankSystem(A=2, alpha=10, K=2, V=2, Fi=1), \n",
    "                                      controller=DiscreteController(DeltaT=1, Kc=-0.5, tau_i=5, bias=0.5))\n",
    "plt.plot(ts, outputs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}