task1-equation-and-manifolds.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Лабораторная работа № 1\n",
    "## студента ПК-16М-1\n",
    "## Бекленищева Владислава\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Постановка задачи"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Условие задачи (Колесников - с. 98)\n",
    "\n",
    "Начальная система x'(t) + ax = u\n",
    "\n",
    "Варианты выбора psi (многообразия):\n",
    "1. psi = x\n",
    "2. psi = tanh x\n",
    "3. psi = tanh A x\n",
    "\n",
    "Управление находится из уравнения: T * psi' + psi = 0\n",
    "\n",
    "В работе рассматривается синтезирование управления для первого и второго многообразия:\n",
    "- u1 = -x (1/T - a)\n",
    "- u2 = (-1/2T) sh(2x) + ax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Задание: \n",
    "1. Найти управление u, подставить его в исходное уравнение и получить замкнутую управлением систему. \n",
    "2. Решить ДУ при заданных начальных условиях\n",
    "3. Построить интегральные кривые для заданных начальных условий."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### Исходный код решения задачи"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Подключаем пакеты:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Определяем замкнутые уравнения систем для первого и второго многообразия соответственно:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def firstClosedEquation(x, t, T):\n",
    "    dxdt = -x / T\n",
    "    return dxdt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def secondClosedEquation(x, t, T):\n",
    "    dxdt = ((-0.5) * np.sinh(2*x)) / T\n",
    "    return dxdt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "вводим параметры для первого уравнения:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x0 = -10; T0 = 0.5\n",
    "x1 = 5; T1 = 2\n",
    "x2 = 10; T2 = 1\n",
    "t = np.arange(0, 11, 0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "решаем уравнения для первого многообразия:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x_first_1 = odeint(firstClosedEquation, x0, t, args=(T0,))\n",
    "x_first_2 = odeint(firstClosedEquation, x1, t, args=(T1,))\n",
    "x_first_3 = odeint(firstClosedEquation, x2, t, args=(T2,))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "вводим параметры для первого уравнения:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x0 = 5; T0 = 0.5\n",
    "x1 = -6; T1 = 2\n",
    "x2 = -5; T2 = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "решаем уравнения для первого многообразия:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x_second_1 = odeint(secondClosedEquation, x0, t, args=(T0,))\n",
    "x_second_2 = odeint(secondClosedEquation, x1, t, args=(T1,))\n",
    "x_second_3 = odeint(secondClosedEquation, x2, t, args=(T2,))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "###### интегральные кривые"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "для первого многообразия:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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Wv/XW+hKfi+XXTyeBsgNweMsIeo7Yy7ncIm+V4BUpKQ061NVsSW7GSWbukdwqLVmyhJ49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\n/wPLx0ujU3dQ4gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x92c9ebacc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, x_first_1, 'r', label='x(0) = -10', linewidth=2)\n",
    "plt.plot(t, x_first_2, 'g', label='x(1) = 5', linewidth=2)\n",
    "plt.plot(t, x_first_2, 'b', label='x(2) = 10', linewidth=2)\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('t')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "для второго многообразия"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Wrl3bLj4HtO2/x+9+97t28Tna8t9j7dq17eJzQNv+e6xdu7ZdfA5o/X+P1atX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\nACEOAIAQBwBAiAMAID7X0iw3dT8wjgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x92c9f7bef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t, x_second_1, 'r', label='x(0) = 5', linewidth=2)\n",
    "plt.plot(t, x_second_2, 'g', label='x(1) = -6', linewidth=2)\n",
    "plt.plot(t, x_second_2, 'b', label='x(2) = -5', linewidth=2)\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel('t')\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "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": 1
}