simuladoeqdiff.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/rnwatanabe/SistemasESinais/blob/master/simuladoeqdiff.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Simulador de equações diferenciais para entradas padrão\n",
        "\n",
        "Renato Naville Watanabe"
      ],
      "metadata": {
        "id": "5Rl3j5Wu4CL_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "O exemplo abaixo é para a seguinte equação diferencial:\n",
        "\n",
        "$\\frac{d^2y}{dt^2} + 3\\frac{dy}{dt} + 2y = x(t)$\n",
        "\n",
        "Para a entrada:\n",
        "\n",
        "$x(t) = e^{-0.2t}\\cos(3t-2)u(t)$"
      ],
      "metadata": {
        "id": "kc5XWv454K_O"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title parâmetros equação diferencial { run: \"auto\", vertical-output: true }\n",
        "d6y_dt6 = 0 #@param {type:\"number\"}\n",
        "d5y_dt5 = 0 #@param {type:\"number\"}\n",
        "d4y_dt4 = 0 #@param {type:\"number\"}\n",
        "d3y_dt3 = 0 #@param {type:\"number\"}\n",
        "d2y_dt2 = 1 #@param {type:\"number\"}\n",
        "dy_dt = 3 #@param {type:\"number\"}\n",
        "y = 2 #@param {type:\"number\"}\n",
        "d6x_dt6 = 0 #@param {type:\"number\"}\n",
        "d5x_dt5 = 0 #@param {type:\"number\"}\n",
        "d4x_dt4 = 0 #@param {type:\"number\"}\n",
        "d3x_dt3 = 0 #@param {type:\"number\"}\n",
        "d2x_dt2 = 0 #@param {type:\"number\"}\n",
        "dx_dt = 0 #@param {type:\"number\"}\n",
        "x = 1 #@param {type:\"number\"}\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "a = np.array([d6y_dt6, d5y_dt5, d4y_dt4, d3y_dt3, d2y_dt2, dy_dt, y])\n",
        "b = np.array([d6x_dt6, d5x_dt5, d4x_dt4, d3x_dt3, d2x_dt2, dx_dt, x])\n",
        "\n",
        "grauy = 6-np.where(a!=0)[0][0]\n",
        "graux = 6-np.where(b!=0)[0][0]\n",
        "\n",
        "if graux > grauy:\n",
        "    print('Sistema não realizável.')\n",
        "\n",
        "b = b[np.where(a!=0)[0][0]:]\n",
        "a = a[np.where(a!=0)[0][0]:]\n",
        "\n",
        "if a[0] != 1:\n",
        "    b = b/a[0]\n",
        "    a = a/a[0]\n",
        "\n",
        "print(a, b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "cellView": "form",
        "id": "hak0MP-IJJxl",
        "outputId": "b450bb40-d8b4-4136-f641-53ea52179fd7"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1 3 2] [0 0 1]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Tipo de Entrada { run: \"auto\", vertical-output: true }\n",
        "tipo_de_entrada = \"cosseno decaindo\" #@param [\"cosseno\", \"exponencial\", \"degrau\", \"cosseno decaindo\", \"impulso\"]\n"
      ],
      "metadata": {
        "cellView": "form",
        "id": "rJLSrDNwJOjm"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Parâmetros da entrada\n",
        "\n",
        "- cosseno - $A\\cos(Dt + E)u(t-C)$\n",
        "\n",
        "- exponencial - $Ae^{Bt}u(t-C)$\n",
        "\n",
        "- degrau - $Au(t-C)$\n",
        "\n",
        "- cosseno decaindo - $Ae^{Bt}\\cos(Dt + E)u(t-C)$\n",
        "\n",
        "- impulso - $A\\delta(t-C)$\n"
      ],
      "metadata": {
        "id": "iX5bGVB3NqUv"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title  { run: \"auto\", vertical-output: true }\n",
        "#@title  { run: \"auto\", vertical-output: true }\n",
        "\n",
        "A = 1 #@param {type:\"slider\", min:0, max:100, step:0.1}\n",
        "B = -0.2 #@param {type:\"slider\", min:-100, max:100, step:0.1}\n",
        "C = 0 #@param {type:\"slider\", min:-100, max:100, step:0.1}\n",
        "D = 3 #@param {type:\"slider\", min:0, max:100, step:0.1}\n",
        "E = -3 #@param {type:\"slider\", min:-100, max:100, step:0.1}"
      ],
      "metadata": {
        "cellView": "form",
        "id": "O0tnRHz3Mp5m"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Tempo de simulação\n",
        "tempo = 5 #@param {type:\"number\"}\n",
        "dt = 0.0001\n",
        "t = np.arange(0, tempo, dt)\n",
        "x = np.zeros(len(t))\n",
        "y = np.zeros(len(t))\n",
        "if tipo_de_entrada == \"impulso\":\n",
        "    delay = int(C//dt)\n",
        "    x[delay] = A/dt\n",
        "if tipo_de_entrada == \"cosseno\":\n",
        "    delay = int(C//dt)\n",
        "    x[delay:] = A*np.cos(D*t[delay:]+E)\n",
        "if tipo_de_entrada == \"exponencial\":\n",
        "    delay = int(C//dt)\n",
        "    x[delay:] = A*np.exp(B*t[delay:])\n",
        "if tipo_de_entrada == \"degrau\":\n",
        "    delay = int(C//dt)\n",
        "    x[delay:] = A*np.ones(len(t[delay:]))\n",
        "if tipo_de_entrada == \"cosseno decaindo\":\n",
        "    delay = int(C//dt)\n",
        "    x[delay:] = A*np.exp(B*t)*np.cos(D*t[delay:]+E)\n",
        "\n",
        "state = np.zeros((len(a)-1,1))\n",
        "Amatrix = np.zeros((len(a)-1, len(a)-1))\n",
        "Bmatrix = np.zeros((len(a)-1,1))\n",
        "Bmatrix[0,0] = 1\n",
        "for i in range(1,len(a)-1):\n",
        "    Amatrix[i,i-1] = 1\n",
        "Amatrix[0,:] = -a[1:]\n",
        "for i in range(0, len(t)):\n",
        "\n",
        "    dstatedt = Amatrix@state + Bmatrix*x[i]\n",
        "    state = state + dt*dstatedt\n",
        "\n",
        "\n",
        "    y[i] = b[1:]@state + b[0]*dstatedt[0]\n",
        "plt.plot(t, y)\n",
        "plt.title('Sinal de saída')\n",
        "plt.xlabel('t(s)')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "cellView": "form",
        "id": "eI2i4roQQsPn",
        "outputId": "4e9cfe2c-eaaa-4042-cb46-64b0b6fc9280"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "jrbL2xTZ6uJQ"
      },
      "execution_count": 5,
      "outputs": []
    }
  ]
}