sel0611_exerc_aula12.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Exerc_Aula12.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ic5njXnVYAlN"
      },
      "source": [
        "# SEL0611 - Fundamentos de Controle. \n",
        "\n",
        "Prof. Valdir Grassi Jr.\n",
        "\n",
        "Exercício para obtenção de presença na **Aula 12 (20/05/21)**. \n",
        "\n",
        "## Modelo de pêndulo sem amortecimento.\n",
        "\n",
        "Execute o código para responder a questão do formulário."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ernJUqf6b0AJ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3300f752-e701-4f41-8d86-715f5be93049"
      },
      "source": [
        "# Install the control package:\n",
        "!pip install control"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Collecting control\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/88/87/ee6cb7cdcf4efe5634231bd688b307773629a100ec4c83b0c3eb03edd39d/control-0.9.0.tar.gz (339kB)\n",
            "\r\u001b[K     |█                               | 10kB 15.2MB/s eta 0:00:01\r\u001b[K     |██                              | 20kB 11.1MB/s eta 0:00:01\r\u001b[K     |███                             | 30kB 7.8MB/s eta 0:00:01\r\u001b[K     |███▉                            | 40kB 6.9MB/s eta 0:00:01\r\u001b[K     |████▉                           | 51kB 5.6MB/s eta 0:00:01\r\u001b[K     |█████▉                          | 61kB 5.9MB/s eta 0:00:01\r\u001b[K     |██████▊                         | 71kB 6.5MB/s eta 0:00:01\r\u001b[K     |███████▊                        | 81kB 6.8MB/s eta 0:00:01\r\u001b[K     |████████▊                       | 92kB 5.8MB/s eta 0:00:01\r\u001b[K     |█████████▋                      | 102kB 5.4MB/s eta 0:00:01\r\u001b[K     |██████████▋                     | 112kB 5.4MB/s eta 0:00:01\r\u001b[K     |███████████▋                    | 122kB 5.4MB/s eta 0:00:01\r\u001b[K     |████████████▋                   | 133kB 5.4MB/s eta 0:00:01\r\u001b[K     |█████████████▌                  | 143kB 5.4MB/s eta 0:00:01\r\u001b[K     |██████████████▌                 | 153kB 5.4MB/s eta 0:00:01\r\u001b[K     |███████████████▌                | 163kB 5.4MB/s eta 0:00:01\r\u001b[K     |████████████████▍               | 174kB 5.4MB/s eta 0:00:01\r\u001b[K     |█████████████████▍              | 184kB 5.4MB/s eta 0:00:01\r\u001b[K     |██████████████████▍             | 194kB 5.4MB/s eta 0:00:01\r\u001b[K     |███████████████████▎            | 204kB 5.4MB/s eta 0:00:01\r\u001b[K     |████████████████████▎           | 215kB 5.4MB/s eta 0:00:01\r\u001b[K     |█████████████████████▎          | 225kB 5.4MB/s eta 0:00:01\r\u001b[K     |██████████████████████▎         | 235kB 5.4MB/s eta 0:00:01\r\u001b[K     |███████████████████████▏        | 245kB 5.4MB/s eta 0:00:01\r\u001b[K     |████████████████████████▏       | 256kB 5.4MB/s eta 0:00:01\r\u001b[K     |█████████████████████████▏      | 266kB 5.4MB/s eta 0:00:01\r\u001b[K     |██████████████████████████      | 276kB 5.4MB/s eta 0:00:01\r\u001b[K     |███████████████████████████     | 286kB 5.4MB/s eta 0:00:01\r\u001b[K     |████████████████████████████    | 296kB 5.4MB/s eta 0:00:01\r\u001b[K     |█████████████████████████████   | 307kB 5.4MB/s eta 0:00:01\r\u001b[K     |██████████████████████████████  | 317kB 5.4MB/s eta 0:00:01\r\u001b[K     |███████████████████████████████ | 327kB 5.4MB/s eta 0:00:01\r\u001b[K     |███████████████████████████████▉| 337kB 5.4MB/s eta 0:00:01\r\u001b[K     |████████████████████████████████| 348kB 5.4MB/s \n",
            "\u001b[?25hRequirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from control) (1.19.5)\n",
            "Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from control) (1.4.1)\n",
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.7/dist-packages (from control) (3.2.2)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->control) (2.4.7)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->control) (1.3.1)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.7/dist-packages (from matplotlib->control) (0.10.0)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib->control) (2.8.1)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.7/dist-packages (from cycler>=0.10->matplotlib->control) (1.15.0)\n",
            "Building wheels for collected packages: control\n",
            "  Building wheel for control (setup.py) ... \u001b[?25l\u001b[?25hdone\n",
            "  Created wheel for control: filename=control-0.9.0-py2.py3-none-any.whl size=344920 sha256=d24cc5fb07b271008c108178d4ed31233141f951e3efdee7f250f9544615446a\n",
            "  Stored in directory: /root/.cache/pip/wheels/35/be/ee/081b68ca3e4b2d253fba2f7f7e51960373903fb7b6d13c5532\n",
            "Successfully built control\n",
            "Installing collected packages: control\n",
            "Successfully installed control-0.9.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Cc52si_2ZvcV"
      },
      "source": [
        "import control as ct\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YKE9SKxg3Mek",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "698bd999-a623-4fc0-b6c7-03ae0a24e1f8"
      },
      "source": [
        "# Parâmetros do modelo do pêndulo sem amortecimento:\n",
        "m = 1\n",
        "g = 9.81\n",
        "l = 1\n",
        "\n",
        "# Função de transferência do pêndulo sem amortecimento:\n",
        "num = np.array([1/(m*(l**2))])\n",
        "den = np.array([1, 0, g/l])\n",
        "H = ct.tf(num, den)\n",
        "\n",
        "print('H(s) = {}'.format(H))"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "H(s) = \n",
            "    1\n",
            "----------\n",
            "s^2 + 9.81\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gueKwBrP0Af2"
      },
      "source": [
        "Resposta no tempo:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zs8d8HXTRWkW",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "8338f5e6-8ef7-40ae-e3b1-b7eb80912735"
      },
      "source": [
        "# Resposta ao degrau unitário:\n",
        "(t, theta) = ct.step_response(H)\n",
        "plt.plot(t, theta)\n",
        "plt.xlabel('Time (s)')\n",
        "plt.ylabel('Angle (rad)')\n",
        "plt.title('Step response')\n",
        "plt.show()"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V2lRI-m7cy5s"
      },
      "source": [
        "Pólos e zeros do sistema:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 346
        },
        "id": "HCfV5yC-c7Fh",
        "outputId": "9e09234f-0f74-4e52-ac9c-0b6a4786d501"
      },
      "source": [
        "# Pólos and zeros:\n",
        "(p, z) = ct.pzmap(H)\n",
        "p = np.reshape(p, (len(p), 1))\n",
        "print('Poles of H(s): \\n{}'.format(p))"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Poles of H(s): \n",
            "[[-0.+3.13209195j]\n",
            " [ 0.-3.13209195j]]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2ut0X9nNdJQD"
      },
      "source": [
        "Diagrama de bode:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "yatewge0dLM9",
        "outputId": "3244ecb8-375b-4493-cb79-d619633ab871"
      },
      "source": [
        "# Diagrama de Bode:\n",
        "#plt.figure(2)\n",
        "ct.bode_plot(H, dB=True)\n",
        "plt.show(block=False)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}