{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Especificações para projeto de compensadores SISO" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib widget\n", "\n", "import numpy as np\n", "import control as ct" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Paleta de cores\n", "cp = {\n", " 'red': (1.0, 0.349, 0.369, 1.0),\n", " 'green': (0.541, 0.788, 0.149, 1.0),\n", " 'blue': (0.098, 0.510, 0.769, 1.0),\n", " 'lred': (1.0, 0.588, 0.6, 1.0),\n", " 'lgreen': (0.722, 0.894, 0.443, 1.0),\n", " 'lblue': (0.369, 0.706, 0.918, 1.0),\n", " 'orange': (1.0, 0.506, 0.227, 1.0),\n", " 'yellow': (1.0, 0.792, 0.227, 1.0),\n", " 'pink': (1.0, 0.349, 0.611, 1.0),\n", " 'purple': (0.416, 0.298, 0.576, 1.0),\n", " 'turquoise': (0.098, 0.761, 0.769, 1.0),\n", " 'brown': (0.576, 0.380, 0.298, 1.0)\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1. Especificações de polos dominantes para projeto via lugar das raízes\n", "\n", "#### 1.1. Aproximação por sistema de primeira ordem em malha fechada\n", "\n", "Caso o *sistema em malha fechada* possua um único polo dominante localizado em $\\bar p_1 = \\displaystyle - \\frac{1}{\\tau}$, seu comportamento pode ser aproximado por uma função de transferência equivalente de *primeira ordem*:\n", "$$\n", "T(s) \\approx \\frac{1}{1 + \\tau s}\n", "$$\n", "em que $\\tau$ é a *constante de tempo*. \n", "\n", "Em termos de resposta a degrau, $5 \\tau$ deve ser o tempo necessário para que a resposta $y(t)$ se aproxime com erro inferior a 1% da referência escolhida." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "abce38eb9cf34986bc6c7bd75b8a6753", "version_major": 2, "version_minor": 0 }, "image/png": 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", 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