{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Simulating a plant with time-dependent control actions\n", "\n", "Todo: clean up descriptions and libraries\n", "\n", "Assume that we have a plant with some simple dynamics described by this transfer function:\n", "\n", "$$G(s) = \\frac{1}{s^2 + 2s + 1}$$\n", "\n", "We can define the system in python-control by doing:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\n", " 1.5\n", "---------------\n", "s^2 + 0.5 s + 1" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import control\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "G_s = control.tf([1.5],[1,0.5,1])\n", "G_s" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Step Response: control.step_response\n", "Here's how to get the step response and plot the output:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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qD7c3ZV29/QS7+3SkICJpy8tQmAvUDLlfG1s23LVmttXMfmZmlSO9kJndYmYb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\nSUVORK5CYII=\n", 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