{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Table of Contents](table_of_contents.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Topic 12. Linear Operators\n", "Author: Michael Eyler, <eyler94@gmail.com>\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction\n", "\n", "Linear operators are an everyday occurance and thus should be well understood. A linear operator is any operation which allows scalar multiplication or operand addition to be performed inside or outside but reaches the same answer eitherway. Some examples include matrix multiplication, integration, differentation, and linear constant coefficient transfer functions. Some special examples include projection matrices, fourier transforms, and convolution. \n", "\n", "These operators help us to condense, understand, or otherwise reformat information contained in matrices, functions, vectors, and sequences.\n", "\n", "Some examples of non-linear operators include rotation matrices, trigonometric functions, logarithmic and exponential functions, as well as most polynomials. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Explanation\n", "\n", "A great definition of linear operators is found on page 108 of the book, Definition 2.34. A simplified version follows.\n", "\n", "For any linear operator, A, scalars, $\\alpha$ and $\\beta$, and operands, $\\textbf{x}$ and $\\textbf{y}$.\n", "\n", "1. $A[\\alpha * \\textbf{x}] = \\alpha * A[\\textbf{x}]$.\n", "\n", "2. $A[\\alpha * \\textbf{x}] + A[\\beta * \\textbf{y}] = A[\\alpha * \\textbf{x} + \\beta * \\textbf{y}]$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simple Numerical Examples\n", "\n", "Following are some examples of linear operators acting on matricies and functions. \n", "\n", "The first solution of each example demonstrates that you can move a scalar outside the operand without impacting the result.\n", "\n", "The second solution of each example shows that the outcome of combined operands is the same as the combined outputs of the individual operands." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Notice that A[B]*beta is the same as A[B*beta].\n", "\n", "A[B]*beta:\n", "\n", " [[15 36]\n", " [63 96]]\n", "\n", "A[B*beta]:\n", "\n", " [[15 36]\n", " [63 96]]\n", "\n", "Notice also that A[B*beta]+A[D*gamma] is the same as A[B*beta+D*gamma].\n", "\n", "A[B*beta]+A[D*gamma]:\n", "\n", " [[ 65 146]\n", " [243 356]]\n", "\n", "A[B*beta+D*gamma]:\n", "\n", " [[ 65 146]\n", " [243 356]]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 576x576 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "#Matrix example of linear operators\n", "\n", "A = np.array([[1,2],[3,4]]) #Linear operator: A\n", "B = np.array([[5,6],[7,8]]) #Operand: B\n", "beta = 3 #Constant: beta\n", "print(\"Notice that A[B]*beta is the same as A[B*beta].\")\n", "print(\"\\nA[B]*beta:\\n\\n\", A*B*beta)\n", "C = B*beta\n", "print(\"\\nA[B*beta]:\\n\\n\", A*C)\n", "D = np.array([[10,11],[12,13]])\n", "gamma = 5\n", "E = D*gamma #Operand D*gamma\n", "print(\"\\nNotice also that A[B*beta]+A[D*gamma] is the same as A[B*beta+D*gamma].\")\n", "print(\"\\nA[B*beta]+A[D*gamma]:\\n\\n\", A*C+A*E)\n", "print(\"\\nA[B*beta+D*gamma]:\\n\\n\", A*(C+E))\n", "\n", "###Numerical differentation example\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "\n", "def deriv(func, ts):\n", " n = np.size(func)\n", " d_func = np.zeros(n-1)\n", " for i in range(0,np.size(d_func)):\n", " d_func[i] = (func[i+1]-func[i])/ts\n", " return d_func\n", "\n", "ts = 0.001\n", "t = np.arange(0,10,ts)\n", "f = np.sin(t)\n", "g = np.cos(t)\n", "\n", "d_f = beta*deriv(f,ts)\n", "d_f_b = deriv(beta*f,ts)\n", "\n", "plt.figure(figsize=(8,8))\n", "plt.plot(t[0:-1],d_f,'-*')\n", "plt.plot(t[0:-1],d_f_b)\n", "plt.title(\"Scalars can be pulled out front.\")\n", "plt.legend(['beta*d/dt[f]','d/dt[beta*f]'])\n", "plt.grid()\n", "plt.show()\n", "\n", "d_f_g_out = deriv(gamma*g,ts)+deriv(beta*f,ts)\n", "d_f_g_in = deriv((gamma*g+beta*f),ts)\n", "\n", "plt.figure(figsize=(8,8))\n", "plt.plot(t[0:-1],d_f_g_out,'-*')\n", "plt.plot(t[0:-1],d_f_g_in)\n", "plt.title(\"Results are consistant whether before or after the linear operation.\")\n", "plt.legend(['d/dt[beta*f]+d/dt[gamma*g]','d/dt[beta*f+gamma*g]'])\n", "plt.grid()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## An Engineering Application\n", "\n", "One engineering application includes modeling dynamic systems and their response to applied forces. This is commonly done with transfer functions. Linear Time Invariant systems are in fact linear operators on the force. Transforming a force into a reaction (that reaction could be motion, energy, or some combination.)\n", "\n", "The following example is of a mass that has a spring and damper restraining it. It is taken from Dr. Randall Beard and Dr. Tim McClain's book, Introduction to Feedback Control Using Design Studies, and modified slightly to work on this Jupyter project." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 432x288 with 2 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "from matplotlib.lines import Line2D\n", "import numpy as np\n", "import random\n", "\n", "\n", "# Mass Parameters\n", "class P:\n", " def __init__(self):\n", " # Physical parameters of the mass known to the controller\n", " self.m = 5.0 # mass kg\n", " self.k = 3.0 # spring constant Kg/s^2\n", " self.b = 0.5 # damping coefficient Kg/s\n", "\n", " # parameters for animation\n", " self.length = 5.0\n", " self.width = 1.0\n", "\n", " # Initial Conditions\n", " self.z0 = 0.0 # initial position of mass, m\n", " self.zdot0 = 0.0 # initial velocity of mass m/s\n", "\n", " # Simulation Parameters\n", " self.t_start = 0.0 # Start time of simulation\n", " self.t_end = 50.0 # End time of simulation\n", " self.Ts = 0.01 # sample time for simulation\n", " self.t_plot = 0.1 # the plotting and animation is updated at this rate\n", "\n", " # dirty derivative parameters\n", " self.sigma = 0.05 # cutoff freq for dirty derivative\n", " self.beta = (2.0*sigma-Ts)/(2.0*sigma+Ts) # dirty derivative gain\n", "\n", " # saturation limits\n", " self.F_max = 2.0 # Max force, N\n", "\n", "# Plotting\n", "\n", "plt.ion() # enable interactive drawing\n", "\n", "\n", "class plotData:\n", " ''' \n", " This class plots the time histories for the mass data.\n", " '''\n", "\n", " def __init__(self,title):\n", " # Number of subplots = num_of_rows*num_of_cols\n", " self.num_rows = 2 # Number of subplot rows\n", " self.num_cols = 1 # Number of subplot columns\n", "\n", " # Crete figure and axes handles\n", " self.fig, self.ax = plt.subplots(self.num_rows, self.num_cols, sharex=True)\n", "\n", " # Instantiate lists to hold the time and data histories\n", " self.time_history = [] # time\n", " self.z_history = [] # position z\n", " self.force_history = [] # control force\n", "\n", " # create a handle for every subplot.\n", " self.handle = []\n", " self.handle.append(myPlot(self.ax[0], ylabel='force(N)', title=title))\n", " self.handle.append(myPlot(self.ax[1], xlabel='t(s)', ylabel='z(m)'))#'Mass Data'))\n", "\n", " def updatePlots(self, t, states, ctrl):\n", " '''\n", " Add to the time and data histories, and update the plots.\n", " '''\n", " # update the time history of all plot variables\n", " self.time_history.append(t) # time\n", " self.z_history.append(states[0]) # mass position\n", " self.force_history.append(ctrl) # force on the base\n", "\n", " # update the plots with associated histories\n", " self.handle[0].updatePlot(self.time_history, [self.force_history])\n", " self.handle[1].updatePlot(self.time_history, [self.z_history])\n", "\n", "\n", "class myPlot:\n", " ''' \n", " Create each individual subplot.\n", " '''\n", " def __init__(self, ax,\n", " xlabel='',\n", " ylabel='',\n", " title='',\n", " legend=None):\n", " ''' \n", " ax - This is a handle to the axes of the figure\n", " xlable - Label of the x-axis\n", " ylable - Label of the y-axis\n", " title - Plot title\n", " legend - A tuple of strings that identify the data. \n", " EX: (\"data1\",\"data2\", ... , \"dataN\")\n", " '''\n", " self.legend = legend\n", " self.ax = ax # Axes handle\n", " self.colors = ['b', 'g', 'r', 'c', 'm', 'y', 'b']\n", " # A list of colors. The first color in the list corresponds\n", " # to the first line object, etc.\n", " # 'b' - blue, 'g' - green, 'r' - red, 'c' - cyan, 'm' - magenta\n", " # 'y' - yellow, 'k' - black\n", " self.line_styles = ['-', '-', '--', '-.', ':']\n", " # A list of line styles. The first line style in the list\n", " # corresponds to the first line object.\n", " # '-' solid, '--' dashed, '-.' dash_dot, ':' dotted\n", "\n", " self.line = []\n", "\n", " # Configure the axes\n", " self.ax.set_ylabel(ylabel)\n", " self.ax.set_xlabel(xlabel)\n", " self.ax.set_title(title)\n", " self.ax.grid(True)\n", "\n", " # Keeps track of initialization\n", " self.init = True \n", "\n", " def updatePlot(self, time, data):\n", " ''' \n", " Adds data to the plot. \n", " time is a list, \n", " data is a list of lists, each list corresponding to a line on the plot\n", " '''\n", " if self.init == True: # Initialize the plot the first time routine is called\n", " for i in range(len(data)):\n", " # Instantiate line object and add it to the axes\n", " self.line.append(Line2D(time,\n", " data[i],\n", " color=self.colors[np.mod(i, len(self.colors) - 1)],\n", " ls=self.line_styles[np.mod(i, len(self.line_styles) - 1)],\n", " label=self.legend if self.legend != None else None))\n", " self.ax.add_line(self.line[i])\n", " self.init = False\n", " # add legend if one is specified\n", " if self.legend != None:\n", " plt.legend(handles=self.line)\n", " else: # Add new data to the plot\n", " # Updates the x and y data of each line.\n", " for i in range(len(self.line)):\n", " self.line[i].set_xdata(time)\n", " self.line[i].set_ydata(data[i])\n", "\n", " # Adjusts the axis to fit all of the data\n", " self.ax.relim()\n", " self.ax.autoscale()\n", "\n", "# Mass Dynamics\n", "\n", "class massDynamics:\n", " '''\n", " Model the physical system\n", " '''\n", "\n", " def __init__(self):\n", " # Initial state conditions\n", " self.state = np.matrix([[P.z0], # initial mass position\n", " [P.zdot0]]) # initial mass velocity\n", " #################################################\n", " # The parameters for any physical system are never known exactly. Feedback\n", " # systems need to be designed to be robust to this uncertainty. In the simulation\n", " # we model uncertainty by changing the physical parameters by a uniform random variable\n", " # that represents alpha*100 % of the parameter, i.e., alpha = 0.2, means that the parameter\n", " # may change by up to 20%. A different parameter value is chosen every time the simulation\n", " # is run.\n", " alpha = 0 # Uncertainty parameter\n", " self.m = P.m * (1+2*alpha*np.random.rand()-alpha) # Mass, kg\n", " self.k = P.k * (1+2*alpha*np.random.rand()-alpha) # spring constant, m\n", " self.b = P.b * (1+2*alpha*np.random.rand()-alpha) # Damping coefficient, Ns\n", " self.Ts = P.Ts # sample rate at which the dynamics are propagated\n", "\n", " def propagateDynamics(self, u):\n", " '''\n", " Integrate the differential equations defining dynamics\n", " P.Ts is the time step between function calls.\n", " u contains the system input(s).\n", " '''\n", " # Integrate ODE using Runge-Kutta RK4 algorithm\n", " k1 = self.derivatives(self.state, u)\n", " k2 = self.derivatives(self.state + self.Ts/2*k1, u)\n", " k3 = self.derivatives(self.state + self.Ts/2*k2, u)\n", " k4 = self.derivatives(self.state + self.Ts*k3, u)\n", " self.state += self.Ts/6 * (k1 + 2*k2 + 2*k3 + k4)\n", "\n", " def derivatives(self, state, u):\n", " '''\n", " Return xdot = f(x,u), the derivatives of the continuous states, as a matrix\n", " '''\n", " # re-label states and inputs for readability\n", " z = state.item(0)\n", " zdot = state.item(1)\n", " force = u\n", " # The equations of motion.\n", " zddot = (force - self.b*zdot - self.k*z)/self.m\n", "\n", " # build xdot and return\n", " xdot = np.matrix([[zdot], [zddot]])\n", " return xdot\n", "\n", " def outputs(self):\n", " '''\n", " Returns the measured outputs as a list\n", " [z] with added Gaussian noise\n", " '''\n", " # re-label states for readability\n", " z = self.state.item(0)\n", " # add Gaussian noise to outputs\n", " z_m = z + random.gauss(0, 0.001)\n", " # return measured outputs\n", " return [z_m]\n", "\n", " def states(self):\n", " '''\n", " Returns all current states as a list\n", " '''\n", " return self.state.T.tolist()[0]\n", "\n", " \n", "# instantiate parameters, mass, controller, and reference classes\n", "P = P()\n", "\n", "mass_f = massDynamics()\n", "mass_g = massDynamics()\n", "mass_f_g = massDynamics()\n", "\n", "# instantiate the simulation plots and animation\n", "dataPlot_f = plotData(\"Force f\")\n", "dataPlot_g = plotData(\"Force g\")\n", "dataPlot_f_g = plotData(\"Forces f and g\")\n", "\n", "t = P.t_start # time starts at t_start\n", "while t < P.t_end: # main simulation loop\n", " # Propagate dynamics in between plot samples\n", " t_next_plot = t + P.t_plot\n", " while t < t_next_plot: # updates control and dynamics at faster simulation rate\n", " f=1\n", " g=3\n", " mass_f.propagateDynamics(f) # Propagate the dynamics\n", " mass_g.propagateDynamics(g) # Propagate the dynamics\n", " mass_f_g.propagateDynamics(f+g) # Propagate the dynamics\n", " t = t + P.Ts # advance time by Ts\n", " # update animation and data plots\n", " dataPlot_f.updatePlots(t, mass_f.states(), f)\n", " dataPlot_g.updatePlots(t, mass_g.states(), g)\n", " dataPlot_f_g.updatePlots(t, mass_f_g.states(), f+g)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice how the force f (1 N) and the force g (3 N) can be placed on the system separately and their outputs summed are equal to the forced being applied to the system together." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "<Figure size 720x720 with 1 Axes>" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(10,10))\n", "f_g = np.zeros(5000)\n", "for i in range(5000):\n", " f_g[i] = dataPlot_f.z_history[i]+dataPlot_g.z_history[i]\n", "\n", "plt.plot(np.arange(P.t_start,P.t_end,P.Ts),dataPlot_f.z_history[:-3])\n", "plt.plot(np.arange(P.t_start,P.t_end,P.Ts),dataPlot_g.z_history[:-3])\n", "plt.plot(np.arange(P.t_start,P.t_end,P.Ts),f_g,'k',linewidth=3)\n", "plt.plot(np.arange(P.t_start,P.t_end,P.Ts),dataPlot_f_g.z_history[:-3])\n", "\n", "plt.title(\"Results are consistant whether operands are combined before or after the linear operation.\")\n", "plt.legend(['Individual force f',\n", " 'Individual force g',\n", " 'The sum of the responses of f and g applied separately to the system.',\n", " 'Forces f and g applied simultaneously to the system.'])\n", "plt.grid()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.15" } }, "nbformat": 4, "nbformat_minor": 2 }