{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Ex 1. Duality of Controllability and Observability\n", "\n", "Prove that a pair of matrices (A,B) is controllable if and only if a pair of matrices (A^T, B^T) is observable.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Ex 2. Controllability is independent of the choice of coordinates.\n", "\n", "Invariance Under Nonsingular Transformations.\n", "\n", "Consider $\\dot x = Ax + Bu$ and similarity transformation $\\tilde x = Tx,$ where $T$ is invertible.\n", "\n", "Prove that the system $\\dot x = Ax + Bu$ is controllable if and only if the system $\\dot {\\tilde x} = \\tilde{A}\\tilde{x} + \\tilde{B}u$ is controllable.\n" ] }, { "attachments": { "rsz_2024-01-30_22-36-17.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "## Ex 3. Quadruple-Tank Process\n", "\n", "![rsz_2024-01-30_22-36-17.png](attachment:rsz_2024-01-30_22-36-17.png)\n", "Let us consider the Quadruple-Tank Process. A schematic diagram of the process is shown in the Figure above. The\n", "target is to control the level in the lower two tanks with two pumps. The process inputs are $v_1$ and $v_2$ (input voltages to the pumps) and the outputs are $y_1$ and $y_2$ (voltages from level measurement devices). Mass balances and Bernoulli’s law yield\n", "\n", "$$\n", "\\dfrac{dh_1}{dt} = -\\dfrac{a_1}{A_1}\\sqrt{2gh_1} + \\dfrac{a_3}{A_1}\\sqrt{2gh_3} + \\dfrac{\\gamma_1k_1}{A_1}v_1 = f_1(h_1,h_2,h_3,h_4,v_1,v_2)\n", "$$\n", "$$\n", "\\dfrac{dh_2}{dt} = -\\dfrac{a_2}{A_2}\\sqrt{2gh_2} + \\dfrac{a_4}{A_2}\\sqrt{2gh_4} + \\dfrac{\\gamma_2k_2}{A_2}v_2 = f_2(h_1,h_2,h_3,h_4,v_1,v_2)\n", "$$\n", "$$\n", "\\dfrac{dh_3}{dt} = -\\dfrac{a_3}{A_3}\\sqrt{2gh_3} + \\dfrac{(1-\\gamma_2)k_2}{A_3}v_2 = f_3(h_1,h_2,h_3,h_4,v_1,v_2)\n", "$$\n", "$$\n", "\\dfrac{dh_4}{dt} = -\\dfrac{a_4}{A_4}\\sqrt{2gh_4} + \\dfrac{(1-\\gamma_1)k_1}{A_4}v_1 = f_4(h_1,h_2,h_3,h_4,v_1,v_2)\n", "$$\n", "where\n", "\n", "$A_i$ is a cross-section of Tank i\n", "\n", "$a_i$ is a cross-section of outlet hole of Tank i\n", "\n", "$h_i$ is a water level.\n", "\n", "The voltage applied to Pump $i$ is $v_i$ and the corresponding flow\n", "is $k_iv_i$. The parameters $\\gamma_1,\\gamma_2\\in (0,1)$ are determined from how the valves are set prior to experiment. The flow to Tank 1\n", "is $\\gamma_1k_1v_1$ and the flow to Tank 4 is $(1-\\gamma_1)k_1v_1$ and similarly\n", "for Tank 2 and Tank 3. The acceleration of gravity is denoted $g$.\n", "The measured level signals are $k_c h_1$ and $k_c h_2$. The parameter\n", "values of the laboratory process are given in the following table\n", "\n", " A_1, A_3 [cm^2] 28\n", " A_2, A_4 [cm^2] 32\n", " a_1, a_3 [cm^2] 0.071\n", " a_2, a_4 [cm^2] 0.057\n", " k_c [V/cm] 0.50\n", " g [cm/s^2] 9.81\n", " k_1 [cm^3/Vs] 3.33\n", " k_2 [cm^3/Vs] 3.35\n", " gamma_1 0.70\n", " gamma_2 0.60\n", " \n", "Check the following paper for more details on the model. \n", "https://www.diva-portal.org/smash/get/diva2:495784/FULLTEXT01.pdf\n", " \n", "## TODO\n", "1. Linearise the system around operating point \n", "$$(h_1^0,h_2^0,h_3^0,h_4^0, v_1^0, v_2^0) = (12.4,12.7,1.8,1.4,3.00,3.00).$$\n", "Pass to shifted variables $x_i = h_i-h_i^0, u_i = v_i - v_i^0.$\n", "\n", "2. Is linear system controllable? Is linear system observable? Use Kalman rank test to answer this quetion.\n", "\n", "3. Imagine that one of the pupms is broken and there is no flow trough it. Does system remain controllable?\n", "\n", "4. Let us measure the signals $x_3, x_4$ (i.e. matix C = [0 0 1 1]) instead of measuring the signals $x_1$ and $x_2.$ Is such a system observable?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "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": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }