{ "cells": [ { "cell_type": "markdown", "id": "be6f2e6b-30f0-4c7e-bbaf-d9fabfc31521", "metadata": {}, "source": [ "# Control theory. Course introduction.\n", "\n", "## TP1. System modeling. State-space representation of dynamical systems.\n", "\n", "## Study load\n", "\n", "Course grade breakdown:\n", "\n", " Labs - 40%\n", " \n", " Final project presentation 30%\n", "\n", " Final test 30%\n", " \n", "File name for lab submission: yourname_labnumber.ipynb (example: elenavanneaux_TP2.ipynb) \n", "\n", "The completed notebooks should be sent to your tutor (elena.vanneaux@ensta.fr or adnan.saood@ensta.fr) before the beginning of the next session. Please add [APM_4AUT2_TA] to the topic of e-mail.\n", "\n", "## Prerequisites for practice\n", "### Math\n", "During the course, we will cover the following areas of mathematics:\n", " \n", " 1. Linear Algebra\n", "\n", " 2. Calculus\n", "\n", " 3. Differential equations\n", "\n", " 4. Dynamics (Mechanics and Physics)\n", "\n", "### Python programming\n", "In the labs we will use a Python programming language and the following libraries:\n", "\n", " 1. NumPy https://numpy.org/doc/stable/\n", "\n", " 2. SciPy https://docs.scipy.org/doc/scipy/\n", "\n", " 3. Matplotlib https://matplotlib.org/stable/tutorials/index\n", "\n", " 4. SymPy https://docs.sympy.org/latest/tutorials/intro-tutorial/intro.html\n", "\n", "### Jupyter Notebook Markdown Cells Documentation\n", "\n", "Please check on Markdown cells documentation, to provide a fancy look for your notebooks!\n", "\n", "https://jupyter-notebook.readthedocs.io/en/stable/examples/Notebook/Working%20With%20Markdown%20Cells.html" ] }, { "cell_type": "markdown", "id": "4fbfeeb3-b9da-4420-a09b-532d6343341b", "metadata": {}, "source": [ "## Ex.1: Open-loop vs Closed-loop system\n", "\n", "### TODO\n", "\n", "Provide one example of open-loop control system and one example of closed-loop control system. What is the difference between them?" ] }, { "cell_type": "markdown", "id": "8e4aae7c-b7dd-41c9-b755-e0c5154390e9", "metadata": {}, "source": [] }, { "attachments": { "6f224bc1-0414-4bf2-a6a4-efda02a63e41.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "b2c3247e-7149-45f9-a900-3643111402bc", "metadata": {}, "source": [ "## Ex.1: Vehicle Suspension System\n", "\n", "Vehicle Suspension System\n", "\n", "![Suspension.png](attachment:6f224bc1-0414-4bf2-a6a4-efda02a63e41.png)\n", "\n", "with the following system parameters:\n", "\n", " (m) mass 1.0 kg\n", "\n", " (k) spring constant 5.0 N/m\n", "\n", " $(c)$ damping constant 2 Ns/m\n", "\n", "### **Equation of Motion:**\n", "\n", "For a mass-spring-damper system, the equation of motion can be derived using Newton's second law or by applying the principles of dynamics. The general form of the equation is:\n", "\n", "$$\n", "m \\frac{d^2x}{dt^2} + c \\frac{dx}{dt} + kx = u + w\n", "$$\n", "\n", "### **State-Space Representation:**\n", "\n", "To convert the second-order differential equation into a system of first-order differential equations, we introduce the following state variables:\n", "- Let $ x_1 = x $ (position),\n", "- Let $ x_2 = \\dot x $ (velocity).\n", "\n", "The system becomes:\n", "\n", "$$\\dot x = Ax+Bu+Dw$$\n", "\n", "where\n", "state vector $x = (position, velocity)$, and state and control matrices are the following:\n", "$$ A = \\begin{pmatrix} 0&1\\\\ -\\frac{k}{m}&-\\frac{c}{m}\\end{pmatrix},\\ B = \\begin{pmatrix} 0\\\\ \\frac{1}{m} \n", "\\end{pmatrix},\\ D =\\begin{pmatrix} 0\\\\ \\frac{1}{m} \n", "\\end{pmatrix}$$\n", "\n", "## TODO\n", "1. Check on the implementation of a bang-bang controller provided below.\n", "\n", "2. Implement a PID controller with parameters Kp = 400, Ki = 200, Kd = 50 that ensures that position of the mass ($y = [1,0]x$) tracks the zero reference input $r(t)=0.$\n", "\n", "3. Let $x_0 = (0, 0).$ Let disturbance input $w(t)$ is given by a step function\n", " $$w = \\left\\{\\begin{aligned}\n", " &0, \\quad t <3.0\\\\\n", " &1.0, \\quad 3.0 \\leq t < 7.0\\\\\n", " &0, \\quad t \\geq 7\n", " \\end{aligned}\\right.$$\n", " Comparer the trajectories of uncontrolled ($u(t) = 0$) and controlled (with bang-bang and with PID controllers correnspondingly) systems." ] }, { "cell_type": "code", "execution_count": 107, "id": "7ab7a343-6f98-4a65-ac11-d1f99cc56a65", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.integrate import odeint\n", "import matplotlib.pyplot as plt\n", "\n", "# x is a state vecot, t is a current time, A is a dynamic matrix, B is a control matrix, D is a disturbance matrix, \n", "# u_func(t) is a control input, w_func(t) is a disturbance input \n", "def StateSpace(x, t, A, B, D, u_func, w_func):\n", " w = w_func(t)\n", " u = u_func(t)\n", " return np.dot(A, x) + np.dot(B, u).flatten() + np.dot(D, w).flatten()\n", "\n", "# OpenLoopInputOutputSystem with time-dependent w(t)\n", "def OpenLoopInputOutputSystem(A, B, D, C, u_func, w_func, T, x0):\n", " # Solve the ODE system with odeint, passing the time-dependent w function\n", " solution = odeint(StateSpace, x0, T, args=(A, B, D, u_func, w_func))\n", " # Output calculation using C and the solution\n", " return (C @ solution.T) \n", "\n", "def BangBangController(A, B, D, C, u_const, ref, delay, w_func, T, x0):\n", " y_res = np.empty(x0.shape).reshape(-1,1)\n", " t0 = 0\n", " t1 = delay\n", " while t1 < T[-1]+delay:\n", " # Extract time segment\n", " T_bang = T[T<=t1]\n", " T = T[T_bang.shape[0]-1:]\n", " # Bang-Bang control logic\n", " u_func = lambda t: -u_const if C @ x0 - ref > 0 else (u_const if C @ x0 - ref < 0 else 0.0)\n", " # Compute system response\n", " sol = odeint(StateSpace, x0, T_bang, args=(A, B, D, u_func, w_func)).T\n", " x0 = sol[:,-1].flatten()\n", " # Update variables\n", " t0 = t1\n", " t1 += delay\n", " y_res = np.hstack((y_res, sol[:,1:]))\n", " return C @ y_res " ] }, { "cell_type": "code", "execution_count": 109, "id": "2db4b1bf-c43d-48d4-860f-a28dc0c3faca", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# System parameters\n", "m = 1\n", "k = 5\n", "c = 2\n", "g = 9.8\n", "\n", "A = np.array([[0, 1],\n", " [-k/m, -c/m]]) # Corrected c instead of rho\n", "\n", "B = np.array([[0],\n", " [1/m]]) # Reshaped to column vecto\n", "D = np.array([[0],\n", " [1/m]]) # Reshaped to column vector\n", "\n", "C = np.array([[1, 0]]) # Output matrix\n", "\n", "R = np.array([0])\n", "\n", "# flatten() to convert to 1D array since scipy.integrate.odeint requires the state vector (x) to have shape (n,), not (n,1).\n", "x0 = np.array([0, 0]).flatten() # Initial state\n", "\n", "# Time settings\n", "t0 = 0 # Initial time \n", "tf = 15# Final time\n", "T = np.linspace(t0, tf, 1000) # Time vector\n", "\n", "def w_func(t):\n", " if t<= 3.0:\n", " return 0.0\n", " elif 3.0<= t and t<7.0:\n", " return 1.0\n", " else:\n", " return 0.0# Disturbance input\n", " \n", "# Compute system response\n", "u_const = 0.8\n", "delay = 0.5\n", "x_ref = 0.0\n", "y = BangBangController(A, B, D, C, u_const, x_ref, delay, w_func, T, x0)\n", "\n", "# Plot the response\n", "plt.plot(T, y[0,:], linewidth=2.0, color='green')\n", "\n", "def u_func(t):\n", " return 0.0\n", "\n", "y = OpenLoopInputOutputSystem(A, B, D, C, u_func, w_func, T, x0)\n", "\n", "# Plot the response\n", "plt.plot(T, y[0,:], linewidth=2.0, color='red')\n", "\n", "plt.grid(color='black', linestyle='--', linewidth=1.0, alpha=0.7)\n", "plt.xlim([t0, tf])\n", "plt.ylabel(r'Position (m)')\n", "plt.xlabel('Time (s)')\n", "plt.title('Active Suspension System ')\n", "plt.plot(T, T* 0, linewidth=2.0, color='blue')\n", "plt.legend(['bang-bang controller', 'not controlled','reference input' ])\n", "plt.show() " ] }, { "attachments": { "c6f456ed-ce15-409a-a8cc-c1e050d956a3.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "d61494ff-64fd-411c-b80e-f25004a38c75", "metadata": {}, "source": [ "## DC Motor Speed: System Modeling\n", "\n", "A common actuator in control systems is the DC motor. It directly provides rotary motion and, coupled with wheels or drums and cables, can provide translational motion. The electric equivalent circuit of the armature and the free-body diagram of the rotor are shown in the following figure.\n", "\n", "![motor.png](attachment:c6f456ed-ce15-409a-a8cc-c1e050d956a3.png)\n", "\n", "For this example, we will assume that the input of the system is the voltage source ($V$) applied to the motor's armature, while the output is the rotational speed of the shaft $\\dot{\\theta}$. The rotor and shaft are assumed to be rigid. We further assume a viscous friction model, that is, the friction torque is proportional to shaft angular velocity. We will assume that the magnetic field is constant and, therefore, that the motor torque is proportional (with constant $K_t$) to only the armature current. Let us remark that in SI units the motor torque and back emf constants are equal, that is, $K_t = K_e$;\n", "\n", "The physical parameters for our example are:\n", "\n", " (J) moment of inertia of the rotor 0.01 kg.m^2\n", "\n", " (b) motor viscous friction constant 0.1 N.m.s\n", "\n", " (Ke) electromotive force constant 0.01 V/rad/sec\n", "\n", " (Kt) motor torque constant 0.01 N.m/Amp\n", "\n", " (R) electric resistance 1 Ohm\n", "\n", " (L) electric inductance 0.5 H\n", " \n", "\n", "Let us suppose that the measured output of the system is the angular velocity of the rotor $\\dot{\\theta}$ and the current intensity $\\dot{i}$. Then the state space model of the system is the following:\n", "$$\\dot x = Ax + Bu$$\n", "\n", "$$ y = Cx$$\n", "\n", "where state vector $x=(\\dot{\\theta}, i)$, control vector $u=V$, and state and control matrices are the following\n", "\n", "$$ A = \\begin{pmatrix} -\\frac{b}{J}&\\frac{K}{J}\\\\ -\\frac{K}{L}&-\\frac{R}{L}\\end{pmatrix},\\ B = \\begin{pmatrix} 0\\\\ \\frac{1}{L} \n", "\\end{pmatrix}$$\n", "\n", "Let us suppose that we only interested in rotation speed (angular velocity of the rotor), i.e. $C=(1,0)$.\n", "\n", "## TODO\n", "\n", "1. For a 1-rad/sec step reference, the design a PID controller that satisfies the following criteria are the following.\n", "\n", " Settling time less than 2 seconds\n", "\n", " Overshoot less than 5%\n", "\n", " Steady-state error less than 1%\n", " \n", "3. Tune a PID controller using the Ziegler-Nichols Methods." ] }, { "cell_type": "markdown", "id": "9a93d41e-8c25-43cd-8ad0-848829d5cc9b", "metadata": {}, "source": [ "## EX. 3 Inverted Pendulum\n", "\n", "The system in this example consists of an inverted pendulum mounted to a motorized cart. The inverted pendulum system is an example commonly found in control system textbooks and research literature. Its popularity derives in part from the fact that it is unstable without control, that is, the pendulum will simply fall over if the cart isn't moved to balance it. Additionally, the dynamics of the system are nonlinear. The objective of the control system is to balance the inverted pendulum by applying a force to the cart that the pendulum is attached to. A real-world example that relates directly to this inverted pendulum system is the attitude control of a booster rocket at takeoff.\n", "\n", "![inverted_pendulum.png](attachment:0a81c6f5-4431-4bf0-a50c-133da7e550cc.png)\n", "\n", "Let us consider the system with the following system parameters\n", " \n", " (M) mass of the cart 0.5 kg\n", " \n", " (m) mass of the pendulum 0.2 kg\n", " \n", " (l) length to pendulum center of mass 0.3 m\n", " \n", " (b) coefficient of friction for cart 0.1 N/m/sec\n", " \n", " (I) mass moment of inertia of the pendulum 0.006 kg.m^2\n", " \n", " (F) force applied to the cart\n", " \n", " (y) cart position coordinate\n", " \n", " (theta) angle between the pendulum and the vertical axis\n", "\n", "## TODO\n", " \n", "The inverted pendulum on the cart can be modeled as follows\n", "\n", "$$(M+m)\\ddot{y} + b\\dot{y} + ml\\ddot{\\theta}\\cos\\theta -ml\\dot\\theta^2\\sin(\\theta) = F$$\n", "\n", "$$ml\\cos(\\theta)\\ddot{y} + (I+ml^2)\\ddot{\\theta} - mgl\\sin\\theta = 0$$ \n", "\n", "1. Check on the code below showing that a linearalised model of the system is the following\n", "\n", "$$\\dot x = Ax + Bu$$\n", "\n", "$$ y = Cx$$\n", "\n", "where state vector $x = (y,\\theta,\\dot{y},\\dot{\\theta})$, control vector $u=F$.\n", "\n", "$$\\left[\\begin{array}{c}\\dot{y} \\\\ \\dot{\\theta} \\\\ \\ddot{y} \\\\ \\ddot{\\theta}\\end{array}\\right]=\n", "\\left[\\begin{array}{cccc}0 & 0 & 1 & 0 \\\\ \n", "0 & 0 & 0 & 1 \\\\ \n", "0 & \\frac{-g m^2 l^2}{I(M+m)+M m l^2} & \\frac{-\\left(I+m l^2\\right) b}{I(M+m)+M m l^2} & 0 \\\\ \n", "0 & \\frac{m g l(M+m)}{I(M+m)+M m l^2} & \\frac{m l b}{I(M+m)+M m l^2} & 0\\end{array}\\right]\n", "\\left[\\begin{array}{c}y \\\\ \\theta \\\\ \\dot{y} \\\\ \\dot{\\theta}\\end{array}\\right]+\n", "\\left[\\begin{array}{c}0 \\\\ 0 \\\\ \\frac{I+m l^2}{I(M+m)+M m l^2} \\\\ \\frac{-m l}{I(M+m)+M m l^2}\\end{array}\\right] u$$\n", "\n", "$$\n", "\\mathbf{y}=\n", "\\left[\\begin{array}{llll}1 & 0 & 0 & 0 \\\\ 0 & 1 & 0 & 0\\end{array}\\right]\n", "\\left[\\begin{array}{c}y \\\\ \\theta \\\\ \\dot{y} \\\\ \\dot{\\theta}\\end{array}\\right]$$\n", "\n", "3) Design a PID controller corresponding to the reference signal $\\theta_{ref}$ = 0 rad, while supposing that the angle is subject to a constant disturbance $w(t) = 0.1$\n", "\n", "4) Plot the position of the cart for the corresponding closed-loop system. What conclusion could you make?" ] }, { "cell_type": "code", "execution_count": 102, "id": "6bc23ec5-8bde-4fe1-8e49-cdf4f7ee6181", "metadata": {}, "outputs": [], "source": [ "import sympy as sp\n", "# Answer to EX1 q1 using symbolic calculs\n", "# Define symbolic variables\n", "M, m, b, l, I, g, F = sp.symbols('M m b l I g F')\n", "y, y1, theta, theta1, doty1, dottheta1 = sp.symbols('y y1 theta theta1 doty1 dottheta1')\n", "\n", "# Define the differential equations of the system\n", "eq1 = (M+m)*doty1 + b*y1 + m*l*dottheta1*sp.cos(theta) - m*l*theta1**2*sp.sin(theta) - F\n", "eq2 = m*l*sp.cos(theta)*doty1 + (I+m*l**2)*dottheta1 - m*g*l*sp.sin(theta)\n", "\n", "# Solve for the first derivative of theta1 (angular velocity)\n", "dottheta1_sol = sp.solve(eq2, dottheta1)[0]\n", "\n", "# Solve for the first derivative of y1 (linear velocity)\n", "doty1_sol = sp.simplify(sp.solve(eq1.subs(dottheta1, dottheta1_sol), doty1)[0])\n", "dottheta1_sol = sp.simplify(dottheta1_sol.subs(doty1,doty1_sol))\n", "\n", "# Define the state-space representation of the system dynamics\n", "f1 = y1\n", "f2 = doty1_sol \n", "f3 = theta1\n", "f4 = dottheta1_sol\n", "f = sp.Matrix([f1, f2, f3, f4])\n", "\n", "# Define state and control variables\n", "variables_x = sp.Matrix([y,y1,theta,theta1])\n", "variables_u = sp.Matrix([F])\n", "\n", "# Compute the Jacobian matrices of the system\n", "jacobian_A = sp.simplify(f.jacobian(variables_x).subs([(theta,0), (theta1,0)]))\n", "jacobian_B = sp.simplify(f.jacobian(variables_u).subs([(theta,0), (theta1,0)]))" ] }, { "cell_type": "code", "execution_count": null, "id": "8a0033ca-4a66-4371-90f8-054b84b6a4c6", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.13.2" } }, "nbformat": 4, "nbformat_minor": 5 }