{ "cells": [ { "cell_type": "markdown", "id": "c017196f", "metadata": {}, "source": [ "# Output feedback control using LQR and extended Kalman filtering\n", "RMM, 14 Feb 2022\n", "\n", "This notebook illustrates the implementation of an extended Kalman filter and the use of the estimated state for LQR feedback of a vectored thrust aircraft model." ] }, { "cell_type": "code", "execution_count": 11, "id": "544525ab", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import matplotlib.patches as patches\n", "import control as ct" ] }, { "cell_type": "markdown", "id": "859834cf", "metadata": {}, "source": [ "## System definition\n", "We consider a (planar) vertical takeoff and landing aircraf model:\n", "\n", "![PVTOL diagram](https://murray.cds.caltech.edu/images/murray.cds/7/7d/Pvtol-diagram.png)\n", "\n", "The dynamics of the system with disturbances on the $x$ and $y$ variables are given by\n", "\n", "$$\n", " \\begin{aligned}\n", " m \\ddot x &= F_1 \\cos\\theta - F_2 \\sin\\theta - c \\dot x + d_x, \\\\\n", " m \\ddot y &= F_1 \\sin\\theta + F_2 \\cos\\theta - c \\dot y - m g + d_y, \\\\\n", " J \\ddot \\theta &= r F_1.\n", " \\end{aligned}\n", "$$\n", "\n", "The measured values of the system are the position and orientation,\n", "with added noise $n_x$, $n_y$, and $n_\\theta$:\n", "\n", "$$\n", " \\vec y = \\begin{bmatrix} x \\\\ y \\\\ \\theta \\end{bmatrix} + \n", " \\begin{bmatrix} n_x \\\\ n_y \\\\ n_z \\end{bmatrix}.\n", "$$" ] }, { "cell_type": "markdown", "id": "198a068d", "metadata": {}, "source": [ "The dynamics are defined in the `pvtol` module:" ] }, { "cell_type": "code", "execution_count": 12, "id": "ffafed74", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Object: pvtol\n", "Inputs (2): F1, F2, \n", "Outputs (6): x0, x1, x2, x3, x4, x5, \n", "States (6): x0, x1, x2, x3, x4, x5, \n", "\n", "Object: pvtol_noisy\n", "Inputs (7): F1, F2, Dx, Dy, Nx, Ny, Nth, \n", "Outputs (6): x0, x1, x2, x3, x4, x5, \n", "States (6): x0, x1, x2, x3, x4, x5, \n" ] } ], "source": [ "# pvtol = nominal system (no disturbances or noise)\n", "# pvtol_noisy = pvtol w/ process disturbances and sensor noise\n", "from pvtol import pvtol, pvtol_noisy, plot_results\n", "\n", "# Find the equiblirum point corresponding to the origin\n", "xe, ue = ct.find_eqpt(\n", " pvtol, np.zeros(pvtol.nstates),\n", " np.zeros(pvtol.ninputs), [0, 0, 0, 0, 0, 0],\n", " iu=range(2, pvtol.ninputs), iy=[0, 1])\n", "\n", "x0, u0 = ct.find_eqpt(\n", " pvtol, np.zeros(pvtol.nstates),\n", " np.zeros(pvtol.ninputs), np.array([2, 1, 0, 0, 0, 0]),\n", " iu=range(2, pvtol.ninputs), iy=[0, 1])\n", "\n", "# Extract the linearization for use in LQR design\n", "pvtol_lin = pvtol.linearize(xe, ue)\n", "A, B = pvtol_lin.A, pvtol_lin.B\n", "\n", "print(pvtol, \"\\n\")\n", "print(pvtol_noisy)" ] }, { "cell_type": "markdown", "id": "be6ec05c", "metadata": {}, "source": [ "We also define the properties of the disturbances, noise, and initial conditions:" ] }, { "cell_type": "code", "execution_count": 13, "id": "1e1ee7c9", "metadata": {}, "outputs": [], "source": [ "# Disturbance and noise intensities\n", "Qv = np.diag([1e-2, 1e-2])\n", "Qw = np.array([[2e-4, 0, 1e-5], [0, 2e-4, 1e-5], [1e-5, 1e-5, 1e-4]])\n", "Qwinv = np.linalg.inv(Qw)\n", "\n", "# Initial state covariance\n", "P0 = np.eye(pvtol.nstates)" ] }, { "cell_type": "markdown", "id": "e4c52c73", "metadata": {}, "source": [ "## Control system design\n", "\n", "We start be defining an extended Kalman filter to estimate the state of the system from the measured outputs." ] }, { "cell_type": "code", "execution_count": 14, "id": "3647bf15", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Object: sys[3]\n", "Inputs (5): x0, x1, x2, F1, F2, \n", "Outputs (6): xh0, xh1, xh2, xh3, xh4, xh5, \n", "States (42): x[0], x[1], x[2], x[3], x[4], x[5], x[6], x[7], x[8], x[9], x[10], x[11], x[12], x[13], x[14], x[15], x[16], x[17], x[18], x[19], x[20], x[21], x[22], x[23], x[24], x[25], x[26], x[27], x[28], x[29], x[30], x[31], x[32], x[33], x[34], x[35], x[36], x[37], x[38], x[39], x[40], x[41], \n" ] } ], "source": [ "# Define the disturbance input and measured output matrices\n", "F = np.array([[0, 0], [0, 0], [0, 0], [1, 0], [0, 1], [0, 0]])\n", "C = np.eye(3, 6)\n", "\n", "# Estimator update law\n", "def estimator_update(t, x, u, params):\n", " # Extract the states of the estimator\n", " xhat = x[0:pvtol.nstates]\n", " P = x[pvtol.nstates:].reshape(pvtol.nstates, pvtol.nstates)\n", "\n", " # Extract the inputs to the estimator\n", " y = u[0:3] # just grab the first three outputs\n", " u = u[3:5] # get the inputs that were applied as well\n", "\n", " # Compute the linearization at the current state\n", " A = pvtol.A(xhat, u) # A matrix depends on current state\n", " # A = pvtol.A(xe, ue) # Fixed A matrix (for testing/comparison)\n", " \n", " # Compute the optimal again\n", " L = P @ C.T @ Qwinv\n", "\n", " # Update the state estimate\n", " xhatdot = pvtol.updfcn(t, xhat, u, params) - L @ (C @ xhat - y)\n", "\n", " # Update the covariance\n", " Pdot = A @ P + P @ A.T - P @ C.T @ Qwinv @ C @ P + F @ Qv @ F.T\n", "\n", " # Return the derivative\n", " return np.hstack([xhatdot, Pdot.reshape(-1)])\n", "\n", "estimator = ct.NonlinearIOSystem(\n", " estimator_update, lambda t, x, u, params: x[0:pvtol.nstates],\n", " states=pvtol.nstates + pvtol.nstates**2,\n", " inputs= pvtol_noisy.state_labels[0:3] \\\n", " + pvtol_noisy.input_labels[0:pvtol.ninputs],\n", " outputs=[f'xh{i}' for i in range(pvtol.nstates)],\n", ")\n", "print(estimator)" ] }, { "cell_type": "markdown", "id": "8c97626d", "metadata": {}, "source": [ "We now define an LQR controller, using a physically motivated weighting:" ] }, { "cell_type": "code", "execution_count": 15, "id": "9787db61", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Object: control\n", "Inputs (14): xd[0], xd[1], xd[2], xd[3], xd[4], xd[5], ud[0], ud[1], xh0, xh1, xh2, xh3, xh4, xh5, \n", "Outputs (2): F1, F2, \n", "States (0): \n", "\n", "A = []\n", "\n", "B = []\n", "\n", "C = []\n", "\n", "D = [[-3.16227766e+00 -1.31948924e-07 8.67680175e+00 -2.35855555e+00\n", " -6.98881806e-08 1.91220852e+00 1.00000000e+00 0.00000000e+00\n", " 3.16227766e+00 1.31948924e-07 -8.67680175e+00 2.35855555e+00\n", " 6.98881806e-08 -1.91220852e+00]\n", " [-1.31948923e-06 3.16227766e+00 -2.32324805e-07 -2.36396241e-06\n", " 4.97998224e+00 7.90913288e-08 0.00000000e+00 1.00000000e+00\n", " 1.31948923e-06 -3.16227766e+00 2.32324805e-07 2.36396241e-06\n", " -4.97998224e+00 -7.90913288e-08]]\n", " \n", "\n", "Object: xh5\n", "Inputs (13): xd[0], xd[1], xd[2], xd[3], xd[4], xd[5], ud[0], ud[1], Dx, Dy, Nx, Ny, Nth, \n", "Outputs (14): x0, x1, x2, x3, x4, x5, F1, F2, xh0, xh1, xh2, xh3, xh4, xh5, \n", "States (48): pvtol_noisy_x0, pvtol_noisy_x1, pvtol_noisy_x2, pvtol_noisy_x3, pvtol_noisy_x4, pvtol_noisy_x5, sys[3]_x[0], sys[3]_x[1], sys[3]_x[2], sys[3]_x[3], sys[3]_x[4], sys[3]_x[5], sys[3]_x[6], sys[3]_x[7], sys[3]_x[8], sys[3]_x[9], sys[3]_x[10], sys[3]_x[11], sys[3]_x[12], sys[3]_x[13], sys[3]_x[14], sys[3]_x[15], sys[3]_x[16], sys[3]_x[17], sys[3]_x[18], sys[3]_x[19], sys[3]_x[20], sys[3]_x[21], sys[3]_x[22], sys[3]_x[23], sys[3]_x[24], sys[3]_x[25], sys[3]_x[26], sys[3]_x[27], sys[3]_x[28], sys[3]_x[29], sys[3]_x[30], sys[3]_x[31], sys[3]_x[32], sys[3]_x[33], sys[3]_x[34], sys[3]_x[35], sys[3]_x[36], sys[3]_x[37], sys[3]_x[38], sys[3]_x[39], sys[3]_x[40], sys[3]_x[41], \n" ] } ], "source": [ "# Shoot for 1 cm error in x, 10 cm error in y. Try to keep the angle\n", "# less than 5 degrees in making the adjustments. Penalize side forces\n", "# due to loss in efficiency.\n", "#\n", "\n", "Qx = np.diag([100, 10, (180/np.pi) / 5, 0, 0, 0])\n", "Qu = np.diag([10, 1])\n", "K, _, _ = ct.lqr(A, B, Qx, Qu)\n", "\n", "#\n", "# Control system construction: combine LQR w/ EKF\n", "#\n", "# Use the linearization around the origin to design the optimal gains\n", "# to see how they compare to the final value of P for the EKF\n", "#\n", "\n", "# Construct the state feedback controller with estimated state as input\n", "statefbk, _ = ct.create_statefbk_iosystem(pvtol, K, estimator=estimator)\n", "print(statefbk, \"\\n\")\n", "\n", "# Reconstruct the control system with the noisy version of the process\n", "# Create a closed loop system around the controller\n", "clsys = ct.interconnect(\n", " [pvtol_noisy, statefbk, estimator],\n", " inplist = statefbk.input_labels[0:pvtol.ninputs + pvtol.nstates] + \\\n", " pvtol_noisy.input_labels[pvtol.ninputs:],\n", " inputs = statefbk.input_labels[0:pvtol.ninputs + pvtol.nstates] + \\\n", " pvtol_noisy.input_labels[pvtol.ninputs:],\n", " outlist = pvtol.output_labels + statefbk.output_labels + estimator.output_labels,\n", " outputs = pvtol.output_labels + statefbk.output_labels + estimator.output_labels\n", ")\n", "print(clsys)" ] }, { "cell_type": "markdown", "id": "7bf558a0", "metadata": {}, "source": [ "## Simulations\n", "\n", "We now simulate the response of the system, starting with an instantiation of the noise:" ] }, { "cell_type": "code", "execution_count": 16, "id": "c2583a0e", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Create the time vector for the simulation\n", "Tf = 10\n", "T = np.linspace(0, Tf, 1000)\n", "\n", "# Create representative process disturbance and sensor noise vectors\n", "np.random.seed(117) # avoid figures changing from run to run\n", "V = ct.white_noise(T, Qv) # smaller disturbances and noise then design\n", "W = ct.white_noise(T, Qw)\n", "plt.plot(T, V[0], label=\"V[0]\")\n", "plt.plot(T, W[0], label=\"W[0]\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "id": "4d944709", "metadata": {}, "source": [ "### LQR with EKF" ] }, { "cell_type": "code", "execution_count": 17, "id": "ad7a9750", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Put together the input for the system\n", "U = np.vstack([\n", " np.outer(xe, np.ones_like(T)), # xd\n", " np.outer(ue, np.ones_like(T)), # ud\n", " V, W # disturbances and noise\n", "])\n", "X0 = np.hstack([x0, np.zeros(pvtol.nstates), P0.reshape(-1)])\n", "\n", "# Initial condition response\n", "resp = ct.input_output_response(clsys, T, U, X0)\n", "\n", "# Plot the response\n", "plot_results(T, resp.states, resp.outputs[pvtol.nstates:])" ] }, { "cell_type": "code", "execution_count": 18, "id": "c5f24119", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Response of the first two states, including internal estimates\n", "plt.figure()\n", "h1, = plt.plot(resp.time, resp.outputs[0], 'b-', linewidth=0.75)\n", "h2, = plt.plot(resp.time, resp.outputs[1], 'r-', linewidth=0.75)\n", "\n", "# Add on the internal estimator states\n", "xh0 = clsys.find_output('xh0')\n", "xh1 = clsys.find_output('xh1')\n", "h3, = plt.plot(resp.time, resp.outputs[xh0], 'k--')\n", "h4, = plt.plot(resp.time, resp.outputs[xh1], 'k--')\n", "\n", "plt.plot([0, 10], [0, 0], 'k--', linewidth=0.5)\n", "plt.ylabel(\"Position $x$, $y$ [m]\")\n", "plt.xlabel(\"Time $t$ [s]\")\n", "plt.legend(\n", " [h1, h2, h3, h4], ['$x$', '$y$', '$\\hat{x}$', '$\\hat{y}$'], \n", " loc='upper right', frameon=False, ncol=2)" ] }, { "cell_type": "markdown", "id": "0c0d5c99", "metadata": {}, "source": [ "### Full state feedback\n", "\n", "As a comparison, we can investigate the response of the system if the exact state was available:" ] }, { "cell_type": "code", "execution_count": 19, "id": "3b6a1f1c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Compute the full state feedback solution\n", "lqr_ctrl, _ = ct.create_statefbk_iosystem(pvtol, K)\n", "\n", "lqr_clsys = ct.interconnect(\n", " [pvtol_noisy, lqr_ctrl],\n", " inplist = lqr_ctrl.input_labels[0:pvtol.ninputs + pvtol.nstates] + \\\n", " pvtol_noisy.input_labels[pvtol.ninputs:],\n", " inputs = lqr_ctrl.input_labels[0:pvtol.ninputs + pvtol.nstates] + \\\n", " pvtol_noisy.input_labels[pvtol.ninputs:],\n", " outlist = pvtol.output_labels + lqr_ctrl.output_labels,\n", " outputs = pvtol.output_labels + lqr_ctrl.output_labels\n", ")\n", "\n", "# Put together the input for the system\n", "U = np.vstack([\n", " np.outer(xe, np.ones_like(T)), # xd\n", " np.outer(ue, np.ones_like(T)), # ud\n", " V, W * 0 # disturbances and noise\n", "])\n", "\n", "# Run a simulation with full state feedback\n", "lqr_resp = ct.input_output_response(lqr_clsys, T, U, x0)\n", "\n", "# Compare the results\n", "plt.plot(resp.states[0], resp.states[1], 'b-', label=\"Extended KF\")\n", "plt.plot(lqr_resp.states[0], lqr_resp.states[1], 'r-', label=\"Full state\")\n", "\n", "plt.xlabel('$x$ [m]')\n", "plt.ylabel('$y$ [m]')\n", "plt.axis('equal')\n", "plt.legend(frameon=False);" ] }, { "cell_type": "code", "execution_count": null, "id": "dc86067c", "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": "3.9.1" } }, "nbformat": 4, "nbformat_minor": 5 }