{ "cells": [ { "cell_type": "code", "execution_count": 7, "id": "74b29ec8-d9c2-4d55-bdb8-afe19b1f51b7", "metadata": {}, "outputs": [], "source": [ "import numpy as np \n", "import matplotlib.pyplot as plt\n", "import control as ctrl\n", "from numpy.linalg import inv\n", "import pandas as pd" ] }, { "cell_type": "markdown", "id": "e612dcbf", "metadata": {}, "source": [ "# First Order Trasfer Function Model Analysis \n", "\n", "$$\n", " P(z) = \\frac{b}{z-a}\\quad\\Longrightarrow\\quad y_k+a*y_{k-1}=b*u_{k-1} \n", "$$\n", "\n", "$$\n", "\\begin{align*}\n", "y'_k = [-y_{k-1} \\quad u_{k-1}] * \\begin{bmatrix} a \\\\ \\quad \\\\ b \\end{bmatrix}\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "code", "execution_count": 17, "id": "b0ddcc95", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[-0. 1.24 1. ]\n", " [-0. 1.08 1. ]\n", " [-0.04 1.16 1. ]\n", " ...\n", " [-3.12 4.36 1. ]\n", " [-3.08 4.28 1. ]\n", " [-3.12 4.44 1. ]]\n", "[[ 0.00807839 0.00800129 -0.00861081]\n", " [ 0.00800129 0.00796538 -0.00864002]\n", " [-0.00861081 -0.00864002 0.00958504]]\n", "[-51966.3728 70227.4192 16613.8 ]\n", "[-0.95289509 0.04663624 -0.0498488 ]\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ ": sys[12]\n", "Inputs (1): ['u[0]']\n", "Outputs (1): ['y[0]']\n", "dt = 1\n", "\n", " 0.04664\n", " ----------\n", " z - 0.9529\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "11291.80538017654\n" ] } ], "source": [ "df = pd.read_csv(\"/home/mgph/Desktop/?/MAESTRIA/HYDROGEN_PROJ/Analysis_Data/step-response-analysis/step-response-analysis/Stp_Resp_20251220_A00.csv\", encoding=\"latin1\")\n", "yk_Ic = df.iloc[:,2] # Values of the current\n", "uk_Vstep = df.iloc[:,1] # Values of the input step \n", "uk_Velec = df.iloc[:,5] # Values of the electrodes voltages\n", "ck = np.ones(len(yk_Ic)) # ones vector \n", "\n", "u_k = uk_Velec # Define which step entrance\n", "\n", "phi = np.c_[-yk_Ic[:-1], u_k[:-1], ck[:-1]]\n", "print(phi)\n", "\n", "#Define the first order model P(z) = b/(z-a)\n", "\n", "arg_1 = inv(phi.T.dot(phi))\n", "print(arg_1)\n", "arg_2 = phi.T.dot(yk_Ic[1:])\n", "print(arg_2)\n", "thetaH = arg_1.dot(arg_2)\n", "print(thetaH)\n", "plt.plot(yk_Ic, ':r', label=\"Current Response\")\n", "plt.legend()\n", "plt.show()\n", "\n", "# Creat the transfer function \n", "num = [thetaH[1]]\n", "den = [1, thetaH[0]]\n", "Ts = 1\n", "\n", "Pz = ctrl.TransferFunction(num, den, Ts)\n", "print(Pz)\n", "\n", "#Simulate model response\n", "\n", "t = np.arange(len(u_k))*Ts\n", "t_out, y_model = ctrl.forced_response(Pz, T=t, U=u_k)\n", "plt.plot(t, yk_Ic, ':b', label=\"Current Data\")\n", "plt.plot(t_out, y_model, ':g', label='Model Response')\n", "plt.legend()\n", "plt.show()\n", "\n", "#Error Calculate \n", "Error = (yk_Ic -y_model).T.dot(yk_Ic-y_model)\n", "print(Error)" ] }, { "cell_type": "markdown", "id": "fa3c22f0", "metadata": {}, "source": [ "# Second Order Transfer Function Analysis " ] }, { "cell_type": "code", "execution_count": 18, "id": "98c591ca", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10000\n", "[[ 0.08451332 -0.08431984 -0.00022256 0.0003645 ]\n", " [-0.08431984 0.08447107 0.0003396 -0.00024069]\n", " [-0.00022256 0.0003396 0.00933068 -0.00924486]\n", " [ 0.0003645 -0.00024069 -0.00924486 0.00933728]]\n", "[-51966.3728 -51961.2464 70227.4192 70221.48 ]\n", "[-5.21011244e-01 -4.77542893e-01 1.41619175e-03 -2.89615104e-04]\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ ": sys[14]\n", "Inputs (1): ['u[0]']\n", "Outputs (1): ['y[0]']\n", "dt = 1\n", "\n", " 0.001416 z - 0.0002896\n", " -----------------------------------\n", " z^3 - 0.521 z^2 - 0.4775 z + 0.0003\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "5619.780816751438\n" ] } ], "source": [ "phi_scnd = np.zeros((len(yk_Ic),4))\n", "\n", "for i in range(1, len(yk_Ic)):\n", " for j in range(4):\n", " if j == 0:\n", " if (i-1) < 0:\n", " phi_scnd[i][j] = 0\n", " else:\n", " phi_scnd[i][j] = -yk_Ic[i-1]\n", " if j == 1:\n", " if (i-2) < 0:\n", " phi_scnd[i][j] = 0\n", " else:\n", " phi_scnd[i][j] = -yk_Ic[i-2]\n", " if j == 2:\n", " if (i-1) < 0:\n", " phi_scnd[i][j] = 0\n", " else:\n", " phi_scnd[i][j] = u_k[i-1]\n", " if j == 3:\n", " if (i-2) < 0:\n", " phi_scnd[i][j] = 0\n", " else:\n", " phi_scnd[i][j] = u_k[i-2]\n", "\n", "print(len(phi_scnd))\n", "\n", "# Define the first argument of the formula \n", "arg_A = inv(phi_scnd[1:].T.dot(phi_scnd[1:]))\n", "print(arg_A)\n", "arg_B = phi_scnd[1:].T.dot(yk_Ic[1:])\n", "print(arg_B)\n", "theta_H = arg_A.dot(arg_B)\n", "print(theta_H)\n", "plt.plot(yk_Ic, ':r', label=\"Current Response\")\n", "plt.legend()\n", "plt.show()\n", "\n", "#Force entrance for the comparative between the real data and model response\n", "k = 0.0003\n", "num_1 = [theta_H[2], theta_H[3]]\n", "den_1 = [1, theta_H[0], theta_H[1], k]\n", "Ts = 1 #time Sampling\n", "\n", "Pz_1 = ctrl.TransferFunction(num_1, den_1, Ts)\n", "print(Pz_1)\n", "\n", "t = np.arange(len(u_k))*Ts\n", "t_out_1, y_model_1 = ctrl.forced_response(Pz_1, T=t, U=u_k)\n", "plt.plot(t, yk_Ic, ':b', label=\"Current Data\")\n", "plt.plot(t_out_1, y_model_1, ':g', label=\"model\")\n", "plt.legend()\n", "plt.show()\n", "\n", "#Error\n", "Error = (yk_Ic-y_model_1).T.dot(yk_Ic-y_model_1)\n", "print(Error)\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python (fenicsproject)", "language": "python", "name": "fenicsproject" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.14.2" } }, "nbformat": 4, "nbformat_minor": 5 }