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Assignment 3 - Routh Table/442385_Nanda_Sisken_Assign_3.ipynb
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229
Assignment 3 - Routh Table/442385_Nanda_Sisken_Assign_3.ipynb
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {
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"id": "aDtFkeqAvLX2"
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},
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"outputs": [],
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"source": [
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"# Import Libraries\n",
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"import numpy as np\n",
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"import pandas as pd"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"id": "Letb52yp47Gb"
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},
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"outputs": [],
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"source": [
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"# Define RouthStability Class \n",
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"class RouthStability():\n",
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"\n",
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" ## constructor takes string of coefficiens from polynomial\n",
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" def __init__(self, den):\n",
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" self.den = np.array([float(item) for item in den.split()])\n",
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" self.deg = len(self.den)\n",
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"\n",
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" ## append k as constant in array\n",
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" def set_k(self, k):\n",
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" self.den = np.append(self.den, float(k))\n",
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" self.deg += 1\n",
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"\n",
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" ## generate routh table and print its state\n",
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" def calc_routh(self):\n",
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" height = (self.deg+1)//2\n",
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" arr = np.zeros((height + 2,height))\n",
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" for index in range(self.deg):\n",
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" if index % 2 == 0:\n",
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" arr[0][index//2] = self.den[index]\n",
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" else:\n",
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" arr[1][(index-1)//2] = self.den[index]\n",
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"\n",
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" for i in range(2, height+2):\n",
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" for j in range(height-1):\n",
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" arr[i][j] = (arr[i-1][0]*arr[i-2][j+1] - arr[i-2][0]*arr[i-1][j+1])\n",
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" arr[i][j] += 0\n",
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" try:\n",
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" arr[i][j] /= arr[i-1][0]\n",
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" except ZeroDivisionError:\n",
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" arr[i][j] = 0\n",
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" \n",
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" self.df = pd.DataFrame(arr)\n",
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" self.show_tab()\n",
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" if self.is_stable() == True:\n",
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" print(\"SYSTEM IS STABLE\")\n",
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" else:\n",
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" print(\"SYSTEM IS UNSTABLE\")\n",
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"\n",
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" ## print generated route table\n",
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" def show_tab(self):\n",
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" print(self.df)\n",
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"\n",
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" ## return generated route DataFrame\n",
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" def get_table(self):\n",
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" return self.df\n",
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"\n",
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" ## return system stability as boolean\n",
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" def is_stable(self):\n",
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" flag = True\n",
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" for item in self.df[0]:\n",
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" if item < 0: flag = False\n",
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" return flag\n",
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" \n",
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" ## return the value of a polynomial\n",
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" def get_poly(self, x):\n",
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" total = 0\n",
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" for i in range(self.deg):\n",
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" total += self.den[self.deg-i-1]*(x**i)\n",
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" print(total)\n",
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" return total"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "Je19fGrvtOu4",
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"outputId": "bcf1f997-2fa1-4838-eac7-3aa5156d4a43"
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Enter your polynomial: 1 3 5 7\n",
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"Enter your K: 9\n",
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" 0 1 2\n",
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"0 1.000000 5.0 9.0\n",
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"1 3.000000 7.0 0.0\n",
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"2 2.666667 9.0 0.0\n",
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"3 -3.125000 0.0 0.0\n",
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"4 9.000000 -0.0 0.0\n",
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"SYSTEM IS UNSTABLE\n"
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]
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}
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],
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"source": [
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"# First Testing\n",
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"den = input(\"Enter your polynomial: \")\n",
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"k_in = input(\"Enter your K: \")\n",
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"\n",
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"rs = RouthStability(den)\n",
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"rs.set_k(k_in)\n",
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"rs.calc_routh()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "kFgcxNcscafI",
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"outputId": "e67322ca-5a85-4434-a690-655b07c9404a"
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Enter your polynomial: 11 15 19 21\n",
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"Enter your K: 29\n",
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" 0 1 2\n",
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"0 11.000000 19.0 29.0\n",
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"1 15.000000 21.0 0.0\n",
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"2 3.600000 29.0 0.0\n",
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"3 -99.833333 0.0 0.0\n",
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"4 29.000000 -0.0 0.0\n",
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"SYSTEM IS UNSTABLE\n"
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]
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}
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],
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"source": [
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"# Second Testing\n",
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"den = input(\"Enter your polynomial: \")\n",
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"k_in = input(\"Enter your K: \")\n",
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"\n",
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"rs = RouthStability(den)\n",
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"rs.set_k(k_in)\n",
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"rs.calc_routh()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "jaif_A4_hfeJ",
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"outputId": "a231e081-6ff2-4e13-db18-759225fcd948"
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Enter your polynomial: 1.2 6.78 11.11\n",
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"Enter your K: 3.141\n",
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" 0 1\n",
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"0 1.200000 11.110\n",
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"1 6.780000 3.141\n",
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"2 10.554071 0.000\n",
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"3 3.141000 0.000\n",
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"SYSTEM IS STABLE\n"
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]
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}
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],
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"source": [
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"# Third Testing\n",
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"den = input(\"Enter your polynomial: \")\n",
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"k_in = input(\"Enter your K: \")\n",
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"\n",
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"rs = RouthStability(den)\n",
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"rs.set_k(k_in)\n",
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"rs.calc_routh()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"id": "SjkQCR9chk6P"
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"colab": {
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"collapsed_sections": [],
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"provenance": []
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},
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"kernelspec": {
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"display_name": "Python 3.8.10 64-bit",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"name": "python",
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"version": "3.8.10"
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},
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"vscode": {
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"interpreter": {
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"hash": "e7370f93d1d0cde622a1f8e1c04877d8463912d04d973331ad4851f04de6915a"
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}
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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134
Assignment 3 - Routh Table/README.md
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134
Assignment 3 - Routh Table/README.md
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# routh_table
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This dir is belong to Control System class contains with Automated Routh Table Calculator based on Python. This code 100% original made by my hand :), please leave some notes if you're going to use it. Thanks!
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## Libraries
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Libraries that used in this program is ```numpy``` and ```pandas```. ```numpy``` works to define and perform array while ```pandas``` is the final form after ```numpy.array``` to simplify the presentation. They imported by write..
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```
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import numpy as np
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import pandas as pd
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```
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## RouthStability Class
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This class contains lots of procedures to simplify our Routh Stability Table Generator process.
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```
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def __init__(self, den):
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self.den = np.array([float(item) for item in den.split()])
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self.deg = len(self.den)
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```
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The constructor ```__init__``` takes string of coefficiens from polynomial, extract the number, and load into class variable. It also define ```self.deg``` variable to save array's length, reducing number to calling ```len()``` function
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```
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def set_k(self, k):
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self.den = np.append(self.den, float(k))
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self.deg += 1
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```
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This function only takes one number from user and append it to ```self.den``` which defined as gain (constant). Also ```self.deg``` will increase by one
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```
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def calc_routh(self):
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height = (self.deg+1)//2
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arr = np.zeros((height + 2,height))
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for index in range(self.deg):
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if index % 2 == 0:
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arr[0][index//2] = self.den[index]
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else:
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arr[1][(index-1)//2] = self.den[index]
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for i in range(2, height+2):
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for j in range(height-1):
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arr[i][j] = (arr[i-1][0]*arr[i-2][j+1] - arr[i-2][0]*arr[i-1][j+1])/arr[i-1][0]
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arr[i][j] += 0
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self.df = pd.DataFrame(arr)
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self.show_tab()
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if self.is_stable() == True:
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print("SYSTEM IS STABLE")
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else:
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print("SYSTEM IS UNSTABLE")
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```
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```calc_routh(self)``` as the core process of this class contains initialization and process about Routh Stability Process. Firstly, it define an empty zero (basically it filled with zeros) and iteratively being inserted by ```self.den``` (refering to Routh Table principle). After that, each cell will be updated by calculating Routh Table formula. Routh Table defined as ```numpy.ndarray``` and converted to ```pandas.DataFrame``` to simplify the presentation of table. ```self.show_tab()``` is called to print the Routh Table and ```self.is_stable()``` to check system's stability.
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```
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def show_tab(self):
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print(self.df)
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```
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This function print the Routh Table, should be called only if Routh Table is generated by ```calc_routh```
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```
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def get_table(self):
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return self.df
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```
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This function return ```pandas.DataFrame``` contained by Routh Table
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```
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def is_stable(self):
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flag = True
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for item in self.df[0]:
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if item < 0: flag = False
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return flag
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```
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This function check the first column's value from Routh Table. The system is define as stable if and only if all the value is positive, else it's unstable
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```
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def get_poly(self, x):
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total = 0
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for i in range(self.deg):
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total += self.den[self.deg-i-1]*(x**i)
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print(total)
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return total
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```
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This function initialize ```x``` value as variable on ```self.den``` polynomial and return the total
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## Testing 1
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The testing can follow below example:
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```
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# First Testing
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den = input("Enter your polynomial: ")
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k_in = input("Enter your K: ")
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rs = RouthStability(den)
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rs.set_k(k_in)
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rs.calc_routh()
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```
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It takes coefficient of polynomial and K from user, insert it into ```RouthStability``` class as constructor parameter, insert the K value, and generate Routh Table. The result can be found below:
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```
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Enter your polynomial: 1 3 5 7
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Enter your K: 9
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0 1 2
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0 1.000000 5.0 9.0
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1 3.000000 7.0 0.0
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2 2.666667 9.0 0.0
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3 -3.125000 0.0 0.0
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4 9.000000 -0.0 0.0
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SYSTEM IS UNSTABLE
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```
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## Testing 2
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```
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Enter your polynomial: 11 15 19 21
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Enter your K: 29
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0 1 2
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0 11.000000 19.0 29.0
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1 15.000000 21.0 0.0
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2 3.600000 29.0 0.0
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3 -99.833333 0.0 0.0
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4 29.000000 -0.0 0.0
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SYSTEM IS UNSTABLE
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```
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## Testing 3
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```
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Enter your polynomial: 1.2 6.78 11.11
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Enter your K: 3.141
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0 1
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0 1.200000 11.110
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1 6.780000 3.141
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2 10.554071 0.000
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3 3.141000 0.000
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SYSTEM IS STABLE
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```
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### Notes
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Contact nanda.r.d@mail.ugm.ac.id for more information
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### Links
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You can access the source code here
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[github.com/nandard/routh_table.git](https://github.com/nandard/routh_table.git)
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