control-system/Assignment 3 - Routh Table

routh_table

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!

Libraries

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..

import numpy as np
import pandas as pd

RouthStability Class

This class contains lots of procedures to simplify our Routh Stability Table Generator process.

def __init__(self, den):
    self.den = np.array([float(item) for item in den.split()])
    self.deg = len(self.den)

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

def set_k(self, k):
    self.den = np.append(self.den, float(k))
    self.deg += 1

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

def calc_routh(self):
    height = (self.deg+1)//2
    arr = np.zeros((height + 2,height))
    for index in range(self.deg):
        if index % 2 == 0:
        arr[0][index//2] = self.den[index]
        else:
        arr[1][(index-1)//2] = self.den[index]

    for i in range(2, height+2):
        for j in range(height-1):
        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]
        arr[i][j] += 0

    self.df = pd.DataFrame(arr)
    self.show_tab()
    if self.is_stable() == True:
        print("SYSTEM IS STABLE")
    else:
        print("SYSTEM IS UNSTABLE")

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.

def show_tab(self):
    print(self.df)

This function print the Routh Table, should be called only if Routh Table is generated by calc_routh

def get_table(self):
    return self.df

This function return pandas.DataFrame contained by Routh Table

def is_stable(self):
    flag = True
    for item in self.df[0]:
        if item < 0: flag = False
    return flag

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

def get_poly(self, x):
    total = 0
    for i in range(self.deg):
        total += self.den[self.deg-i-1]*(x**i)
        print(total)
    return total

This function initialize x value as variable on self.den polynomial and return the total

Testing 1

The testing can follow below example:

# First Testing
den = input("Enter your polynomial: ")
k_in = input("Enter your K: ")

rs = RouthStability(den)
rs.set_k(k_in)
rs.calc_routh()

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:

Enter your polynomial: 1 3 5 7
Enter your K: 9
          0    1    2
0  1.000000  5.0  9.0
1  3.000000  7.0  0.0
2  2.666667  9.0  0.0
3 -3.125000  0.0  0.0
4  9.000000 -0.0  0.0
SYSTEM IS UNSTABLE

Testing 2

Enter your polynomial: 11 15 19 21
Enter your K: 29
           0     1     2
0  11.000000  19.0  29.0
1  15.000000  21.0   0.0
2   3.600000  29.0   0.0
3 -99.833333   0.0   0.0
4  29.000000  -0.0   0.0
SYSTEM IS UNSTABLE

Testing 3

Enter your polynomial: 1.2 6.78 11.11
Enter your K: 3.141
           0       1
0   1.200000  11.110
1   6.780000   3.141
2  10.554071   0.000
3   3.141000   0.000
SYSTEM IS STABLE

Notes

Contact nanda.r.d@mail.ugm.ac.id for more information

Links

You can access the source code here github.com/nandard/routh_table.git