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442385_Nanda_Sisken_Assign_3.ipynb → Assignment 3 - Routh Table/442385_Nanda_Sisken_Assign_3.ipynb
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# 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](https://github.com/nandard/routh_table.git)

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# Integral Effect on Control System
This dir is belong to Control System class contains with Integral Effect on Control System. This code 100% original made by my hand :), please leave some notes if you're going to use it. Thanks!
## Software
This program run in Matlab
## Variables
`s = tf('s');` defines s as 'frequency domain' for transfer function and will be used further.
```
J = 0.01;
b = 0.1;
K = 0.01;
R = 1;
L = 0.5;
```
Those variable comes from BLDC control system.
```
Kp = 1;
% Ki = 1;
% Ki = 3;
% Ki = 5;
Ki = 7;
% Ki = 9;
```
Variable above is the constant from PI control, we're trying to varies the constant to analyze integral effect on control system
## Process
The BLDC motor control system should be defined as transfer function by initialize its numerator-denumerator and *tf()* function.
```
num_motor = [K];
den_motor = [J*L J*R+b*L R*b+K*K];
motor = tf(num_motor,den_motor)
```
Besides the plant function, the PI-control system defined by `C = tf([Kp Ki],[1 0])`. The vector is set according to PI formula which `PI = Kp * Ki/s`. After that, both of system are multiplied each others without feedback by `complete = feedback(motor*C,1);`
That system will be test with step, ramp, and impulse input by call below lines
```
subplot(311), impulse(complete); % Impulse reponse
subplot(312), step(complete); % Step Response
subplot(313), step(complete / s); % Ramp response
stepinfo(complete)
```
Since Matlab doesn't provide any steady-state error calculation, we process it by call below lines
```
[y,t] = step(complete); % Calculate Steady-State error
sse = abs(1 - y(end))
```
Last line works to limit the graph
```
xlim([0 50])
ylim([0 3])
```
## Testing
| Kp = 1 | Ki = 1 | Ki = 3 | Ki = 5 | Ki = 7 | Ki = 9 |
|--- |--- |--- |--- |--- |--- |
| Rise Time | 22.7723 | 6.7782 | 3.5914 | 2.3175 | 2.3175 |
| Settling Time | 40.3716 | 12.1907 | 6.3158 | 3.6779 | 3.6779 |
| Overshoot | 0 | 0 | 0 | 0.3523 | 0 |
| SSE | 1.7396e-06 | 0.0034 | 0.0033 | 0.0034 | 6.6536e-05 |
### 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](https://github.com/nandard/routh_table.git)

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% Variable
s = tf('s');
J = 0.01;
b = 0.1;
K = 0.01;
R = 1;
L = 0.5;
Kp = 1;
% Ki = 1;
% Ki = 3;
% Ki = 5;
Ki = 7;
% Ki = 9;
% Define Transfer Function
num_motor = [K];
den_motor = [J*L J*R+b*L R*b+K*K];
motor = tf(num_motor,den_motor)
% Define Control Function
C = tf([Kp Ki],[1 0])
% Define Closed-Loop function
complete = feedback(motor*C,1);
% Process system responses
subplot(311), impulse(complete); % Impulse reponse
subplot(312), step(complete); % Step Response
subplot(313), step(complete / s); % Ramp response
stepinfo(complete)
% Calculate the Stead-State Error
[y,t] = step(complete); % Calculate Steady-State error
sse = abs(1 - y(end))
% Limit the graph
xlim([0 50])
ylim([0 3])

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README.md
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# routh_table # routh_table
This repo 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! This repo is belong to Control System class and Mr. Muhammad Auzan as lecturer. 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 ### Notes
Contact nanda.r.d@mail.ugm.ac.id for more information Contact nanda.r.d@mail.ugm.ac.id for more information
### Links ### Links