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nandard
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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69
Assignment 4 - PI/README.md
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69
Assignment 4 - PI/README.md
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# Integral Effect on Control System
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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!
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## Software
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This program run in Matlab
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## Variables
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`s = tf('s');` defines s as 'frequency domain' for transfer function and will be used further.
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```
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J = 0.01;
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b = 0.1;
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K = 0.01;
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R = 1;
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L = 0.5;
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```
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Those variable comes from BLDC control system.
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```
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Kp = 1;
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% Ki = 1;
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% Ki = 3;
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% Ki = 5;
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Ki = 7;
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% Ki = 9;
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```
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Variable above is the constant from PI control, we're trying to varies the constant to analyze integral effect on control system
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## Process
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The BLDC motor control system should be defined as transfer function by initialize its numerator-denumerator and *tf()* function.
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```
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num_motor = [K];
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den_motor = [J*L J*R+b*L R*b+K*K];
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motor = tf(num_motor,den_motor)
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```
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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);`
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That system will be test with step, ramp, and impulse input by call below lines
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```
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subplot(311), impulse(complete); % Impulse reponse
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subplot(312), step(complete); % Step Response
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subplot(313), step(complete / s); % Ramp response
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stepinfo(complete)
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```
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Since Matlab doesn't provide any steady-state error calculation, we process it by call below lines
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```
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[y,t] = step(complete); % Calculate Steady-State error
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sse = abs(1 - y(end))
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```
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Last line works to limit the graph
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```
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xlim([0 50])
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ylim([0 3])
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```
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## Testing
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| Kp = 1 | Ki = 1 | Ki = 3 | Ki = 5 | Ki = 7 | Ki = 9 |
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|--- |--- |--- |--- |--- |--- |
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| Rise Time | 22.7723 | 6.7782 | 3.5914 | 2.3175 | 2.3175 |
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| Settling Time | 40.3716 | 12.1907 | 6.3158 | 3.6779 | 3.6779 |
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| Overshoot | 0 | 0 | 0 | 0.3523 | 0 |
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| SSE | 1.7396e-06 | 0.0034 | 0.0033 | 0.0034 | 6.6536e-05 |
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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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35
Assignment 4 - PI/integral_tf.m
Normal file
35
Assignment 4 - PI/integral_tf.m
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@@ -0,0 +1,35 @@
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% Variable
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s = tf('s');
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J = 0.01;
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b = 0.1;
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K = 0.01;
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R = 1;
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L = 0.5;
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Kp = 1;
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% Ki = 1;
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% Ki = 3;
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% Ki = 5;
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Ki = 7;
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% Ki = 9;
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% Define Transfer Function
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num_motor = [K];
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den_motor = [J*L J*R+b*L R*b+K*K];
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motor = tf(num_motor,den_motor)
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% Define Control Function
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C = tf([Kp Ki],[1 0])
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% Define Closed-Loop function
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complete = feedback(motor*C,1);
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% Process system responses
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subplot(311), impulse(complete); % Impulse reponse
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subplot(312), step(complete); % Step Response
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subplot(313), step(complete / s); % Ramp response
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stepinfo(complete)
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% Calculate the Stead-State Error
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[y,t] = step(complete); % Calculate Steady-State error
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sse = abs(1 - y(end))
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% Limit the graph
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xlim([0 50])
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ylim([0 3])
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128
README.md
128
README.md
@@ -1,132 +1,6 @@
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# routh_table
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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!
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||||
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!
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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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```
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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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```
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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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```
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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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|
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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
|
||||
Contact nanda.r.d@mail.ugm.ac.id for more information
|
||||
### Links
|
||||
|
||||
Reference in New Issue
Block a user