Analysis of Dynamic Systems

Schedule:

Getting started
Introduction
Mathematical bases
Bode diagrams
Modeling with linear elements
State variables
Block diagrams
Time response
Frequency response
Stability
Root Locus
Final project
Course evaluation

Mathematical bases

Complex Variable Theory.
Differential equations.
Laplace transform.
Theory of matrices.
Bode diagrams.

Bode plots



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from IPython.display import Image
Image(filename='img/bode1.png')



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from IPython.display import Image
Image(filename='img/bode2.png')



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from IPython.display import Image
Image(filename='img/bode3.png')



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from IPython.display import Image
Image(filename='img/bode4.png')



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from IPython.display import Image
Image(filename='img/bode5.png')



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from IPython.display import Image
Image(filename='img/bode6.png')



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from IPython.display import Image
Image(filename='img/bode7.png')

Whit Python:



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import sympy
from sympy import *

sympy.init_printing()
s = Symbol('s')
t = Symbol('t', positive=True)



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G = ((10)*(s+10))/((s)*(s+2)*(s+5))



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G



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G.expand()



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import numpy as np
from scipy import signal
import matplotlib.pyplot as plt

s1 = signal.lti([10, 100], [1, 7, 10])
w, mag, phase = signal.bode(s1, np.arange(0.01, 100.0, 0.01).tolist())

plt.figure(figsize=(15,8))
plt.subplot(2,1,1)
plt.semilogx(w, mag, lw=5)    # Bode magnitude plot

plt.ylim([-30, 30])
plt.xlabel('Hz')
plt.ylabel('Magnitude (dB)')
plt.grid(True)

plt.subplot(2,1,2)
plt.semilogx(w, phase, lw=5, label="real bode plot")  # Bode phase plot

plt.xlabel('Hz')
plt.ylim([-120, 10])
plt.ylabel('Phase (deg)')
plt.grid(True)
plt.show()



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