I-Glied¶

Integrator (I-Glied)¶

\[y(t) = V_i \int_{0}^{t} u(t) \qquad y(0)=0\]

\[G(s) = \frac{V_i}{s}.\]

import control
import numpy as np
import matplotlib.pyplot as plt
plt.style.use('ggplot')

s = control.TransferFunction.s

Vi = 10
Gs = Vi/s
Gs

\[\frac{10}{s}\]

def check_proper_tf(Gs):
    """check if transferfunction is proper"""
    return len(Gs.num[0][0]) <= len(Gs.den[0][0])
    
check_proper_tf(Gs)

True

# step response
(tout, yout)  = control.step_response(Gs)
plt.plot(tout,yout)
plt.title("Sprung Antwort")
plt.ylabel("y")
plt.xlabel("t (s)")

Text(0.5, 0, 't (s)')

# bode diagram
(mag, phase_rad, w) = control.bode_plot(Gs)

# nyquist plot
res_nyquist = control.nyquist_plot(Gs)

# pole zero map
poles, zeros = control.pzmap(Gs, plot=True)