CH08_SEC08_3_PlantInversion.ipynb

Kernel: Python 3

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rcParams
from control.matlab import *
import slycot
from scipy import signal
# Python control toolbox available at https://python-control.readthedocs.io/

plt.rcParams['figure.figsize'] = [8, 8]
plt.rcParams.update({'font.size': 18})

s = tf(np.array([1,0]),np.array([0,1]))
G = (s+1)/(s-2)
Gtrue = (s+0.9)/(s-1.9)

K = 1/G

L = K*Gtrue


fig = plt.figure()
gm, pm, wg, wp = margin(L)
_,_,_ = bode(L)
for ax in fig.axes:
    xl = ax.get_xlim()
    yl = ax.get_ylim()
    ax.plot(wg*np.ones(2),ax.get_ylim(),'k--',linewidth=2)
    ax.plot(wp*np.ones(2),ax.get_ylim(),'k--',linewidth=2)
    ax.plot(ax.get_xlim(),np.zeros(2),'k--',linewidth=2)
    ax.set_xlim(xl)
    ax.set_ylim(yl)
    
CL = feedback(L,1)
CL

$$\frac{s^2 - 1.1 s - 1.8}{2 s^2 - 2 s - 3.7}$$