如何在 python 波德图中绘制边距？

Question

我想用 python 控制系统库绘制系统波特图。这很容易。问题是边距的情节。绘制相位裕度是没有问题的。但是如何绘制增益裕度？

到目前为止，这是我的代码的一部分：

import control as cn
%matplotlib notebook
import matplotlib.pyplot as plt

Ks=2
T1=5
T2=0.3
T3=0.1
Gs=cn.tf(Ks,[T1*T2*T3, T1*T2+T1*T3+T2*T3, T1+T2+T3, 1])

Vr=1
Tn=1
plt.close()
R=cn.tf([Vr*Tn, Vr],[1, 0])
L=Gs*R
gm, pm, wg, wp = cn.margin(L)

_,_,_ = cn.bode(L,dB=True)
plt.axvline(x = wp,color='r')

Answer 1

不是最优雅的解决方案，但它对我有用。

###Import modules
import numpy as np
import control as ctl
import matplotlib.pyplot as plt

##Functions
def plot_margins(sys):
    mag,phase,omega = ctl.bode(sys,dB=True,Plot=False)
    magdB = 20*np.log10(mag)
    phase_deg = phase*180.0/np.pi
    Gm,Pm,Wcg,Wcp = ctl.margin(sys)
    GmdB = 20*np.log10(Gm)
    ##Plot Gain and Phase
    f,(ax1,ax2) = plt.subplots(2,1)
    ax1.semilogx(omega,magdB)
    ax1.grid(which="both")
    ax1.set_xlabel('Frequency (rad/s)')
    ax1.set_ylabel('Magnitude (dB)')
    ax2.semilogx(omega,phase_deg)
    ax2.grid(which="both")
    ax2.set_xlabel('Frequency (rad/s)')
    ax2.set_ylabel('Phase (deg)')
    ax1.set_title('Gm = '+str(np.round(GmdB,2))+' dB (at '+str(np.round(Wcg,2))+' rad/s), Pm = '+str(np.round(Pm,2))+' deg (at '+str(np.round(Wcp,2))+' rad/s)')
    ###Plot the zero dB line
    ax1.plot(omega,0*omega,'k--',lineWidth=2)
    ###Plot the -180 deg lin
    ax2.plot(omega,-180+0*omega,'k--',lineWidth=2)
    ##Plot the vertical line from -180 to 0 at Wcg
    ax2.plot([Wcg,Wcg],[-180,0],'r--',lineWidth=2)
    ##Plot the vertical line from -180+Pm to 0 at Wcp
    ax2.plot([Wcp,Wcp],[-180+Pm,0],'g--',lineWidth=2)
    ##Plot the vertical line from min(magdB) to 0-GmdB at Wcg
    ax1.plot([Wcg,Wcg],[np.min(magdB),0-GmdB],'r--',lineWidth=2)
    ##Plot the vertical line from min(magdB) to 0db at Wcp
    ax1.plot([Wcp,Wcp],[np.min(magdB),0],'g--',lineWidth=2)
    return Gm,Pm,Wcg,Wcp

#%%%Actuator Dynamics
G = ctl.tf([1],[1,2,1,0])
Gm,Pm,Wcg,Wcp=plot_margins(G)
plt.show()

Answer 2

从 control 的 0.8 版开始，bode_plot 函数（也称为 bode）有一个绘制边距的选项。

import control

sys = control.tf([1], [1, 1]) # example transfer function

control.bode_plot(sys, margins=True)
# or
control.bode(sys, margins=True)

但是，这种方法并不总是如我所愿，尤其是在有多个传递函数的情况下。如果你想要更多的控制（双关语），你可以做一些类似于@monte-carlo 的回答，但是通过直接在 bode_plot/bode 命令生成的图上绘制边距。

import control
import matplotlib as plt

sys = control.tf([1], [1, 1]) # example transfer function

control.bode(sys, dB=True)
gm, pm, wg, wp = control.margin(sys)

fig = plt.gcf() # Get a handle to the current figure (the bode plot)
mag_axis, phase_axis = fig.axes # Get the magnitude and phase subplots

mag_axis.plot([wg, wg], [0, control.mag2db(gm)])
phase_axis.plot([wp, wp], [-180, pm])

如何在 python 波德图中绘制边距？

How can I plot the margins in a python bode plot?

python

plot

system

matplotlib