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Hey, To get a short time fix, I took the frequency response of the original functions, converted magnitude and phase into a complex number and redid the calculation, which returned a the expected form of Hcl, as seen in the plot below.
The code i used is the following: Since I want to use control.feedback() later on as well, this problem is especially problematic, since it also appears there. EDIT: I should mention, that I don't see this kind of behaviour for simple transfer functions. |
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The frequency response is wrong due to numerical problems with the transfer function form. Transfer function form isn't good for high order systems, say order 10 or more. I can get the right result using state-space form, but it isn't quite as easy to construct the feedback loop as with TF form, since StateSpace doesn't support division. Your feedback arrangement is unusual, but I've taken it at face value. The import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import control
# Importing State-Space matrices and check if dimensions are correct
ssAspoiler = np.loadtxt(open('ssA_spoiler.csv', 'rb'), delimiter=',')
ssB = np.loadtxt(open('ssB.csv', 'rb'), delimiter=',')
ssC = np.loadtxt(open('ssC.csv', 'rb'), delimiter=',')
ssD = np.loadtxt(open('ssD.csv', 'rb'), delimiter=',')
print('dim(A) =', np.shape(ssAspoiler))
print('dim(B) =', np.shape(ssB))
print('dim(C) =', np.shape(ssC))
print('dim(D) =', np.shape(ssD))
# Define Frequency Array
Frequency_Array = np.linspace(0.1, 100, int(1e5))
Omega_Array = Frequency_Array * (2*np.pi)
# Create State-Space System
sys = control.StateSpace(ssAspoiler, ssB, ssC, ssD)
# Choose in- and outputs
i1 = 0
i2 = 6
o = 12
# Extract TFs from State-Space System
H = control.minreal(sys[o,i1])
P = control.minreal(sys[o,i2])
# Calculating (closed loop) TF from existing TF's
# Feedback form inferred from Hcl = H/(1+P = H * (1 / (1+P) = H * feedback(1,P)
Hcl = control.minreal(H * control.feedback(1, P))
# Compute frequency_response() of all TF from above
mag_H, phase_H, _ = control.frequency_response(H, Omega_Array)
mag_P, phase_P, _ = control.frequency_response(P, Omega_Array)
mag_Hcl, phase_Hcl, _ = control.frequency_response(Hcl, Omega_Array)
# Try different way to get proper frequency response of Hcl
P_comp = mag_P * np.exp(1j*phase_P)
H_comp = mag_H * np.exp(1j*phase_H)
Hcl_comp = (H_comp) / (1 + P_comp)
# Plot frequency responses
plt.figure(dpi = 150, figsize = (10, 6))
plt.loglog(Frequency_Array, mag_Hcl, color = 'k', label = 'Hcl from frequency_reponse()')
plt.loglog(Frequency_Array, np.abs(Hcl_comp), linewidth = .75, color = 'r', label = 'Hcl from complex calcs')
plt.loglog(Frequency_Array, mag_H, label = 'H', linewidth = .75)
plt.loglog(Frequency_Array, mag_P, label = 'P', linewidth = .75)
plt.grid(True, which = 'both')
plt.xlabel('Frequency [Hz]')
plt.ylabel('Magnitude')
plt.legend(loc = 'lower left')
plt.show()
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The frequency response is wrong due to numerical problems with the transfer function form. Transfer function form isn't good for high order systems, say order 10 or more. I can get the right result using state-space form, but it isn't quite as easy to construct the feedback loop as with TF form, since StateSpace doesn't support division.
Your feedback arrangement is unusual, but I've taken it at face value. The
minrealcalls aren't necessary, but made a difference when I had the wrong feedback form (feedback(H, P)instead ofH * feedback(1, P)).