def main():
dt = 0.1
T = np.arange(0, 6, dt)
plt.figure(1)
plt.xticks(np.arange(min(T), max(T) + 1, 1.0))
plt.xlabel("Time (s)")
plt.ylabel("Step response")
tf = ct.TransferFunction(1, [1, -0.6], dt)
sim(tf, T, "Single pole in RHP")
tf = ct.TransferFunction(1, [1, 0.6], dt)
sim(tf, T, "Single pole in LHP")
if "--noninteractive" in sys.argv:
latex.savefig("z_oscillations_1p")
plt.figure(2)
plt.xlabel("Time (s)")
plt.ylabel("Step response")
den = [np.real(x) for x in conv([1, 0.6 + 0.6j], [1, 0.6 - 0.6j])]
tf = ct.TransferFunction(1, den, dt)
sim(tf, T, "Complex conjugate poles in LHP")
den = [np.real(x) for x in conv([1, -0.6 + 0.6j], [1, -0.6 - 0.6j])]
tf = ct.TransferFunction(1, den, dt)
sim(tf, T, "Complex conjugate poles in RHP")
if "--noninteractive" in sys.argv:
latex.savefig("z_oscillations_2p")
else:
plt.show()
def main():
# (s - 9 + 9i)(s - 9 - 9i)
# G(s) = ------------------------
# s(s + 10)
G = cnt.tf(conv([1, -9 + 9j], [1, -9 - 9j]), conv([1, 0], [1, 10]))
cnt.root_locus(G, grid=True)
# Show plot
plt.title("Root Locus")
plt.xlabel("Real Axis (seconds$^{-1}$)")
plt.ylabel("Imaginary Axis (seconds$^{-1}$)")
plt.gca().set_aspect("equal")
if "--noninteractive" in sys.argv:
latexutils.savefig("rlocus_zeroes")
else:
plt.show()
def main():
dt = 0.0001
T = np.arange(0, 6, dt)
plt.xlabel("Time ($s$)")
plt.ylabel("Position ($m$)")
# Make plant
G = ct.TransferFunction(1, conv([1, 5], [1, 0]))
sim(ct.TransferFunction(1, 1), T, "Setpoint")
K = ct.TransferFunction(120, 1)
Gcl = ct.feedback(G, K)
sim(Gcl, T, "Underdamped")
K = ct.TransferFunction(3, 1)
Gcl = ct.feedback(G, K)
sim(Gcl, T, "Overdamped")
K = ct.TransferFunction(6.268, 1)
Gcl = ct.feedback(G, K)
sim(Gcl, T, "Critically damped")
if "--noninteractive" in sys.argv:
latex.savefig("pid_responses")
else:
plt.show()
def main():
dt = 0.1
T = np.arange(0, 6, dt)
plt.figure(1)
plt.xticks(np.arange(min(T), max(T) + 1, 1.0))
plt.xlabel("Time (s)")
plt.ylabel("Step response")
tf = cnt.TransferFunction(1, [1, -0.6], dt)
sim(tf, T, "Single pole in RHP")
tf = cnt.TransferFunction(1, [1, 0.6], dt)
sim(tf, T, "Single pole in LHP")
plt.savefig("z_oscillations_1p.svg")
plt.figure(2)
plt.xlabel("Time (s)")
plt.ylabel("Step response")
tf = cnt.TransferFunction(1, conv([1, 0.6 + 0.6j], [1, 0.6 - 0.6j]), dt)
sim(tf, T, "Complex conjugate poles in LHP")
tf = cnt.TransferFunction(1, conv([1, -0.6 + 0.6j], [1, -0.6 - 0.6j]), dt)
sim(tf, T, "Complex conjugate poles in RHP")
plt.savefig("z_oscillations_2p.svg")
def main():
# 1
# G(s) = --------------
# (s + 2)(s + 3)
G = ct.tf(1, conv([1, 0], [1, 2], [1, 3]))
ct.root_locus(G, grid=True)
plt.title("Root Locus")
plt.xlabel("Real Axis (seconds$^{-1}$)")
plt.ylabel("Imaginary Axis (seconds$^{-1}$)")
if "--noninteractive" in sys.argv:
latex.savefig("rlocus_asymptotes")
else:
plt.show()
def main():
dt = 0.0001
T = np.arange(0, 6, dt)
plt.xlabel("Time ($s$)")
plt.ylabel("Position ($m$)")
# Make plant
G = cnt.TransferFunction(1, conv([1, 5], [1, 0]))
sim(cnt.TransferFunction(1, 1), T, "Reference")
Gcl = make_closed_loop_plant(G, 120)
sim(Gcl, T, "Underdamped")
Gcl = make_closed_loop_plant(G, 3)
sim(Gcl, T, "Overdamped")
Gcl = make_closed_loop_plant(G, 6.268)
sim(Gcl, T, "Critically damped")
plt.savefig("pid_responses.svg")
#!/usr/bin/env python3
import matplotlib as mpl
mpl.use("svg")
import control as cnt
from frccontrol import conv
import matplotlib.pyplot as plt
# (s - 9 + 9i)(s - 9 - 9i)
# G(s) = ------------------------
# s(s + 10)
G = cnt.tf(conv([1, -9 + 9j], [1, -9 - 9j]), conv([1, 0], [1, 10]))
cnt.root_locus(G)
# Show plot
plt.title("Root Locus")
plt.xlabel("Real Axis (seconds$^{-1}$)")
plt.ylabel("Imaginary Axis (seconds$^{-1}$)")
plt.gca().set_aspect("equal")
plt.savefig("rlocus_zeroes.svg")
#!/usr/bin/env python3
import matplotlib as mpl
mpl.use("svg")
import control as cnt
from frccontrol import conv
import matplotlib.pyplot as plt
# 1
# G(s) = --------------
# (s + 2)(s + 3)
G = cnt.tf(1, conv([1, 0], [1, 2], [1, 3]))
cnt.root_locus(G)
plt.title("Root Locus")
plt.xlabel("Real Axis (seconds$^{-1}$)")
plt.ylabel("Imaginary Axis (seconds$^{-1}$)")
plt.savefig("rlocus_asymptotes.svg")