def test_fbs_bode(self):
ct.use_fbs_defaults()
# Generate a Bode plot
plt.figure()
omega = np.logspace(-3, 3, 100)
ct.bode_plot(self.sys, omega)
# Get the magnitude line
mag_axis = plt.gcf().axes[0]
mag_line = mag_axis.get_lines()
mag_data = mag_line[0].get_data()
mag_x, mag_y = mag_data
# Make sure the x-axis is in rad/sec and y-axis is in natural units
np.testing.assert_almost_equal(mag_x[0], 0.001, decimal=6)
np.testing.assert_almost_equal(mag_y[0], 10, decimal=3)
# Get the phase line
phase_axis = plt.gcf().axes[1]
phase_line = phase_axis.get_lines()
phase_data = phase_line[0].get_data()
phase_x, phase_y = phase_data
# Make sure the x-axis is in rad/sec and y-axis is in degrees
np.testing.assert_almost_equal(phase_x[-1], 1000, decimal=0)
np.testing.assert_almost_equal(phase_y[-1], -180, decimal=0)
# Override the defaults and make sure that works as well
plt.figure()
ct.bode_plot(self.sys, omega, dB=True)
mag_x, mag_y = (((plt.gcf().axes[0]).get_lines())[0]).get_data()
np.testing.assert_almost_equal(mag_y[0], 20 * log10(10), decimal=3)
plt.figure()
ct.bode_plot(self.sys, omega, Hz=True)
mag_x, mag_y = (((plt.gcf().axes[0]).get_lines())[0]).get_data()
np.testing.assert_almost_equal(mag_x[0], 0.001 / (2 * pi), decimal=6)
plt.figure()
ct.bode_plot(self.sys, omega, deg=False)
phase_x, phase_y = (((plt.gcf().axes[1]).get_lines())[0]).get_data()
np.testing.assert_almost_equal(phase_y[-1], -pi, decimal=2)
ct.reset_defaults()
def test_fbs_bode(self):
ct.use_fbs_defaults();
# Generate a Bode plot
plt.figure()
omega = np.logspace(-3, 3, 100)
ct.bode_plot(self.sys, omega)
# Get the magnitude line
mag_axis = plt.gcf().axes[0]
mag_line = mag_axis.get_lines()
mag_data = mag_line[0].get_data()
mag_x, mag_y = mag_data
# Make sure the x-axis is in rad/sec and y-axis is in natural units
np.testing.assert_almost_equal(mag_x[0], 0.001, decimal=6)
np.testing.assert_almost_equal(mag_y[0], 10, decimal=3)
# Get the phase line
phase_axis = plt.gcf().axes[1]
phase_line = phase_axis.get_lines()
phase_data = phase_line[0].get_data()
phase_x, phase_y = phase_data
# Make sure the x-axis is in rad/sec and y-axis is in degrees
np.testing.assert_almost_equal(phase_x[-1], 1000, decimal=0)
np.testing.assert_almost_equal(phase_y[-1], -180, decimal=0)
# Override the defaults and make sure that works as well
plt.figure()
ct.bode_plot(self.sys, omega, dB=True)
mag_x, mag_y = (((plt.gcf().axes[0]).get_lines())[0]).get_data()
np.testing.assert_almost_equal(mag_y[0], 20*log10(10), decimal=3)
plt.figure()
ct.bode_plot(self.sys, omega, Hz=True)
mag_x, mag_y = (((plt.gcf().axes[0]).get_lines())[0]).get_data()
np.testing.assert_almost_equal(mag_x[0], 0.001 / (2*pi), decimal=6)
plt.figure()
ct.bode_plot(self.sys, omega, deg=False)
phase_x, phase_y = (((plt.gcf().axes[1]).get_lines())[0]).get_data()
np.testing.assert_almost_equal(phase_y[-1], -pi, decimal=2)
ct.reset_defaults()
#!/usr/bin/env python
# coding: utf-8
import numpy as np
import matplotlib.pyplot as plt
import control as ct
import control.optimal as opt
ct.use_fbs_defaults()
#
#
# ## Vehicle steering dynamics
# ##
def vehicle_update(t, x, u, params):
# Get the parameters for the model
a = params.get('refoffset', 1.5) # offset to vehicle reference point
b = params.get('wheelbase', 3.) # vehicle wheelbase
maxsteer = params.get('maxsteer', 0.5) # max steering angle (rad)
# Saturate the steering input
delta = np.clip(u[1], -maxsteer, maxsteer)
alpha = np.arctan2(a * np.tan(delta), b)
# Return the derivative of the state
return np.array([
u[0] * np.cos(x[2] + alpha), # xdot = cos(theta + alpha) v
u[0] * np.sin(x[2] + alpha), # ydot = sin(theta + alpha) v
(u[0] / b) * np.tan(delta) # thdot = v/l tan(phi)