Figure 5.3: Phase portraits - Revision history

Murray at 01:09, 7 April 2024

2024-04-07T01:09:43Z

Murray at 01:09, 7 April 2024

2024-04-07T01:09:10Z

Murray at 01:04, 7 April 2024

2024-04-07T01:04:36Z

Murray: Created page with "{{Figure |Chapter=Dynamic Behavior |Figure number=5.3 |Sort key=503 |Figure title=Phase portraits |GitHub URL=https://github.com/murrayrm/fbs2e-python/blob/main/figure-5.3-pha..."

2024-04-07T00:55:39Z

Created page with "{{Figure |Chapter=Dynamic Behavior |Figure number=5.3 |Sort key=503 |Figure title=Phase portraits |GitHub URL=https://github.com/murrayrm/fbs2e-python/blob/main/figure-5.3-pha..."

New page

{{Figure
|Chapter=Dynamic Behavior
|Figure number=5.3
|Sort key=503
|Figure title=Phase portraits
|GitHub URL=https://github.com/murrayrm/fbs2e-python/blob/main/figure-5.3-phase_portraits.py
}}
[[Image:figure-5.3-phase_portraits-vf.png]]  
[[Image:figure-5.3-phase_portraits-sl.png]]

'''Figure 5.3:''' Phase portraits. (a) This plot shows the vector field for a planar dynamical system. Each arrow shows the velocity at that point in the state space. (b) This plot includes the solutions (sometimes called streamlines) from different initial conditions, with the vector field superimposed.

@@ Line 30: / Line 30: @@
 damposc = ct.nlsys(damposc_update, states=2, params=damposc_params)
-# Set the slimits for the plot
+# Set the limits for the plot
 limits = [-1, 1, -1, 1]

@@ Line 35: / Line 35: @@
 # Vector field
 fbs.figure('mlh')
-ct.pp.vectorfield(damposc, limits, gridspec=[15, 12])
+ct.phase_plane_plot(
-ct.pp.equilpoints(damposc, limits)
+    damposc, limits, plot_streamlines=False,
-plt.suptitle("Vector field")
+    plot_vectorfield=True, gridspec=[15, 12])
 fbs.savefig('figure-5.3-phase_portraits-vf.png')
@@ Line 43: / Line 44: @@
 fbs.figure('mlh')
 ct.phase_plane_plot(damposc, limits, 8)
-plt.suptitle("Phase portrait")
+plt.suptitle(""); plt.title("Phase portrait")
 fbs.savefig('figure-5.3-phase_portraits-sl.png')
 </nowiki>

← Older revision		Revision as of 01:04, 7 April 2024
Line 10:		Line 10:

	'''Figure 5.3:''' Phase portraits. (a) This plot shows the vector field for a planar dynamical system. Each arrow shows the velocity at that point in the state space. (b) This plot includes the solutions (sometimes called streamlines) from different initial conditions, with the vector field superimposed.		'''Figure 5.3:''' Phase portraits. (a) This plot shows the vector field for a planar dynamical system. Each arrow shows the velocity at that point in the state space. (b) This plot includes the solutions (sometimes called streamlines) from different initial conditions, with the vector field superimposed.
		+
		+	<nowiki>
		+	# phase_portraits.py - phase portrait examples
		+	# RMM, 6 Apr 2024
		+
		+	import matplotlib.pyplot as plt
		+	import numpy as np
		+	import control as ct
		+	import control.phaseplot as pp
		+	import fbs # FBS plotting customizations
		+
		+	# Oscillator parameters
		+	damposc_params = {'m': 1, 'b': 1, 'k': 1}
		+
		+	# System model (as ODE)
		+	def damposc_update(t, x, u, params):
		+	m, b, k = params['m'], params['b'], params['k']
		+	return np.array([x[1], -k/m * x[0] - b/m * x[1]])
		+	damposc = ct.nlsys(damposc_update, states=2, params=damposc_params)
		+
		+	# Set the slimits for the plot
		+	limits = [-1, 1, -1, 1]
		+
		+	# Vector field
		+	fbs.figure('mlh')
		+	ct.pp.vectorfield(damposc, limits, gridspec=[15, 12])
		+	ct.pp.equilpoints(damposc, limits)
		+	plt.suptitle("Vector field")
		+	fbs.savefig('figure-5.3-phase_portraits-vf.png')
		+
		+	# Streamlines
		+	fbs.figure('mlh')
		+	ct.phase_plane_plot(damposc, limits, 8)
		+	plt.suptitle("Phase portrait")
		+	fbs.savefig('figure-5.3-phase_portraits-sl.png')
		+	</nowiki>