small documentation fixes

murrayrm · murrayrm · commit fba1f7461d4a · 2020-01-01T13:25:04.000-08:00
diff --git a/control/timeresp.py b/control/timeresp.py
@@ -245,7 +245,7 @@ def forced_response(sys, T=None, U=0., X0=0., transpose=False,
     Notes
     -----
     For discrete time systems, the input/output response is computed using the
-    :ref:`scipy.signal.dlsim` function.
+    :scipy-signal:ref:`scipy.signal.dlsim` function.
 
     For continuous time systems, the output is computed using the matrix
     exponential `exp(A t)` and assuming linear interpolation of the inputs
diff --git a/doc/classes.rst b/doc/classes.rst
@@ -16,10 +16,11 @@ these directly.
    TransferFunction
    StateSpace
    FrequencyResponseData
-   InputOutputSystem
+   ~iosys.InputOutputSystem
 
-Input/Output system subclasses
+Input/output system subclasses
 ==============================
+.. currentmodule:: control.iosys
 
 Input/output systems are accessed primarily via a set of subclasses
 that allow for linear, nonlinear, and interconnected elements:
diff --git a/doc/conf.py b/doc/conf.py
@@ -89,15 +89,15 @@
 # directories to ignore when looking for source files.
 # This pattern also affects html_static_path and html_extra_path .
 exclude_patterns = [u'_build', 'Thumbs.db', '.DS_Store',
-                    '**.ipynb_checkpoints']
+                    '*.ipynb_checkpoints']
 
 # The name of the Pygments (syntax highlighting) style to use.
 pygments_style = 'sphinx'
 
 #This config value contains the locations and names of other projects that 
 #should be linked to in this documentation.
 intersphinx_mapping = \
-    {'scipy':('https://docs.scipy.org/doc/scipy/reference/', None),
+    {'scipy':('https://docs.scipy.org/doc/scipy/reference', None),
      'numpy':('https://docs.scipy.org/doc/numpy', None)}
 
 #If this is True, todo and todolist produce output, else they produce nothing. 
diff --git a/doc/control.rst b/doc/control.rst
@@ -32,6 +32,9 @@ System interconnections
     parallel
     series
 
+See also the :ref:`iosys-module` module, which can be used to create and
+interconnect nonlinear input/output systems.
+
 Frequency domain plotting
 =========================
 
@@ -134,8 +137,9 @@ Nonlinear system support
 .. autosummary::
    :toctree: generated/
 
-   find_eqpt
-   linearize
+   ~iosys.find_eqpt
+   ~iosys.linearize
+   flatsys.point_to_point
 
 .. _utility-and-conversions:
 
diff --git a/examples/steering.ipynb b/examples/steering.ipynb
@@ -50,7 +50,7 @@
     "\n",
     "Assuming no slipping of the wheels, the motion of the vehicle is given by a rotation around a point O that depends on the steering angle $\\delta$.  To compute the angle $\\alpha$ of the velocity of the reference point with respect to the axis of the vehicle, we let the distance from the center of rotation O to the contact point of the rear wheel be $r_\\text{r}$ and it the follows from Figure 3.17 in FBS that $b = r_\\text{r} \\tan \\delta$ and $a = r_\\text{r} \\tan \\alpha$, which implies that $\\tan \\alpha = (a/b) \\tan \\delta$.\n",
     "\n",
-    "Reasonable limits for the steering angle depend on the speed.  The physical limit is given in our model as 0.5 radians (about 30 degrees).  However, this limit is rarely possible when the car is driving since it would cause the tires to slide on the pavement.  We us a limit of 0.1 radians (about 6 degrees) at 10 m/s ($\\sim$35 kph) and 0.05 radians (about 3 degrees) at 30 m/s ($\\sim$110 kph).  Note that a steering angle of 0.05 rad  gives a cross acceleration of $(v^2/b) \\tan \\delta \\approx (100/3) 0.05 = 1.7$ $\\text{m/s}^2$ at 10 m/s and 15 $\\text{m/s}^2$ at 30 m/s ($\\approx$ 1.5 times the force of gravity)."
+    "Reasonable limits for the steering angle depend on the speed.  The physical limit is given in our model as 0.5 radians (about 30 degrees).  However, this limit is rarely possible when the car is driving since it would cause the tires to slide on the pavement.  We us a limit of 0.1 radians (about 6 degrees) at 10 m/s ($\\approx$ 35 kph) and 0.05 radians (about 3 degrees) at 30 m/s ($\\approx$ 110 kph).  Note that a steering angle of 0.05 rad  gives a cross acceleration of $(v^2/b) \\tan \\delta \\approx (100/3) 0.05 = 1.7$ $\\text{m/s}^2$ at 10 m/s and 15 $\\text{m/s}^2$ at 30 m/s ($\\approx$ 1.5 times the force of gravity)."
    ]
   },
   {
@@ -259,7 +259,7 @@
     "We want to design a controller that stabilizes the dynamics of the vehicle and tracks a given reference value $r$ of the lateral position of the vehicle.  We use feedback to design the dynamics of the system to have the characteristic polynomial\n",
     "$p(s) = s^2 + 2 \\zeta_\\text{c} \\omega_\\text{c} + \\omega_\\text{c}^2$.\n",
     "\n",
-    "To find reasonable values of $\\omega_\\text{c}$ we observe that the initial response of the steering angle to a unit step change in the steering command is $\\omega_\\text{c}^2 r$, where $r$ is the commanded lateral transition. Recall that the model is normalized so that the length unit is the wheelbase $b$ and the time unit is the time $b/v_0$ to travel one wheelbase. A typical car has a wheelbase of about 3 m and, assuming a speed of 30 m/s, a normalized time unit corresponds to 0.1 s. To determine a reasonable steering angle when making a gentle lane change, we assume that the turning radius is $R$ = 600 m. For a wheelbase of 3 m this corresponds to a steering angle $\\delta ≈ 3/600 = 0.005$ rad and a lateral acceleration of $v^2/R$ = 302/600 = 1.5 m/s$^2$. Assuming that a lane change corresponds to a translation of one wheelbase we find $ω_\\text{c} = \\sqrt{0.005}$ = 0.07 rad/s.\n",
+    "To find reasonable values of $\\omega_\\text{c}$ we observe that the initial response of the steering angle to a unit step change in the steering command is $\\omega_\\text{c}^2 r$, where $r$ is the commanded lateral transition. Recall that the model is normalized so that the length unit is the wheelbase $b$ and the time unit is the time $b/v_0$ to travel one wheelbase. A typical car has a wheelbase of about 3 m and, assuming a speed of 30 m/s, a normalized time unit corresponds to 0.1 s. To determine a reasonable steering angle when making a gentle lane change, we assume that the turning radius is $R$ = 600 m. For a wheelbase of 3 m this corresponds to a steering angle $\\delta \\approx 3/600 = 0.005$ rad and a lateral acceleration of $v^2/R$ = 302/600 = 1.5 m/s$^2$. Assuming that a lane change corresponds to a translation of one wheelbase we find $\\omega_\\text{c} = \\sqrt{0.005}$ = 0.07 rad/s.\n",
     "\n",
     "The unit step responses for the closed loop system for different values of the design parameters are shown below. The effect of $\\omega_c$ is shown on the left, which shows that the response speed increases with increasing $\\omega_\\text{c}$. All responses have overshoot less than 5% (15 cm), as indicated by the dashed lines. The settling times range from 30 to 60 normalized time units, which corresponds to about 3–6 s, and are limited by the acceptable lateral acceleration of the vehicle. The effect of $\\zeta_\\text{c}$ is shown on the right. The response speed and the overshoot increase with decreasing damping. Using these plots, we conclude that a reasonable design choice is $\\omega_\\text{c} = 0.07$ and $\\zeta_\\text{c} = 0.7$. "
    ]

Original file line number	Diff line number	Diff line change
`@@ -50,7 +50,7 @@`
`50`	`50`	`"\n",`
`51`	`51`	"Assuming no slipping of the wheels, the motion of the vehicle is given by a rotation around a point O that depends on the steering angle $\\delta$. To compute the angle $\\alpha$ of the velocity of the reference point with respect to the axis of the vehicle, we let the distance from the center of rotation O to the contact point of the rear wheel be $r_\\text{r}$ and it the follows from Figure 3.17 in FBS that $b = r_\\text{r} \\tan \\delta$ and $a = r_\\text{r} \\tan \\alpha$, which implies that $\\tan \\alpha = (a/b) \\tan \\delta$.\n",
`52`	`52`	`"\n",`
`53`		- "Reasonable limits for the steering angle depend on the speed. The physical limit is given in our model as 0.5 radians (about 30 degrees). However, this limit is rarely possible when the car is driving since it would cause the tires to slide on the pavement. We us a limit of 0.1 radians (about 6 degrees) at 10 m/s ($\\sim$35 kph) and 0.05 radians (about 3 degrees) at 30 m/s ($\\sim$110 kph). Note that a steering angle of 0.05 rad gives a cross acceleration of $(v^2/b) \\tan \\delta \\approx (100/3) 0.05 = 1.7$ $\\text{m/s}^2$ at 10 m/s and 15 $\\text{m/s}^2$ at 30 m/s ($\\approx$ 1.5 times the force of gravity)."
	`53`	+ "Reasonable limits for the steering angle depend on the speed. The physical limit is given in our model as 0.5 radians (about 30 degrees). However, this limit is rarely possible when the car is driving since it would cause the tires to slide on the pavement. We us a limit of 0.1 radians (about 6 degrees) at 10 m/s ($\\approx$ 35 kph) and 0.05 radians (about 3 degrees) at 30 m/s ($\\approx$ 110 kph). Note that a steering angle of 0.05 rad gives a cross acceleration of $(v^2/b) \\tan \\delta \\approx (100/3) 0.05 = 1.7$ $\\text{m/s}^2$ at 10 m/s and 15 $\\text{m/s}^2$ at 30 m/s ($\\approx$ 1.5 times the force of gravity)."
`54`	`54`	`]`
`55`	`55`	`},`
`56`	`56`	`{`
`@@ -259,7 +259,7 @@`
`259`	`259`	`"We want to design a controller that stabilizes the dynamics of the vehicle and tracks a given reference value $r$ of the lateral position of the vehicle. We use feedback to design the dynamics of the system to have the characteristic polynomial\n",`
`260`	`260`	`"$p(s) = s^2 + 2 \\zeta_\\text{c} \\omega_\\text{c} + \\omega_\\text{c}^2$.\n",`
`261`	`261`	`"\n",`
`262`		- "To find reasonable values of $\\omega_\\text{c}$ we observe that the initial response of the steering angle to a unit step change in the steering command is $\\omega_\\text{c}^2 r$, where $r$ is the commanded lateral transition. Recall that the model is normalized so that the length unit is the wheelbase $b$ and the time unit is the time $b/v_0$ to travel one wheelbase. A typical car has a wheelbase of about 3 m and, assuming a speed of 30 m/s, a normalized time unit corresponds to 0.1 s. To determine a reasonable steering angle when making a gentle lane change, we assume that the turning radius is $R$ = 600 m. For a wheelbase of 3 m this corresponds to a steering angle $\\delta ≈ 3/600 = 0.005$ rad and a lateral acceleration of $v^2/R$ = 302/600 = 1.5 m/s$^2$. Assuming that a lane change corresponds to a translation of one wheelbase we find $ω_\\text{c} = \\sqrt{0.005}$ = 0.07 rad/s.\n",
	`262`	+ "To find reasonable values of $\\omega_\\text{c}$ we observe that the initial response of the steering angle to a unit step change in the steering command is $\\omega_\\text{c}^2 r$, where $r$ is the commanded lateral transition. Recall that the model is normalized so that the length unit is the wheelbase $b$ and the time unit is the time $b/v_0$ to travel one wheelbase. A typical car has a wheelbase of about 3 m and, assuming a speed of 30 m/s, a normalized time unit corresponds to 0.1 s. To determine a reasonable steering angle when making a gentle lane change, we assume that the turning radius is $R$ = 600 m. For a wheelbase of 3 m this corresponds to a steering angle $\\delta \\approx 3/600 = 0.005$ rad and a lateral acceleration of $v^2/R$ = 302/600 = 1.5 m/s$^2$. Assuming that a lane change corresponds to a translation of one wheelbase we find $\\omega_\\text{c} = \\sqrt{0.005}$ = 0.07 rad/s.\n",
`263`	`263`	`"\n",`
`264`	`264`	"The unit step responses for the closed loop system for different values of the design parameters are shown below. The effect of $\\omega_c$ is shown on the left, which shows that the response speed increases with increasing $\\omega_\\text{c}$. All responses have overshoot less than 5% (15 cm), as indicated by the dashed lines. The settling times range from 30 to 60 normalized time units, which corresponds to about 3–6 s, and are limited by the acceptable lateral acceleration of the vehicle. The effect of $\\zeta_\\text{c}$ is shown on the right. The response speed and the overshoot increase with decreasing damping. Using these plots, we conclude that a reasonable design choice is $\\omega_\\text{c} = 0.07$ and $\\zeta_\\text{c} = 0.7$. "
`265`	`265`	`]`