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murrayrm merged 2 commits into from
Jan 4, 2020
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Small doc updates #364

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759f301
small fixes to iosys documentation
murrayrm Jan 4, 2020
8681c40
fix code blocks in iosys.rst
murrayrm Jan 4, 2020
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3 changes: 3 additions & 0 deletions doc/control.rst
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Expand Up @@ -139,6 +139,9 @@ Nonlinear system support

~iosys.find_eqpt
~iosys.linearize
~iosys.input_output_response
~iosys.ss2io
~iosys.tf2io
flatsys.point_to_point

.. _utility-and-conversions:
Expand Down
23 changes: 13 additions & 10 deletions doc/iosys.rst
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Expand Up @@ -66,7 +66,7 @@ values in FBS2e.

We begin by defining the dynamics of the system

.. code-block::
.. code-block:: python

import control
import numpy as np
Expand Down Expand Up @@ -96,7 +96,7 @@ We begin by defining the dynamics of the system

We now create an input/output system using these dynamics:

.. code-block::
.. code-block:: python

io_predprey = control.NonlinearIOSystem(
predprey_rhs, None, inputs=('u'), outputs=('H', 'L'),
Expand All @@ -108,7 +108,7 @@ will be used as the output of the system.
The `io_predprey` system can now be simulated to obtain the open loop dynamics
of the system:

.. code-block::
.. code-block:: python

X0 = [25, 20] # Initial H, L
T = np.linspace(0, 70, 500) # Simulation 70 years of time
Expand All @@ -127,7 +127,7 @@ We can also create a feedback controller to stabilize a desired population of
the system. We begin by finding the (unstable) equilibrium point for the
system and computing the linearization about that point.

.. code-block::
.. code-block:: python

eqpt = control.find_eqpt(io_predprey, X0, 0)
xeq = eqpt[0] # choose the nonzero equilibrium point
Expand All @@ -137,7 +137,7 @@ We next compute a controller that stabilizes the equilibrium point using
eigenvalue placement and computing the feedforward gain using the number of
lynxes as the desired output (following FBS2e, Example 7.5):

.. code-block::
.. code-block:: python

K = control.place(lin_predprey.A, lin_predprey.B, [-0.1, -0.2])
A, B = lin_predprey.A, lin_predprey.B
Expand All @@ -149,7 +149,7 @@ applies a corrective input based on deviations from the equilibrium point.
This system has no dynamics, since it is a static (affine) map, and can
constructed using the `~control.ios.NonlinearIOSystem` class:

.. code-block::
.. code-block:: python

io_controller = control.NonlinearIOSystem(
None,
Expand All @@ -162,7 +162,7 @@ populations followed by the desired lynx population.
To connect the controller to the predatory-prey model, we create an
`InterconnectedSystem`:

.. code-block::
.. code-block:: python

io_closed = control.InterconnectedSystem(
(io_predprey, io_controller), # systems
Expand All @@ -177,7 +177,7 @@ To connect the controller to the predatory-prey model, we create an

Finally, we simulate the closed loop system:

.. code-block::
.. code-block:: python

# Simulate the system
t, y = control.input_output_response(io_closed, T, 30, [15, 20])
Expand Down Expand Up @@ -205,10 +205,13 @@ Input/output system classes
LinearIOSystem
NonlinearIOSystem

Flat systems functions
----------------------
Input/output system functions
-----------------------------
.. autosummary::

find_eqpt
linearize
input_output_response
ss2io
tf2io