Control+pto docs (WEC-Sim#1108)

* start doc updates * Update docs * Finish docs * Revert environment * Update docs some * Update docs and pngs * Updated with power plots
agmoore4 · Sep 20, 2023 · 930f58d · 930f58d
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diff --git a/docs/_static/images/piGainSweep.png b/docs/_static/images/piGainSweep.png
diff --git a/docs/_static/images/piPTOSimulink.png b/docs/_static/images/piPTOSimulink.png
diff --git a/docs/_static/images/reactiveWithPTOCC.png b/docs/_static/images/reactiveWithPTOCC.png
diff --git a/docs/_static/images/reactiveWithPTOCCPower.png b/docs/_static/images/reactiveWithPTOCCPower.png
diff --git a/docs/_static/images/reactiveWithPTOOpt.png b/docs/_static/images/reactiveWithPTOOpt.png
diff --git a/docs/_static/images/reactiveWithPTOOptPower.png b/docs/_static/images/reactiveWithPTOOptPower.png
diff --git a/docs/_static/images/reactiveWithPTOSweep.png b/docs/_static/images/reactiveWithPTOSweep.png
diff --git a/docs/refs/WEC-Sim_Adv_Features.bib b/docs/refs/WEC-Sim_Adv_Features.bib
@@ -58,4 +58,16 @@ @inproceedings{so2017development
   pages={1--5},
   year={2017},
   organization={IEEE}
-}
+}
+
+@misc{allied,
+  title={Megaflux™ Frameless Direct Drive Torque Motors},
+  author={},
+  journal={},
+  volume={28},
+  number={2},
+  pages={77--91},
+  year={2006},
+  publisher={Allied Motion},
+  url={https://www.alliedmotion.com/brushless-motors/brushless-direct-drive-torque-motors/megaflux-frameless-direct-drive-torque-motors/}
+}
diff --git a/docs/user/advanced_features.rst b/docs/user/advanced_features.rst
@@ -903,7 +903,8 @@ own controls.
 	+--------------------------------+-------------------------------------------+
 	|   Model Predictive Control   	 | Sphere with model predictive control      |
 	+--------------------------------+-------------------------------------------+
-
+	|   Reactive with PTO   	 | Sphere with reactive control and DD PTO   |
+	+--------------------------------+-------------------------------------------+
 
 
 Examples: Sphere Float with Various Controllers
@@ -1243,6 +1244,69 @@ computation time and complex setup.
 	| Avg Mechanical Power (kW)  |      N/A     |    300      |    241     |
 	+----------------------------+--------------+-------------+------------+
 
+.. _control-reactive-with-PTO:
+
+Reactive Control with Direct Drive Power Take-Off
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The previous controllers only considered the mechanical power output. Although maximization
+of mechanical power allows for the maximum energy transfer from waves to body, it often does 
+not lead to maximum electrical power. The previous controller examples demonstrate the 
+controller types and energy transfer from waves to body, but the important consideration of 
+electrical power requires a PTO model. This example applies a reactive controller to the 
+sphere body with a simplified direct drive PTO model to maximize electrical power. Within 
+the Simulink subsystem for determining the PTO force, the controller prescribes the ideal or 
+desired force which is fed into the direct drive PTO. The current in the generator is then 
+used to control the applied force. 
+
+.. figure:: /_static/images/piPTOSimulink.png
+   :width: 500pt 
+   :align: center
+
+The PTO parameters used for this example are defined in the ``wecSimInputFile.m`` and correspond to 
+the Allied Motion Megaflux Frameless Brushless Torque Motors–MF0310 :cite:`allied`. The 
+results in terms of capture width (ratio of absorbed power (W) to wave power (W/m)) and resultant power for the 
+applied gains from Section :ref:`control-reactive` are shown in the figures 
+below for a regular wave with a period of 9.6664 s and a height of 2.5 m. The "Controller (Ideal)" 
+power is the ideal power absorbed according to the applied controller gains. 
+The "Mechanical (Drivetrain)" power is the actual mechanical power absorbed by 
+the PTO system including the inertial, damping, and shaft torque power. Lastly, the 
+"Electrical (Generator)" power is the electrical power absorbed by the 
+generator including the product of induced current and voltage (based on shaft torque and velocity, 
+respectively) and the resultant generator losses (product of current squared and winding resistance).
+Mechanical power maximization requires significant net input electrical power 
+(signified by red bar) which leads to an extremely negative capture width. Thus, 
+instead of harvesting electrical power, power would need to be taken from the grid or energy 
+storage component to achieve mechanical power maximization. 
+
+.. figure:: /_static/images/reactiveWithPTOCCPower.png
+   :width: 300pt 
+   :align: center
+
+.. figure:: /_static/images/reactiveWithPTOCC.png
+   :width: 300pt 
+   :align: center
+
+On the other hand, by testing different controller gains in the same wave conditions 
+(regular wave: period = 9.6664 s, height = 2.5 m), the gains which optimize for 
+maximum electrical power can be found as shown below. Increasing the proportional gain 
+and decreasing the integral gain magnitude leads to a maximum power of about 84 kW and capture width of about 
+1.5 m. The resultant motion is almost ten times smaller than for the mechanical power 
+maximization which leads to a lower current and much lower generator power losses 
+(product of current squared and winding resistance).
+
+.. figure:: /_static/images/reactiveWithPTOSweep.png
+   :width: 300pt 
+   :align: center
+
+.. figure:: /_static/images/reactiveWithPTOOptPower.png
+   :width: 300pt 
+   :align: center
+
+.. figure:: /_static/images/reactiveWithPTOOpt.png
+   :width: 300pt 
+   :align: center
+
 
 .. _user-advanced-features-cable:
 
@@ -1257,7 +1321,7 @@ class in the ``wecSimInputFile.m`` along with the base and follower connections
 	cable(i) = cableClass('cableName','baseConnection','followerConnection');
 
 where ``baseConnection`` is a PTO or constraint block that defines the cable connection on the base side, and ``followerConnection``
-is  a PTO or constraint block that defineds the connection on the follower side.  
+is a PTO or constraint block that defineds the connection on the follower side.  
 
 
 It is necessary to define, at a minimum: ::