.. _mrppd:

=====
mrpPD
=====


Executive Summary
-----------------
This module provides a MRP based PD attitude control module. It is similar to :ref:`mrpFeedback`, but without the RW or the integral feedback option. The feedback control is able to asymptotically track a reference attitude if there are no unknown dynamics and the attitude control torque is implemented with a thruster set.

Message Connection Descriptions
-------------------------------
The following table lists all the module input and output messages.  The module msg variable name is set by the
user from python.  The msg type contains a link to the message structure definition, while the description
provides information on what this message is used for.

.. list-table:: Module I/O Messages
    :widths: 25 25 50
    :header-rows: 1

    * - Msg Variable Name
      - Msg Type
      - Description
    * - vehConfigInMsg
      - :ref:`VehicleConfigMsgPayload`
      - Attitude guidance input message
    * - guidInMsg
      - :ref:`AttGuidMsgPayload`
      - Vehicle configuration input message
    * - cmdTorqueOutMsg
      - :ref:`CmdTorqueBodyMsgPayload`
      - Commanded torque output message


Detailed Module Description
---------------------------
This attitude feedback module using the MRP feedback control related to the control in section 8.4.1 in `Analytical Mechanics of Space Systems <http://dx.doi.org/10.2514/4.105210>`_:

.. math::
    :label: eq-mrppd-1

    {\bf L}_{r} =  -K \pmb\sigma - [P] \delta\pmb\omega   + [I](\dot{\pmb\omega}_{r} - [\tilde{\pmb\omega}]\pmb\omega_{r})
			+[\tilde{\pmb \omega}_{r}] ]
			[I]\pmb\omega   - \bf L

Note that this control solution creates an external control torque which must be produced with a cluster of thrusters.  No reaction wheel information is used here.  Further, the feedback control component is a simple proportional and derivative feedback formulation.  As shown in `Analytical Mechanics of Space Systems <http://dx.doi.org/10.2514/4.105210>`_, this control can asymptotically track a general reference trajectory given by the reference frame :math:`\cal R`.


Module Assumptions and Limitations
----------------------------------
This control assumes the spacecraft is rigid and that the inertia tensor does not vary with time.


User Guide
----------
The required module configuration is::

    module = mrpPD.mrpPD()
    module.modelTag = "mrpPD"
    module.setProportionalGainK(K)
    module.setDerivativeGainP(P)
    module.setKnownTorquePntB_B(knownTorquePntB_B)


Class MrpPD
-----------

.. doxygenclass:: MrpPD
   :project: xmera
   :members: