meanOEFeedback#

Summary#

The primary purpose of this module is to calculate feedback control input for deputy spacecraft in terms of mean orbital element difference. This module uses Lyapunov control theory described in chapter 14 of Analytical Mechanics of Space Systems. In addition to classic orbital element set \((a,e,i,\Omega,\omega,M)\), this module can also deal with equinoctial orbital element \((a,e\sin{(\omega+\Omega)},e\cos{(\omega+\Omega)},\tan{(i/2)}\sin{(\Omega)},\tan{(i/2)}\cos{(\Omega)},\Omega+\omega+M)\) in order to avoid singularity. A control input \(\bf{u}\) used in this module is described in Eq. (1).

(1)#\[\bf{u} = -[B(\bf{oe_d})]^T[K]\Delta \bf{oe}\]

Control matrix \(B(oe)\) derived from Gauss’s Planetary Equation is given in Eq.(14.213) of Analytical Mechanics of Space Systems for classic orbital element, or in Application of several control techniques for the ionospheric observation nanosatellite formation for equinoctial one. Depending on preference, you can change which orbital element set to use by setting \(oe_{type}\) parameter. In order to calculate mean oe, position and velocity input messages are converted to osculating oe. Then, osculating oe is converted to mean oe by Brower’s theory.

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.

Module I/O Messages#
Msg Variable Name	Msg Type	Description
chiefTransInMsg	NavTransMsgPayload	The name of the chief’s position and velocity input message
deputyTransInMsg	NavTransMsgPayload	The name of the deputy’s position and velocity input message
forceOutMsg	CmdForceInertialMsgPayload	Calculated Force to control orbital element difference output message

Module Assumptions and Limitations#

This module assumes that target orbital element differnce is constant during simulation.

User Guide#

This module requires the following variables to be set as parameters:

oeType 0 for classic oe (default), 1 for equinoctial oe
mu gravitational constant for a central body in m^3/s^2
req equatorial radius of a central body in meters
J2 J2 constant of a central body
targetDiffOeMean desired mean orbital element difference. Assumed oe is linked to oeType.
K control gain matrix

You must be careful about a meter unit used for mu and req. For targetDiffOeMean, normalized semi major axis must be used.

Class MeanOEFeedback#

class MeanOEFeedback : public SysModel#

Top level structure for the sub-module routines.

Public Functions

void reset(uint64_t callTime) override#

This method performs a complete reset of the module. Local module variables that retain time varying states between function calls are reset to their default values. The local copy of the message output buffer should be cleared.

Parameters:: callTime – The clock time at which the function was called (nanoseconds)
Returns:: void

void updateState(uint64_t callTime) override#

Add a description of what this main Update() routine does for this module

Parameters:: callTime – The clock time at which the function was called (nanoseconds)
Returns:: void

void calcLyapunovFeedback(NavTransMsgPayload chiefTransMsg, NavTransMsgPayload deputyTransMsg, CmdForceInertialMsgPayload *forceMsg)#

This function calculates Lyapunov Feedback Control output based on current orbital element difference and target orbital element difference. Mean orbital elements are used.

Parameters:

chiefTransMsg – Chief’s position and velocity
deputyTransMsg – Deputy’s position and velocity
forceMsg – force output (3-axis)

Returns:

void

Public Members

ReadFunctor<NavTransMsgPayload> chiefTransInMsg#: chief orbit input message

ReadFunctor<NavTransMsgPayload> deputyTransInMsg#: deputy orbit input message

Message<CmdForceInertialMsgPayload> forceOutMsg#: deputy control force output message

double K[36]#: Lyapunov Gain (6*6)

double targetDiffOeMean[6]#: target mean orbital element difference

uint8_t oeType#: 0: classic (default), 1: equinoctial

double mu#: [m^3/s^2] gravitational constant

double req#: [m] equatorial planet radius

double J2#: [] J2 planet oblateness parameter

BSKLogger bskLogger = {}#: BSK Logging.