HRB Torque Mapping Software

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Description

The HRB Torque Mapping Software is a flight software module that computes motor torque commands to drive a hinged rigid body (HRB) to a desired angular state. Using a proportional-derivative (PD) control law, the module calculates the torque required to minimize the error between the sensed and reference hinge angles and angular rates. This is commonly used for deployable structures such as solar array panels, antenna booms, and articulated appendages that require precise angular positioning.

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Example Use Cases

• Solar Array Deployment: Control the deployment angle of hinged solar panels to achieve optimal sun pointing.
• Antenna Articulation: Drive a gimbaled antenna to track a ground station or relay satellite.
• Appendage Positioning: Command deployable booms or instruments to specific angular configurations.

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Module Implementation

The HRB Torque Mapping Software is a Software component that implements a PD controller for hinged rigid body angle control.

Control Law

The motor torque is computed using a proportional-derivative control law based on the error between the sensed and reference states:

$$\tau =-K(\theta -{\theta }_{\text{ref}})-P(\dot{\theta }-{\dot{\theta }}_{\text{ref}})$$

where:

• $\tau$ is the commanded motor torque [N·m]
• $K$ is the proportional gain [N·m/rad]
• $P$ is the derivative gain [N·m·s/rad]
• $\theta$ is the sensed hinge angle [rad]
• ${\theta }_{\text{ref}}$ is the reference hinge angle [rad]
• $\dot{\theta }$ is the sensed angular rate [rad/s]
• ${\dot{\theta }}_{\text{ref}}$ is the reference angular rate [rad/s]

The negative sign ensures that positive torque is applied in the direction that reduces the error.

Input Messages

Input Message	Type	Description
In_HRBSensedMsg	HRBAngleMessage	Sensed hinge angle and angular rate
In_HRBReferenceMsg	HRBAngleMessage	Reference hinge angle and angular rate

Output Message

The module produces a MotorTorqueArrayMessage containing the computed torque command:

Field	Units	Description
MotorTorques	N·m	Array containing the single motor torque command

Gain Selection

The proportional gain $K$ determines the stiffness of the response to angular errors, while the derivative gain $P$ provides damping. For a second-order system with desired natural frequency ${\omega }_n$ and damping ratio $\zeta$:

$$K=J{\omega }_n^2$$ $$P=2\zeta J{\omega }_n$$

where $J$ is the rotational inertia of the hinged body about the hinge axis.

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Assumptions/Limitations

• The controller assumes a single hinge axis; multi-axis articulation requires multiple instances.
• Torque saturation and motor dynamics are not modeled within this module.
• The control law is linear; nonlinear effects such as friction and backlash are not compensated.
• Both input messages must be connected for the controller to produce output.