Prenote

• The diagrams use block algebra. If you are infamiliar, the following articles may help:
• https://www.tutorialspoint.com/control_systems/control_systems_block_diagram_algebra.htm
• https://www.wisdomjobs.com/e-university/control-systems-tutorial-2468/block-diagram-algebra-25880.html
• https://www.youtube.com/watch?v=OE9Va_ky6yU

ADCS Actuator Control Model

We approximate the dynamics using the following relationships:

• T corresponds to torque
  • d means refers to disturbance torques (external torque)
  • c suffix refers to control torque (generated by reaction wheels)
• I is inertia
  • in the x,y,z axes respectively
• We assume the inertia matrix is diagonal and we use the principal axes of inertia as the system's reference axes.

ADCS Plant

• Mathematical model for the actuator and process to be controlled (in our case, our actuator = reaction wheels and we're controlling the reaction wheels)
• We use a transfer function in the frequency domain, which is a function of Laplace's variable, s.

We take Laplace transform of the previous torque equations to obtain:

• Torque as input, and attitude as output.
• I is system inertia, with respect to the rotation axis from where the Euler angle is being measured (theta)

Reaction Wheel Model

• The torque input comes from the reaction wheel when in torque command mode. Below is a table of experimental values used to model the reaction wheel dynamics as a torque actuator.