Spec_SimpleThruster.md

Specification for Thruster

1. Overview

• This class simulates a thruster and contains functions for it.

1. functions

• By setting the thruster valve open and close, thruster torque and force are generated.
• The thruster model includes the magnitude and directional errors in the ini file.
• According to the thruster output, users can set the thrust duty to the value between 0 and 1.

2. files

• simple_thruster.cpp , simple_thruster.hpp
  • Definitions and declarations of the class
• thruster.ini
  • Parameters for a/multiple thruster(s)
• plot_simple_thruster.py: An example of a Python script to plot simple thruster output

3. how to use

• Set the parameters written in thruster.ini.
  • Users can set multiple thrusters.
• Create an instance by SimpleThruster function.
• Add calc_thrust function to GenerateForce_b() in SatComponents class and calc_torque function to GenerateTorque_b() in SatComponents class
  • calc_torque function requires a position of the spacecraft's mass center as an argument.
• When a thruster is open, set the duty to 1 by set_duty(1) function.
  • Users can set duty to the value between 0 and 1.

2. Explanation of Algorithm

1. Thrust

1. overview

• Thrust magnitude is a scalar value of thrust.
• Thrust contains the magnitude and direction errors according to the ini file setting.
• Thrust magnitude calculation considers the duty of thruster. If the thruster valve is closed, the thrust magnitude is 0.

2. input and output

• input
  • Thruster duty ratio
  • Maximum thrust magnitude thrust_magnitude_N
  • Thrust direction thruster_direction_b
  • Thrust magnitude error thrust_error_standard_deviation_N
  • Thrust direction error direction_error_standard_deviation_deg
• output
  • Thrust magnitude and direction

3. algorithms

Thrust magnitude can be calculated as follows:

$$F_{thrust} = \epsilon * F_{max} + n_{f}$$

where $F_{thrust}$ is thrust magnitude, $\epsilon$ is the duty of thruster, $F_{max}$ is the maximum thrust magnitude, and $n_{f}$ is the error of thrust magnitude.

Thrust direction can be calculated as follows:

$$\boldsymbol{d}_{err} = \boldsymbol{q}(\boldsymbol{d}_{true},n) * \boldsymbol{d}_x$$ $$\boldsymbol{d}_{thrust} = \boldsymbol{q}(\boldsymbol{d}_{err},n_{d}) * \boldsymbol{d}_{true}$$

where

• $\boldsymbol{d}_{true}$ is the thrust vector without errors
• $n$ is the random angles to rotate the direction of error $\boldsymbol{d}_{err}$
• $\boldsymbol{d}{x}$ is the vector which is not equal to $\boldsymbol{d}{true}$
• $n_d$ is the directional error
• $\boldsymbol{d}_{thrust}$ is the thrust vector with errors
• $\boldsymbol{q}(\boldsymbol{d},n)$ is the quaternion which has the rotation axis $\boldsymbol{d}$ and the rotation angle $n$ .

Thrust can be calculated as follows:

$$\boldsymbol{F}_{thrust} = F_{thrust} * \boldsymbol{d}_{thrust}$$

where $\boldsymbol{F}_{thrust}$ is thrust.

2. Torque

1. overview

• Torque by thruster is calculated from the thrust vector and the vector between the center of mass of the spacecraft and thruster.

2. input and output

• input
  • Thruster position thruster_position_b_m
  • Mass center of spacecraft
  • Thrust magnitude and direction
• output
  • Torque

3. algorithms

Torque by the thruster can be calculated as follows:

$$\boldsymbol{T}_{thrust} = (\boldsymbol{v}_{thruster}-\boldsymbol{v}_{SC}) \times \boldsymbol{F}_{thrust}$$

where

• $\boldsymbol{T}_{thrust}$ is torque by the thruster
• $\boldsymbol{v}_{thruster}$ is thruster position
• $\boldsymbol{v}_{SC}$ is the mass center of spacecraft.

3. Results of verifications

1. Case1

• input

  • Position thruster_position_b_m : [0m, 0m, 0.1m]
  • Direction thruster_direction_b : [0, 0, 1]
  • Thrust magnitude thrust_magnitude_N : 0.001N
  • Thrust magnitude error thrust_error_standard_deviation_N : 0.0N
  • Thrust direction error direction_error_standard_deviation_deg : 0.0deg
  • Simulation time: 100sec

• result

  • Force Mean: [0,0,0.001] N

  • Force Std Dev: [0,0,0] N

    Thrust force values in N unit.

  • Torque Mean: [0,0,0] Nm

  • Torque Std Dev: [0,0,0] Nm

    Thrust torque values in Nm unit.

2. Case2

• input
  • Position thruster_position_b_m : [0, 0, 0.1] m
  • Direction thruster_direction_b : [0, 0, 1]
  • Thrust magnitude thrust_magnitude_N : 0.001N
  • Thrust magnitude error thrust_error_standard_deviation_N : 0.00001N
  • Thrust direction error direction_error_standard_deviation_deg : 0.0deg
  • Simulation time: 100sec
• result

  • Force Mean: [0,0,0.999611e-3] N

  • Force Std Dev: [0,0,1.09804e-5] N

    Thrust force values in N unit.

  • Torque Mean: [0,0,0] Nm

  • Torque Std Dev: [0,0,0] Nm

    Thrust torque values in Nm unit.

3. Case3

• input
  • Position thruster_position_b_m : [0, 0, 0.1] m
  • Direction thruster_direction_b : [0, 0, 1]
  • Thrust magnitude thrust_magnitude_N : 0.001N
  • Thrust magnitude error thrust_error_standard_deviation_N : 0.0N
  • Thrust direction error direction_error_standard_deviation_deg : 10.0deg
  • Simulation time: 100sec
• result

  • Force Mean: [-4.93e-6, -1.04e-5, 0.9834e-3] N

  • Force Std Dev: [1.0e-4, 9.79e-5, 1.216e-5] N

    Thrust force values in N unit.

  • Torque Mean: [1.04e-6,-4.94e-7,0] Nm

  • Torque Std Dev: [1.29e-5, 1.26e-5, 0] Nm

    Thrust torque values in Nm unit.

4. Case4

• input
  • Position thruster_position_b_m : [0, 0.1, 0] m
  • Direction thruster_direction_b : [0, 0, 1]
  • Thrust magnitude thrust_magnitude_N : 0.001N
  • Thrust magnitude error thrust_error_standard_deviation_N : 0.0N
  • Thrust direction error direction_error_standard_deviation_deg : 0.0deg
  • Simulation time: 100sec
• result

  • Force Mean: [0,0,0.001] N

  • Force Std Dev: [0,0,0] N

    Thrust force values in N unit.

  • Torque Mean: [0.0001,0,0] Nm

  • Torque Std Dev: [0,0,0] Nm

    Thrust torque values in Nm unit.