This course covers the analysis and modelling of the attitude dynamics of a spacecraft in Earth orbit.  You will develop the knowledge to implement modern determination and control algorithms using typical attitude actuators and sensors. You will develop a complete simulation of the attitude dynamics, determination and control of a nano-spacecraft in Earth orbit suitable for preliminary mission analysis and control design. You will also learn to use analysis tools from dynamical systems and control theory to design determination and control algorithms. 

Learning outcome 1 - To understand the natural dynamics of a spacecraft in a typical space environment. To understand how you can exploit the natural dynamics for passive stabilization.

Learning outcome 2 - To understand how the attitude of the spacecraft is determined autonomously using various sensor portfolios.

Learning outcome 3 - To understand how the attitude of the spacecraft is controlled autonomously using various actuators.

Learning outcome 4 - To be able to understand the fundamental theory and analytical analysis tools required to design attitude determination and control algorithms.

Learning outcome 5 - To be able to develop an attitude dynamics model and implement attitude determination and control algorithms in Matlab/Simulink.

Attitude Dynamics and kinematics of spacecraft

- Spacecraft Dynamics: Angular momentum and Energy, Euler equations – Torque-free motion of a rigid body - stability - simple spin stability (with and without energy dissipation), dual-spin spacecraft - numerical and analytical analysis, passive control methods.

- Attitude Representation and kinematics:  Mathematical representation of rotational motion using (i) Direction cosine matrices (ii) Euler axis and angle (iii) Quaternions (iv) Gibbs vector (v) Euler angles. Frames of reference - inertial frame, body fixed frame and the LVLH frame.

- Space environment modelling: Developing models of environmental disturbance torques due to air drag, solar radiation pressure, magnetic torque, gravity gradient.

Attitude Determination 

- Attitude determination: Determination algorithms (for pointing and 3-stabilization applications) based on Linear state observers in the LVLH frame using single vector reference sensors e.g. Earth horizon sensors and Sun sensors. 

- Static determination methods: using combinations of sensors to compute the attitude of the spacecraft e.g magnetometers, Sun sensors, Earth horizon sensors and star sensors. The development of algorithms based on algebraic methods e.g TRIAD and numerical methods e.g. q-method, QUEST method, constrained and unconstrained optimization.

- Dynamic determination methods: nonlinear observers for filtering noise and dynamic attitude determination.

Spacecraft attitude control

- De-tumbling: development of basic de-tumbling control algorithms for spacecraft in the case of continuous actuation and "on-off" actuation typical of thrusters. Stability analysis of the controlled system via energy-based methods. Consideration of disturbances in the proof of stability. Angular velocity measurement with gyros.

- Attitude pointing and 3-axis stabilization: Control algorithms for pointing and 3-axis stabilization in Earth orbit based on the Local vertical Local horizontal frame and linear control methods such as LQR for continuous and discrete controls. Stability analysis of spacecraft motion in Earth orbit.

-Introduction to linear and nonlinear control design: Attitude control design for spacecraft based on state space methods and Lyapunov control functions. An application to de-tumbling and slew motions.

-Attitude control for typical spacecraft actuators: Based on the control laws developed in the previous sections (ideal control) develop control laws for real actuators such as reaction wheels, control moment gyros, magnetic torquers and thrusters. Use SIMULINK to size actuators. Develop unique control laws for thrusters and magnetic torquers including the case where you cannot provide torque instantaneously in every direction. 

-Nonlinear tracking control: Designing attitude tracking references and controls that can undertake continuous motion such as pointing to the Earth while motioning to maximise power generation. 

-Implementation in Simulink: Implementing the dynamic and kinematic equations of a spacecraft in low Earth orbit for analysis, control development and actuator sizing. Implementation of determination and control algorithms.

Prerequisits for this course are an understanding of linear dynamical systems theory and experience of Matlab. Exposure to control theory would be an advantage.

The course includes traditional classroom lectures and laboratory sessions using Matlab and Simulink. Previous experience with Matlab and/or Simulink is highly desirable but not essential. Students will have to develop a group project, consisting in the development of a simulation of an assigned attitude dynamics and control problem. Groups will be composed by 4 students.

The final examination will be based on the evaluation of:

- (i) the simulation model and a 20 page report describing the model and simulation results, where model and report must be delivered before January 7, independently from the date of the oral exam;

- (iii) an individual oral examination, in one of the available examination sessions.