Attitude estimation and reaction wheels based control of an earth-pointing small satellite

Abstract

A satellite is an artificial object that is sent into orbit around a celestial body, usually the Earth. Depending on their mission design, they can perform various tasks from communication to military. Satellites consist of various subsystems to perform their assigned mission. Attitude Determination and Control Systems (ADCS) is responsible for orienting the satellite in the desired direction and maintaining its orientation in space. It uses various sensors and actuators to measure and control the satellite's attitude. The sensors, such as sun sensors, magnetometers and gyroscopes, provide data about the satellite's current orientation. The measurement data coming from these sensors are processed by various attitude estimation methods. The actuators, like reaction wheels, magnetorquers and thrusters, apply the necessary torques to adjust the satellite's attitude. The ADCS ensures that the satellite's payload is correctly positioned for its mission. If the satellite cannot be brought to the required orientation, it may not be able to fulfil its mission. In this thesis, some of the prominent vector measurement-based attitude estimation methods are compared. To make this comparison, the dynamic and kinematic model of an Earth-pointing satellite is derived and subsequently, this highly nonlinear model is linearized by using the Taylor series method. Following this, mathematical models of the sun sensor and magnetometer were also presented. Real sensor measurements are simulated by adding white noise to these mathematical models. The compared attitude estimation methods can be named as TRIAD, Q-Method, and SVD. The comparison is made through conducting simulations in the Matlab/Simulink environment. Root mean square errors of the estimation methods are computed by comparing their outputs with the output of the deterministic satellite system model. After comparing the attitude estimation methods, a comparison was made between the two types of the optimal controllers. The LQR controller is a feedback control method that aims to minimize a quadratic cost function, which is typically defined in terms of deviations from desired states and control inputs. It provides an optimal solution for controlling the satellite's attitude while considering both system dynamics and control effort. The LQG controller improves the capabilities of LQR by adding a Kalman filter, improving the estimation of system states from noisy sensor measurements. This integration improves the controller's ability to handle uncertainties and disturbances, making it more suitable for real-world satellite applications where sensor data may be prone to noise or inaccuracies. Reaction wheels are selected as the actuators. Reaction wheels are based on the principle of conservation of angular momentum. When it is necessary to change the orientation of the satellite, reaction wheels start to rotate according to the control signal; causing a change in angular momentum. The satellite body produces an angular velocity in the opposite direction to preserve the total momentum. In this way, the orientation of the satellite can be controlled. Although three reaction wheels are sufficient for attitude control in three axes, satellites generally use reaction wheel configurations consisting of four wheels. An extra fourth wheel creates actuator redundancy. If one of the reaction wheels fails, the other remaining three reaction wheels can still complete the mission. The internal dynamics of the reaction wheels are modelled as a DC motor on Simulink. There are various disturbance torques that affect the satellite along its orbit. For example, gravity-gradient torque comes from the Earth's unequal gravitational force acting on different parts of the satellite. The parts of the satellite that are closer to the Earth are exposed to more gravitational force. This imbalance creates a torque on the satellite. Disturbance torques like gravity-gradient torque however can also be used to keep the satellite stable. In this thesis, the gravity-gradient stability behaviour of the simulated satellite was also examined.