Attitude Determination and Control Simulation: TIROS I
In this project, I used Simulink to simulate the Attitude Determination and Control System (ADCS) of the TIROS 1 satellite.
OVERVIEW
This ADC system was developed using Simulink. The simulation contains five parts: Dynamics, Actuators, Attitude Controller, Attitude Determination, and Sensors. Artificial noise was injected into the simulation at magnitudes described by the equipment chosen. The satellite orbits about and points toward the Earth with the use of 3 orthogonal reaction wheels. The primary force action on the satellite is gravity, but two perturbations were simulated: Gravity Gradient & Magnetic Torque. One orbit about the Earth was simulated with orbital elements matching that of the reference mission. The reference mission for this simulation is the TIROS I satellite (launched in 1960). The inclination for this orbit was 48.4°, and the orbit was nearly circular with a radius of 700km. The inclination used in the simulation was rounded to 45° for simplicity in the model. The satellite was an oblate cylinder with a diameter of 1.07m, a height of .56m, and a mass of 122.5kg.
The simulation consists of the following connected modules:
Dynamics
Simulates the position and velocity vectors for the specified orbit over time
Additionally, the attitude perturbations due to Gravity Gradient and Magnetic Torque were modeled
Sensors:
A gyroscope, magnetometer, and earth horizon sensor were used as sensors for this spacecraft.
Measurement error was modeled for each of these sensors.
Attitude Determination
The TRIAD system of attitude determination was used in this simulation. This system requires two vectors known in both the inertial and body frames. The vectors used for this were the direction of the Earth’s magnetic field and the direction of the center of the Earth gathered via the earth horizon sensor.
Attitude Control
A PD controller was used to control the attitude of the spacecraft. The controller receives information about the position and velocity of the spacecraft, the measured angular velocities of the reaction wheels, and the estimated angular velocity of the spacecraft. It then sends commands to the reaction wheels based on the error between the nominal and measured attitude of the satellite.
Actuators
Three orthogonal reaction wheels were used for attitude control aboard this spacecraft
DYNAMICS MODULE
The dynamics block simulates the actual orbit of and attitude perturbation torques acting on the satellite. The starting “Orbital Mechanics” block sets the position, velocity, initial angular velocity, and initial inertial-to-body quaternion of the spacecraft. From here, these parameters, along with the inputted angular momentum and change in angular momentum of the satellite (in body coordinates) are used to continuously calculate
The magnetic field vector of the Earth and the torque acting on the satellite by that field
The torque produced by the gravity gradient acting on the satellite
The inertial-to-body quaternion
The angular velocity of the satellite
SENSOR MODULE
The sensor block takes an input of the actual angular velocity, inertial-to-body quaternion, and inertial position vector of the spacecraft and simulates measurement error for each of the sensors (gyroscope, earth horizon sensor, and magnetometer). The gyroscope is given error in the form of gyroscope bias and angular random walk. The earth horizon sensor is given a small white noise error which is crossed with the inertial-to-body quaternion to get the measured vector to the Earth in body coordinates. Next, the inertial position is used to calculate the inertial magnetic field vector of the Earth which is then converted to body coordinates using the inertial-to-body quaternion. Finally, white noise is added to the vector as the measurement error and the vector is outputted.
ATTITUDE DETERMINATION MODULE
The attitude determination block passes the measured angular velocity through as the estimated angular velocity and calculates the estimated inertial-to-body directional cosine matrix (DCM). That DCM is calculated using the TRIAD method of gathering two vectors (in this case the Earth’s magnetic field and vector between the Earth and the satellite measured by the sensors) to determine the attitude of the spacecraft. The attitude is represented by a coordinate transform DCM going from inertial to body coordinates.
ATTITUDE CONTROL MODULE
The attitude control block takes in measurements and estimations from the sensors and attempts to reduce the error between the nominal and estimated attitude of the satellite. For this mission, the nominal attitude of the spacecraft is for one face of the cylindrical satellite to be pointed towards the Earth at all times. In this simulation, the nominal attitude is calculated using the actual dynamics of the spacecraft. The nominal and estimated attitudes are matrix multiplied to calculate the error, and that error is inputted to the controller. The error in angular velocity from nominal and the measured angular velocities of the reaction wheels are also inputted to the controller. The controller is a PD controller. It uses the inputted information, along with the inertia matrices of the entire satellite and its reaction wheels, to command a change in angular momentum to each of the reaction wheels. These commands are send to the actuator block to control the attitude of the satellite.
ACTUATOR MODULE
The actuator block received the commanded changes in angular velocity for the reaction wheels, simulates those changes, and outputs both a measurement of the angular velocity for the reaction wheels and the angular momentum of the reaction wheels. Actuator error and a max spinrate limit are modeled to make the system more realistic.
RESULTS OF SIMULATION
These graphs compare the inertial-to-body DCM’s of the spacecraft across a single orbit. The graph on the left shows the actual DCM of the spacecraft while the graph on the right shows the nominal or desired DCM. Each DCM contains 9 elements which are shown over time on these graphs. With a small amount of error, these graphs show that the attitude determination and control system is maintaining the desired attitude for the mission. The satellite successfully points at the Earth for the entirety of the single orbit simulated.