🛰️Spacecraft Attitude Control Unit 11 – Attitude Control: Strategies & Feedback Laws

Key Concepts & Fundamentals

• Attitude control involves orienting a spacecraft to a desired orientation and maintaining that orientation over time
• Spacecraft attitude is described using Euler angles (roll, pitch, yaw) or quaternions
• Reference frames commonly used include body-fixed frame, orbital frame, and inertial frame
  • Body-fixed frame is attached to the spacecraft and rotates with it
  • Orbital frame is centered on the spacecraft with axes aligned with the orbit
  • Inertial frame is a fixed frame in space, not rotating with the spacecraft
• Rigid body dynamics govern the rotational motion of the spacecraft
  • Moment of inertia tensor characterizes the mass distribution of the spacecraft
  • External torques (gravity gradient, solar radiation pressure, etc.) affect the spacecraft's attitude
• Kinematics describes the geometric aspects of motion without considering forces or masses
• Attitude determination involves estimating the current orientation of the spacecraft using sensors (star trackers, sun sensors, magnetometers)
• Attitude control actuators apply torques to the spacecraft to change or maintain its orientation (reaction wheels, thrusters, magnetorquers)

Attitude Control Systems Overview

• Attitude control systems consist of sensors, actuators, and control algorithms working together to achieve the desired spacecraft orientation
• Sensors measure the spacecraft's current attitude and provide feedback to the control system
  • Star trackers use images of stars to determine the spacecraft's orientation
  • Sun sensors measure the direction of the sun relative to the spacecraft
  • Magnetometers measure the Earth's magnetic field to determine the spacecraft's orientation
• Actuators apply torques to the spacecraft to change or maintain its orientation
  • Reaction wheels are spinning flywheels that exchange angular momentum with the spacecraft
  • Thrusters use propellant to generate forces and torques on the spacecraft
  • Magnetorquers create magnetic dipoles that interact with the Earth's magnetic field to generate torques
• Control algorithms process sensor data and generate commands for the actuators to achieve the desired attitude
• Attitude control modes include detumbling, pointing, and tracking
  • Detumbling reduces the spacecraft's initial angular rates after launch or deployment
  • Pointing maintains a fixed orientation relative to a target (Earth, Sun, star)
  • Tracking follows a moving target or a predefined trajectory
• Attitude control performance is evaluated using metrics such as pointing accuracy, stability, and response time

Attitude Determination Techniques

• Attitude determination estimates the spacecraft's current orientation using sensor measurements and mathematical models
• TRIAD algorithm is a deterministic method that uses two vector measurements (e.g., Sun direction and magnetic field) to calculate the attitude
• Wahba's problem seeks to find the optimal attitude that minimizes the weighted sum of squared errors between measured and reference vectors
  • Solutions to Wahba's problem include the QUEST algorithm and the Singular Value Decomposition (SVD) method
• Kalman filtering is a recursive algorithm that combines sensor measurements with a dynamic model to estimate the attitude and angular rates
  • Extended Kalman Filter (EKF) linearizes the nonlinear system model around the current estimate
  • Unscented Kalman Filter (UKF) uses a deterministic sampling approach to capture the mean and covariance of the state distribution
• Star trackers provide high-accuracy attitude determination by comparing observed star patterns with a star catalog
• Gyroscopes measure angular rates, which can be integrated to estimate the change in attitude over time
• Sensor fusion techniques combine measurements from multiple sensors to improve attitude estimation accuracy and robustness

Control Strategies & Algorithms

• PID (Proportional-Integral-Derivative) control is a simple and effective feedback control strategy
  • Proportional term applies a control signal proportional to the attitude error
  • Integral term accumulates the attitude error over time to eliminate steady-state errors
  • Derivative term responds to the rate of change of the attitude error to improve stability
• Linear Quadratic Regulator (LQR) is an optimal control technique that minimizes a quadratic cost function
  • LQR design involves selecting appropriate weighting matrices for the state and control inputs
  • Riccati equation is solved to obtain the optimal feedback gain matrix
• Sliding mode control is a nonlinear control strategy that drives the system state onto a sliding surface
  • Sliding surface is designed to represent the desired system behavior
  • Control law switches between two states to maintain the system on the sliding surface
• Adaptive control adjusts the control parameters in real-time to account for changes in the system or environment
  • Model Reference Adaptive Control (MRAC) uses a reference model to define the desired system behavior
  • Adaptive laws update the control parameters based on the error between the actual and reference models
• Robust control techniques, such as H-infinity control, are designed to maintain performance in the presence of uncertainties and disturbances

Feedback Laws & Control Loops

• Feedback control uses sensor measurements to adjust the control inputs and reduce the error between the desired and actual system states
• Attitude error is the difference between the desired and actual spacecraft orientation
  • Attitude error can be represented using Euler angles, quaternions, or direction cosine matrices
• Control torques are generated based on the attitude error and the chosen feedback law
  • Feedback laws map the attitude error to the required control torques
  • Examples of feedback laws include proportional, proportional-derivative, and nonlinear feedback laws
• Closed-loop control systems continuously monitor the system output and adjust the control inputs to achieve the desired performance
  • Stability of the closed-loop system is crucial to ensure convergence to the desired attitude
  • Gain margins and phase margins are used to assess the stability and robustness of the control system
• Feed-forward control can be used in conjunction with feedback control to improve performance
  • Feed-forward control uses knowledge of the system model and expected disturbances to generate control inputs
  • Gyro-based feed-forward control uses angular rate measurements to compensate for external torques
• Control allocation distributes the desired control torques among the available actuators
  • Optimization-based control allocation methods consider actuator constraints and minimize power consumption

Actuators & Hardware Components

• Reaction wheels are momentum exchange devices that generate control torques by changing their angular velocity
  • Reaction wheel assemblies typically consist of three or more wheels mounted orthogonally
  • Wheel speed is controlled using electric motors and power electronics
  • Momentum dumping is required to prevent reaction wheel saturation
• Thrusters are propulsive devices that generate control torques by expelling propellant
  • Chemical thrusters use combustion of fuel and oxidizer to generate thrust
  • Electric thrusters, such as ion engines and Hall thrusters, use electric fields to accelerate propellant
  • Thruster placement and orientation affect the control authority and efficiency
• Magnetorquers are electromagnetic devices that interact with the Earth's magnetic field to generate control torques
  • Magnetorquers consist of current-carrying coils or magnetic rods
  • Control torque is generated by varying the current in the magnetorquers
  • Magnetorquers are often used for detumbling and momentum dumping
• Control moment gyroscopes (CMGs) are advanced actuators that provide high torque output with low power consumption
  • CMGs consist of a spinning rotor and a gimbal that changes the rotor's angular momentum direction
  • CMG steering laws, such as singularity avoidance and momentum management, are used to control the CMG array
• Actuator sizing and placement are critical design considerations for attitude control systems
  • Actuator saturation limits the maximum control torque that can be generated
  • Redundancy and fault tolerance are important for ensuring the reliability of the attitude control system

Stability Analysis & Performance Metrics

• Stability analysis assesses the ability of the attitude control system to converge to and maintain the desired orientation
• Lyapunov stability theory is used to analyze the stability of nonlinear systems
  • Lyapunov functions are scalar functions that decrease along system trajectories
  • Asymptotic stability is achieved if the Lyapunov function is positive definite and its time derivative is negative definite
• Linear stability analysis techniques, such as eigenvalue analysis and Routh-Hurwitz criterion, are used for linearized system models
  • Eigenvalues of the closed-loop system matrix determine the stability and transient response
  • Routh-Hurwitz criterion checks the stability of a linear system based on the coefficients of its characteristic equation
• Pointing accuracy is a key performance metric that quantifies the angular deviation between the actual and desired spacecraft orientation
  • Pointing error is typically expressed in terms of roll, pitch, and yaw angles or total angular error
  • Pointing stability refers to the ability to maintain the desired orientation over time
• Settling time is the time required for the spacecraft attitude to converge within a specified tolerance of the desired orientation
• Bandwidth is the frequency range over which the attitude control system can effectively track reference inputs and reject disturbances
• Robustness measures the ability of the control system to maintain performance in the presence of uncertainties, disturbances, and parameter variations
  • Gain and phase margins quantify the robustness of the control system to variations in system parameters
  • Monte Carlo simulations are used to assess the robustness of the control system under various scenarios

Practical Applications & Case Studies

• Earth observation satellites require precise pointing to capture high-resolution images of the Earth's surface
  • Pointing requirements for Earth observation satellites are typically in the range of arcseconds
  • High-accuracy attitude determination using star trackers and gyroscopes is essential
  • Reaction wheels and thrusters are commonly used for pointing control
• Communication satellites need to maintain accurate pointing to ensure reliable signal transmission and reception
  • Pointing requirements for communication satellites are typically in the range of tenths of a degree
  • Dual-spin stabilization is often used, with the antenna platform despun from the main body
  • Momentum wheels and thrusters are used for attitude control and station-keeping
• Interplanetary spacecraft require attitude control for navigation, communication, and scientific observations
  • Attitude control challenges include long communication delays, limited power and computational resources, and varying environmental conditions
  • Spin stabilization is often used for simplicity and reliability
  • Thrusters and reaction wheels are used for attitude maneuvers and pointing control
• Formation flying missions involve the coordination and control of multiple spacecraft in a precise geometric configuration
  • Relative attitude control is required to maintain the desired formation geometry
  • Decentralized control architectures and consensus algorithms are used for coordination among spacecraft
  • Examples of formation flying missions include NASA's Magnetospheric Multiscale (MMS) mission and ESA's Proba-3 mission
• Rendezvous and docking operations require precise attitude control for successful spacecraft mating
  • Relative navigation and attitude determination between the chaser and target spacecraft are critical
  • Model predictive control and vision-based control techniques are used for autonomous rendezvous and docking
  • Examples include the docking of crewed spacecraft with the International Space Station (ISS) and autonomous satellite servicing missions