Spacecraft Attitude Control Using SDRE for Nonlinear Disturbances
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Solution Overview
Problem
Existing attitude control systems for spacecraft are defective due to uncertainties and nonlinearities, making them inefficient and prone to suboptimal performance.
Innovation Solution
The use of an optimal regulator derived from the State-Dependent Riccati Equation (SDRE) technique, which allows for real-time determination of optimal trajectories and control laws, autonomously adapting to unmodeled disturbances and system nonlinearities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional linear control techniques (LQR, PID) are used for spacecraft attitude control, then the control system is simple to implement, but the system performance deteriorates due to nonlinearities and uncertainties in spacecraft dynamics
Solution Approach 1:
The patent transforms the fixed-parameter linear control approach into a variable-parameter nonlinear control approach. The State-Dependent Riccati Equation (SDRE) method continuously adapts the control parameters based on the current system state, allowing the controller to optimize performance for each operating condition while maintaining mathematical tractability through the Riccati framework.
Solution Approach 2:
The patent transitions from static linear control to dynamic nonlinear control by formulating the control law as a differential game where the value function satisfies a Hamilton-Jacobi-Isaacs (HJI) equation. This dynamic formulation allows the control strategy to adapt in real-time to changing system conditions, nonlinearities, and uncertainties, improving reliability while maintaining implementation feasibility through structured solution methods.
2Measurement precision
If predefined trajectories with feed-forward terms are used for LQR control, then the system can track desired trajectories, but the system becomes vulnerable to fortuitous deviations and requires complex linearization at multiple operation points
Solution Approach 1:
The patent emphasizes feedback-based control through the differential game formulation and value function approach. Rather than relying on open-loop feed-forward trajectories, the control law continuously uses state feedback to adjust control inputs, making the system robust to deviations while avoiding the complexity of multiple linearization points. The feedback structure naturally handles nonlinearities and uncertainties.
Solution Approach 2:
The SDRE-based differential game controller is self-adapting, automatically adjusting its control strategy based on the current system state without requiring external trajectory re-planning or manual intervention. The value function computation inherently accounts for the current operating conditions, allowing the system to self-correct from deviations and maintain optimal performance across varying conditions.
3Stability of the object's composition
If Lyapunov-derived control laws are used for nonlinear systems, then stability can be proven, but the control laws are difficult to tune and may heavily tax the actuators
Solution Approach 1:
The patent replaces the mechanical tuning process of Lyapunov controllers with an automated mathematical optimization framework based on differential games and value functions. Instead of manually adjusting controller parameters to achieve stability, the HJI-based formulation automatically generates optimal control laws that guarantee stability while optimizing performance criteria, eliminating the need for difficult manual tuning and reducing actuator stress through optimal control allocation.
Data Source
AI summary
Systems and method for controlling the attitude maneuvers of a spacecraft in space are provided. The method automatically generates optimal trajectories in real-time to guide a spacecraft, providing a much more robust and efficient method than predefined trajectories, to model errors or disturbances. These methods do not rely in predefined trajectories and their associated feed-forward term. The systems comprise sensors, attitude control mechanisms, and a control module to orient the spacecraft in real-time, such that the spacecraft reaches a desired target attitude following an optimal path in the state space and is locally and asymptotically stable.