A Systematic Methodology for Modeling and Attitude Control of Multi-body Space Telescopes

TL;DR

The paper addresses precise pointing control for a complex multi-body space telescope by deriving a symbolic nonlinear model via Kane's method in Stoneking form and then linearizing it about a designated equilibrium to obtain a linear state-space system. It designs and compares two controllers, LQR and robust pole assignment, on the rigid linearized model and validates performance against a high-fidelity flexible model. Results show robust pole assignment offers better energy efficiency and reduced low-frequency oscillations for pointing accuracy, while LQR serves as a practical, informative starting point to guide pole placement. The methodology, validated on LUVOIR, is generalizable to other multi-body systems and demonstrates how to integrate symbolic modeling, linearization, and robust control design for complex aerospace platforms.

Abstract

This paper derives a symbolic multi-body rigid nonlinear model for a space telescope using Stoneking's implementation of Kane's method. This symbolic nonlinear model is linearized using Matlab symbolic functions {\tt diff} and {\tt inv} because the analytic linearization is intractable for manual derivation. The linearized system model is then used to design the controllers using both linear quadratic regulator (LQR) and robust pole assignment methods. The closed-loop systems for the two designs are simulated using both the rigid model as well as a second model containing flexible modes. The performances of the two designs are compared based on the simulation testing results. Our conclusion is that the robust pole assignment design offers better performance than that of the LQR system in terms of actuator usage and pointing accuracy. However, the LQR approach remains an effective first design step that can inform the selection of real eigenvalues for robust pole assignment. The proposed method may be used for the modeling and controller designs for various multi-body systems.

Figures (13)

• Figure 1: The concept of LUVOIR telescope.
• Figure 2: The description of the three bodies of LUVOIR telescope.
• Figure 3: LQR and robust pole assignment design comparison for rigid model: (a) $x_1$ initial state response (b) $x_2$ initial state response.
• Figure 4: LQR and robust pole assignment design comparison for rigid model: (a) $x_3$ initial state response (b) $x_4$ initial state response.
• Figure 5: LQR and robust pole assignment design comparison for rigid model: (a) $x_5$ initial state response (b) $x_6$ initial state response.

Theorems & Definitions (3)

• Remark 3.1
• Remark 4.1
• Remark 4.2