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Linear Parameter Varying Attitude Control For CubeSats Using Electrospray Thrusters

Felix Biertümpfel, Emily Burgin, Hanna-Lee Harjono, Paulo Lozano, Harald Pfifer

TL;DR

This work develops a single LPV attitude controller for CubeSats actuated by electro spray thrusters, addressing low torque capability and the need to perform both large slews and precise pointing. By employing a mixed-sensitivity framework with scheduling parameter $\rho=|\theta-\theta_{\text{final}}|$, the controller differentially shapes performance for slewing and pointing within a unified design. The synthesized controller minimizes the induced $L_2$-norm of the closed-loop and provides guaranteed robustness across the scheduling domain, demonstrated via nonlinear simulations on the MagLev testbed. Compared to fixed-gain or discretely switched controllers, the LPV approach yields superior robustness to disturbances and smooth transitions between maneuver phases, with stability margins satisfying aerospace requirements. The results indicate significant practical impact for complex CubeSat operations using compact, throttleable iESE thrusters, enabling more ambitious missions while avoiding actuator saturation.

Abstract

This paper proposes the design of a single linear parameter-varying (LPV) controller for the attitude control of CubeSats using electro spray thrusters. CubeSat attitude control based on electro spray thrusters faces two main challenges. Firstly, the thruster can only generate a small control torque leading to easily saturating the actuation system. Secondly, CubeSats need to operate multiple different maneuvers from large to small slews to pointing tasks. LPV control is ideally suitable to address these challenges. The proposed design follows a mixed-sensitivity control scheme. The parameter-varying weights depend on the attitude error and are derived from the performance and robustness requirements of individual typical CubeSat maneuvers. The controller is synthesized by minimizing the induced L2-norm of the closed-loop interconnections between the controller and weighted plant. The performance and robustness of the controller is demonstrated on a simulation of the MIT Space Propulsion Lab's Magnetic Levitation CubeSat Testbed.

Linear Parameter Varying Attitude Control For CubeSats Using Electrospray Thrusters

TL;DR

This work develops a single LPV attitude controller for CubeSats actuated by electro spray thrusters, addressing low torque capability and the need to perform both large slews and precise pointing. By employing a mixed-sensitivity framework with scheduling parameter , the controller differentially shapes performance for slewing and pointing within a unified design. The synthesized controller minimizes the induced -norm of the closed-loop and provides guaranteed robustness across the scheduling domain, demonstrated via nonlinear simulations on the MagLev testbed. Compared to fixed-gain or discretely switched controllers, the LPV approach yields superior robustness to disturbances and smooth transitions between maneuver phases, with stability margins satisfying aerospace requirements. The results indicate significant practical impact for complex CubeSat operations using compact, throttleable iESE thrusters, enabling more ambitious missions while avoiding actuator saturation.

Abstract

This paper proposes the design of a single linear parameter-varying (LPV) controller for the attitude control of CubeSats using electro spray thrusters. CubeSat attitude control based on electro spray thrusters faces two main challenges. Firstly, the thruster can only generate a small control torque leading to easily saturating the actuation system. Secondly, CubeSats need to operate multiple different maneuvers from large to small slews to pointing tasks. LPV control is ideally suitable to address these challenges. The proposed design follows a mixed-sensitivity control scheme. The parameter-varying weights depend on the attitude error and are derived from the performance and robustness requirements of individual typical CubeSat maneuvers. The controller is synthesized by minimizing the induced L2-norm of the closed-loop interconnections between the controller and weighted plant. The performance and robustness of the controller is demonstrated on a simulation of the MIT Space Propulsion Lab's Magnetic Levitation CubeSat Testbed.
Paper Structure (13 sections, 1 theorem, 9 equations, 9 figures)

This paper contains 13 sections, 1 theorem, 9 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Background
  3. Linear Parameter-Varying Systems
  4. Linear Parameter-Varying Mixed-Sensitivity Design
  5. CubeSat Control Design Problem
  6. Magnetic Levitation CubeSat Testbed
  7. Parameter-Varying Control for CubeSat Attitude Maneuvers
  8. Scheduling Parameter
  9. Pointing Phase Design
  10. Slewing Phase Design
  11. Controller Synthesis
  12. Controller Evaluation
  13. Conclusions

Key Result

Theorem 1

wu1996induced: $G_\rho$ is exponentially stable and $\left\|G_\rho\right\| \leq \gamma$ if there exists a continuously differentiable symmetric matrix function $X: \mathcal{P} \rightarrow {\mathbb{R}}$$^{n_x \times n_x}$ such that $X(p) \geq 0$ and hold for all $p \in \mathcal{P}$ and $q \in \dot{\mathcal{P}}$, where $\partial X$ is defined as $\partial X(p,q) = \sum_{i=1}^{n_\rho} \frac{\partial

Figures (9)

  • Figure 1: LPV weighted four-block mixed-sensitivity problem.
  • Figure 2: Diagram of MagLev with main components labeled
  • Figure 3: MagLev device inside the SPL AstroVac vacuum chamber
  • Figure 4: Top-down view in axis of rotation demonstrating MagLev model satellite setup with two pairs of thrusters mounted
  • Figure 5: Definition of the scheduling parameter $\rho$: Reference signal $|\theta_\text{ref}|$ (\ref{['pl:thref']}), current attitude $\theta$ (\ref{['pl:th']}), final attitude $\theta_\text{ref}(t\rightarrow \infty)$ (\ref{['pl:thfinal']})
  • ...and 4 more figures

Theorems & Definitions (1)

  • Theorem 1