Structured Adaptive Attitude Control Applied on a Myriade Simulation Benchmark

Abstract

This paper considers the problem of reaction-wheel attitude control inside the mission mode of the Myriade satellites. A structured adaptive algorithm, allowing to extend the operating domain of a static proportionalderivative controller is presented and conditions for designing a stabilizing, continuous-time adaptive law are given. In view of implementation, a discrete-time adaptive algorithm is derived and tested on a benchmark of the DEMETER satellite, which was part of the Myriade program. Simulation results show that the structured adaptation and the use of the σ-modification allow the adaptive closed-loop to follow attitude step references of up to 20 degrees without saturating the reaction wheels. This allows the adaptive law to cover the whole mission mode and replace the currently-implemented switched-based control strategy, thus potentially simplifying the verification and validation. process.

In-flight results of adaptive attitude control law for a microsatellite

“…Let us assume that system (7) is asymptotically stabilized by LTI PD controller T a = K 0 e = [K re K rv ] e. In the following, the closedloop state matrix A s + B s K 0 will be denoted as A(K 0 ). Then the following propositions hold: Proposition 1 [6] If system (7) is asymptotically stabilized by K 0 , then there exists a positive definite matrix P∈ℜ nxn , and scalars D θ , D ω , G θ , and G ω are solutions to the following LMI problem:…”

“…Proposition 2 [6] Consider some given scalar parameter β > 1. If K 0 , D θ , D ω , G θ , and G ω are solutions of LMIs (8), then there exists a positive definite matrix Q∈ℜ nxn and scalars R θ , R ω , T θ , T ω , F θ , F ω , α θ , and α ω are solutions to the following LMI problem:…”

“…Suitable values can be found by solving a linear matrix inequality (LMI) problem for a chosen value β > 1 (barrier function parameter), proving a passivity property of the closed loop. The two-step synthesis procedure is recalled here, for one single axis (see [6] for proof and details). Consider the open-loop system "seen" by the PD controller, such that:…”

“…The decoupled structured adaptive control with σ-modification (see [6]) has been chosen for controller synthesis. In the following, the controller expression and design will be explained for one satellite's axis (the same design procedure has been used for each axis).…”