Christelle Pittet

Reaction Wheels Desaturation Using Magnetorquers and Static Input Allocation

Considering the most widely spread configuration of actuators for low orbit satellites, namely a set of reaction wheels and set of magnetorquers, we revisit the classical cross-product control law solution for achieving attitude stabilization and momentum dumping. We show how the classical solution has a quasi-cascade structure that, under a suitable input-to-state (ISS) assumption, can be stabilized by high gain, thereby making the actuators more inclined to saturate. Motivated by this, we propose a revisited version of this control law that transforms the quasi-cascade into a real cascade. Then, we show that both strategies are such that the attitude control is affected by the momentum dumping, and that they both require a suitable ISS property. To overcome these drawbacks, we propose a new allocation-based controller, which makes the attitude dynamics completely independent of the momentum dumping and induces global asymptotic stability without any ISS requirement. Several formal statements and simulation results support our discussions and highlight the pros and cons of the different control strategies.

Periodic FIR controller synthesis for discrete-time uncertain linear systems

This paper is concerned with robust state-feedback controller synthesis for discrete-time linear periodic/time-invariant systems subject to polytopic-type parametric uncertainties. In recent studies, some of the authors conceived an LMI-based approach to periodically time-varying memory controller (PTVMC) synthesis and proved that this approach is indeed effective to get less conservative robust controller design procedures. However, since the peculiar controller structure requires to reset memory to zero in a periodic way, it is pointed out that the control performance depends on the timing of implementation. In this paper we tackle this issue and propose a reset-less state-feedback Periodic FIR Controller (PFIRC), which turns out to be suitable to improve robustness on periodic and time-invariant systems. Moreover, as a special case, a design condition is provided for FIR-type LTI controllers that robustly stabilize uncertain LTI systems. Numerical examples illustrate the efficiency of the proposed approaches.

Simple Adaptive Control without Passivity Assumptions and Experiments on Satellite Attitude Control DEMETER Benchmark

Abstract The paper gives a simple LMI procedure to design simple adaptive control laws for ‘almost stable’ systems. It relaxes existing ‘almost passive’ assumptions making simple adaptive control possible for all systems stabilizable by LTI controllers. The expected advantage of the adaptive control compared to the initial LTI control is to improve performances and robustness. The proposed results apply to multi-input multi-output systems and rely on LMI optimization. The theory is illustrated on a satellite attitude control DEMETER benchmark.

Linear Dynamic Modeling of Spacecraft with Open-Chain Assembly of Flexible Bodies for ACS/Structure Co-design

This work presents a method to build a linear dynamic model of openchain assembly of spacecraft flexible appendages for future Attitude Control System (ACS)/Structure co-design. This kind of modeling takes into account the flexible interactions between all the spacecraft substructures, called bodies or appendages, to finally provide the loads (forces and torques) induced to the main body. More generally, this method can be applied to any open mechanical chain, such as segments of robotic arms, segments of antenna mast or masts linking solar panels to the main hub. Therefore, the dynamics model of the entire spacecraft can be derived easily in order to design the spacecraft ACS. The method is based on the Craig-Bampton modal synthesis, from which a state-space representation is obtained.

Periodic H 2 synthesis for spacecraft attitude control with magnetorquers and reaction wheels

Particularly attractive for small satellites, the use of magnetic torquers for attitude control is still a difficult problem. Indeed, equations are naturally time-varying and suffers from controllability issues. In this paper, a generic model, taking different kinds of pointing and different kinds of actuators into account, is proposed, linearized and then discretized. Recent studies demonstrate how combining magnetorquers and reaction wheels is attractive. Following this line, latest LMI synthesis techniques for static periodic controller are applied in this paper to the attitude control problem of a spacecraft equipped with both actuation systems. Simulation results are provided, showing the performance of the obtained control law.

Anti-windup Design for Satellite Control with Microthrusters

Future space missions (e.g. microscope, formation flying, rendez-vous) demand for an acceleration or relative position control. That requires actuators that can provide an effort in the linear axis. Therefore propulsion systems apply. Then, these same systems are used for the attitude control instead of the reaction wheels. At the same time a high precision is demanded. Thus microthrusters are needed as they are able to perform an almostcontinuous propulsion, between zero and its maximum, with a quantization. Even though they satisfy the demands on high precision, the maximal propulsion capacity appears to be critically low, which could lead to the saturation of the actuator. A model of the systems needing longitudinal efforts with high precision is presented. Microthrusters used in these kind of systems are also characterized. An anti-windup controller design technique is proposed for this kind of actuators. Simulations consider the attitude control of an axis of a satellite. They show how the anti-windup controller increases the level of saturation allowed as well as the disturbance amplitude. Simulations are based on a nominal model provided by CNES and developed in matlab/simulink.

Multi-saturation anti-windup structure for satellite control

Future space missions demand high precision control in both angular and linear axes. Therefore propulsion systems providing effort in both axes with a high precision are needed. Microthrusters can satisfy these requirements. These actuators are usually subject to present an allocation problem. Moreover, because of this demand on high precision, the maximal propulsion capacity appears to be critically low, leading to a possible saturation of the actuators. A multi-saturation based model for a highly non-linear allocation function is presented. An anti-windup strategy dealing with the actuator saturation is proposed. Simulations consider a two satellites flight formation scenario. They show the improvement on performance and stability tolerance to off-nominal initial conditions. Simulations are based on a nominal model provided by Thales Alenia Space (TAS).

Flexible Multibody System Linear Modeling for Control Using Component Modes Synthesis and Double-Port Approach

The main objective of this study is to propose a methodology for building a parametric linear model of flexible multibody systems (FMS) for control design. This new method uses a combined finite element (FE)–state-space approach based on component mode synthesis and a double-port approach. The proposed scheme offers the advantage of an automatic assembly of substructures, preserving the elastic dynamic behavior of the whole system. Substructures are connected following the double-port approach for considering the dynamic coupling among them, i.e., dynamic coupling is expressed through the transfer of accelerations and loads at the connection points. The proposed model allows the evaluation of arbitrary boundary conditions among substructures. In addition, parametric variations can be included in the model for integrated control/structure design purposes. The method can be applied to combinations of chainlike or/and starlike flexible systems, and it has been validated through its comparison with the assumed modes method (AMM) in the case of a rotatory spacecraft and with a nonlinear model of a two-link flexible arm.

Robust Stability of Periodic Systems with Memory: New Formulations, Analysis and Design Results

Abstract In this paper, the general formulation of periodically time-varying state-feedback controllers with memory is considered for the first time. New analysis and synthesis conditions for robust stability are proposed. The flexibility of these new results allows the user to freely add degrees-of-freedom to the control law which appears to effectively reduce the conservatism of the synthesis condition and to increase the stability domain of the closed-loop system in the presence of uncertainties. Furthermore, it is shown that for a particular structure of controllers a more efficient version of the design theorem can be derived by enriching the matrix of slack-variables.

Robust analysis of Demeter benchmark via quadratic separation

Abstract The purpose of this paper is to give numerical illustrations of recent results obtained in the area of robust analysis of uncertain parametric LTI systems. The idea is to highlight theoretical as well as numerical issues pertaining to real life applications of sophisticated robust analysis of spaceborne control systems. The framework of quadratic separation applied to interconnected implicit linear transformations and uncertain operators as defined in Peaucelle et al. (2007) is renewed. Improved robust stability tests involving more complex parameter-dependent Lyapunov functions are applied on a benchmark from the space industry. It is based on the problem of attitude control of a flexible satellite developed at CNES and it is used to analyze the relevance as well as some shortcomings of the proposed approach.