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Abstract

Application of the passification-based adaptive control technique for control of Quanser/LAAS ``Helicopter'' laboratory setup is presented. Two adaptive control laws for pitch angle control are designed and experimentally tested. The MATLAB/Simulink and WinCon software environment is used for adaptive control laws implementation and the real-world experiments. The experimental results demonstrate high closed loop system performance and robustness of the suggested control laws with respect to parametric uncertainties and unmodeled plant dynamics and actuator faults.

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Abstract

This is a continuation of our preceding study dealing with robust stabilizing controller synthesis for uncertain discrete-time linear periodic/time-invariant systems. In this preceding study, we dealt with the case where the underlying systems are affected by polytopic-type uncertainties and revealed a particular periodically time-varying dynamical controller (PTVDC) structure that allows LMI-based robust stabilizing controller synthesis. Based on these preliminary results, in this paper, we provide LMI conditions for robust H2 and H PTVDC synthesis. One of the salient features of the proposed method is that we can reduce the conservatism and improve the control performance gradually by increasing the period of the controller to be designed. In addition, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based design methods as particular cases. Through numerical experiments, we illustrate that our design method is indeed effective to achieve less conservative results under both the periodic and time-invariant settings. keywords: Robust control, periodic systems, polytopic uncertainties, linear matrix inequalities.

Abstract

Passification-based direct adaptive control is considered for polytopic uncertain linear time-invariant multi-input multi-output systems. Linear Matrix Inequality based results are provided to guarantee that the adaptive algorithm passifies the system whatever the uncertain parameters in some given set. Contributions are based on the introduction of a parallel feed-forward shunt that liberates the strong equality constraint PB=CtGt often used for strict passification. The shunt, combined with the introduction of slack variables, allows a conclusion with easy to test conditions without restrictions on which data is uncertain in the process model. The resulting adaptive control is such that control gain is bounded in a chosen set whatever the bounded disturbance. Moreover, it proves to be not worse than computable parameter-dependent static output-feedback controls with respect to L2 gain attenuation. A simple academic example illustrates the results.

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Passivity is a widely used concept in control theory having led to many significant results. This paper concentrates on one characteristic of passivity, namely passification-based adaptive control. This concept applies to multi-input multi-output systems for which exists a combination of outputs that renders the open-loop system hyper-minimum phase. Under such assumptions, the system may be passified by both high-gain static output feedback and by a particular adaptive control algorithm. This last control law is modified here to guarantee its coefficients to be bounded. The contribution of this paper is to investigate its robustness with respect to parametric uncertainty. Time response characteristics are illustrated on examples including realistic situations with noisy output and saturated input. Theoretical results are formulated as linear matrix inequalities and can hence be readily solved with semi-definite programming solvers.

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Recent papers in the field of LMI-based robust control have provided extensions of known results for linear time-invariant systems to the case of periodically time varying linear systems. These results, theoretically satisfactory because formulated in terms of optimization problems of polynomial complexity, may still have limited applications in practice because the number of variables and constraints is very large. The present paper proposes a new formulation of these results that allows to reduce the computational burden both by reducing the number of decision variables and the size of the constraints. Along with this numerical improvement, the paper produces a new modeling of periodic discrete-time systems in descriptor form that is believed promising for future research.

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Groups of satellites flying in formation require maintaining the specific relative geometry of the formation with high precision. This requirement implies to consider the problem of relative station keeping in a renewed framework. In this framework, issues related to the derivation of reliable relative models as well as to the peculiarity of the synthesis problems must be jointly considered. This paper presents some preliminary results of a robust multi- objective control approach applied to the station keeping of a low Earth observation system, i.e. the interferometric cartwheel, patented by CNES. This wheel is made up of three receiving spacecrafts, which follow an emitting Earth observation radar satellite. The particular geometry of this formation of satellites leads to the derivation of a simplified uncertain state-space model. Atmospheric drag perturbations are included in the linearized equations of the relative motion and the atmospheric density part of the definition of the atmospheric drag force is considered to be uncertain due to its dependence upon the solar activity. In the first part of the paper, an uncertain polytopic state-space model is derived. The second part describes the station keeping strategy of the formation. The station keeping strategy is performed using pure passive actuators. Due to the high stability of the relative eccentricity of the formation, only the relative semi major axis has to be controlled. Differential drag due to a differential orientation of the solar panel is used here to control relative altitude. A robust multi-objective control strategy via state-feedback is developed and tested as autonomous orbit controller. These results are analyzed via highly non linear simulations performed on a platform of CNES.

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