2,503 research outputs found

    Flat systems, equivalence and trajectory generation

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    Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector field. After recalling the definition of a Lie-Backlund mapping, we say that two systems are equivalent if they are related by a Lie-Backlund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft

    Non-linear estimation is easy

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    Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint

    Variations sur la notion de contrƓlabilitƩ

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    DoctoralThis paper was read on June 17th, 2000, at the "JournƩe de la SociƩtƩ mathƩmatique de France". It aims at presenting "flatness-based" control, which has become quite popular in industry, by revisiting the apparently familiar notion of controllability. We are discussing finite-dimensional linear and nonlinear systems, as well as delay systems and some partial differential equations

    Flat systems, equivalence and trajectory generation

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    3rd cycleIntroduction : Control systems are ubiquitous in modern technology. The use of feedback control can be found in systems ranging from simple thermostats that regulate the temperature of a room, to digital engine controllers that govern the operation of engines in cars, ships, and planes, to flight control systems for high performance aircraft. The rapid advances in sensing, computation, and actuation technologies is continuing to drive this trend and the role of control theory in advanced (and even not so advanced) systems is increasing..

    Acta Cybernetica : Volume 25. Number 1.

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    Experimental comparison of classical pid and model-free control: position control of a shape memory alloy active spring

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    WOSInternational audienceShape memory alloys (sma) are more and more integrated in engineering applications. These materials with their shape memory effect permit to simplify mechanisms and to reduce the size of actuators. sma parts can easily be activated by Joule effect but their modelling and consequently their control remains difficult, it is principally due to their hysteretic thermomechanical behaviour. Most of successful control strategy applied to sma actuator are not often suitable for industrial applications: they are particularly heavy and use the Preisach model or neural networks to model the hysteretic behaviour of these material; this kind of models are difficult to identify and to use in real time. That is why this paper deals with an application of the new framework of model-free control (mfc) to a sma spring based actuator. This control strategy is based on new results on fast derivatives estimation of noisy sig- nals, its main advantages are: its simplicity and its robustness. Experimental results and comparisons with pi control are exposed that demonstrate the efficiency of this new control strategy. Key words: Nonlinear control, Model-free control, Shape memory alloy, Derivative estimation, Nonphysical modelling

    Relaminarisation of Re_Ļ„=100 channel flow with globally stabilising linear feedback control

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    The problems of nonlinearity and high dimension have so far prevented a complete solution of the control of turbulent flow. Addressing the problem of nonlinearity, we propose a flow control strategy which ensures that the energy of any perturbation to the target profile decays monotonically. The controllerā€™s estimate of the flow state is similarly guaranteed to converge to the true value. We present a one-time off-line synthesis procedure, which generalises to accommodate more restrictive actuation and sensing arrangements, with conditions for existence for the controller given in this case. The control is tested in turbulent channel flow (Re_Ļ„ā€‰=ā€‰100) using full-domain sensing and actuation on the wall-normal velocity. Concentrated at the point of maximum inflection in the mean profile, the control directly counters the supply of turbulence energy arising from the interaction of the wall-normal perturbations with the flow shear. It is found that the control is only required for the larger-scale motions, specifically those above the scale of the mean streak spacing. Minimal control effort is required once laminar flow is achieved. The response of the near-wall flow is examined in detail, with particular emphasis on the pressure and wall-normal velocity fields, in the context of Landahlā€™s theory of sheared turbulence

    Autonomous supervision and optimization of product quality in a multi-stage manufacturing process based on self-adaptive prediction models.

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    In modern manufacturing facilities, there are basically two essential phases for assuring high production quality with low (or even zero) defects and waste in order to save costs for companies. The first phase concerns the early recognition of potentially arising problems in product quality, the second phase concerns proper reactions upon the recognition of such problems. In this paper, we address a holistic approach for handling both issues consecutively within a predictive maintenance framework at an on-line production system. Thereby, we address multi-stage functionality based on (i) data-driven forecast models for (measure-able) product quality criteria (QCs) at a latter stage, which are established and executed through process values (and their time series trends) recorded at an early stage of production (describing its progress), and (ii) process optimization cycles whose outputs are suggestions for proper reactions at an earlier stage in the case of forecasted downtrends or exceeds of allowed boundaries in product quality. The data-driven forecast models are established through a high-dimensional batch time-series modeling problem. In this, we employ a non-linear version of PLSR (partial least squares regression) by coupling PLS with generalized Takagiā€“Sugeno fuzzy systems (termed as PLS-fuzzy). The models are able to self-adapt over time based on recursive parameters adaptation and rule evolution functionalities. Two concepts for increased flexibility during model updates are proposed, (i) a dynamic outweighing strategy of older samples with an adaptive update of the forgetting factor (steering forgetting intensity) and (ii) an incremental update of the latent variable space spanned by the directions (loading vectors) achieved through PLS; the whole model update approach is termed as SAFM-IF (self-adaptive forecast models with increased flexibility). Process optimization is achieved through multi-objective optimization using evolutionary techniques, where the (trained and updated) forecast models serve as surrogate models to guide the optimization process to Pareto fronts (containing solution candidates) with high quality. A new influence analysis between process values and QCs is suggested based on the PLS-fuzzy forecast models in order to reduce the dimensionality of the optimization space and thus to guarantee high(er) quality of solutions within a reasonable amount of time (ā†’ better usage in on-line mode). The methodologies have been comprehensively evaluated on real on-line process data from a (micro-fluidic) chip production system, where the early stage comprises the injection molding process and the latter stage the bonding process. The results show remarkable performance in terms of low prediction errors of the PLS-fuzzy forecast models (showing mostly lower errors than achieved by other model architectures) as well as in terms of Pareto fronts with individuals (solutions) whose fitness was close to the optimal values of three most important target QCs (being used for supervision): flatness, void events and RMSEs of the chips. Suggestions could thus be provided to experts/operators how to best change process values and associated machining parameters at the injection molding process in order to achieve significantly higher product quality for the final chips at the end of the bonding process

    Flat systems

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    Flat systems, Mini-course ECC'97, Brussel
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