Distributed Control of Nonlinear Diffusion Systems by Input-Output Linearization

International audienceThis paper addresses the distributed control by input-output linearization of a non linear diffusion equation, which describes a particular but important class of distributed parameter systems. Both manipulated and controlled variables are assumed to be distributed in space. The control law is designed using the concept of characteristic index from geometric control by using directly the PDE model without any approximation or reduction. The main idea consists in the control design in assuming an equivalent linear diffusion equation obtained by use of the Cole-Hopf transformation. This framework helps to demonstrate the closed-loop stability using some concepts from the powerful semi-group theory. The performance of the proposed controller is successfully tested, through simulation, by considering a nonlinear heat conduction problem concerning the control of the temperature of a steel plate modeled by a non linear heat equation with Dirichlet boundary conditions

Boundary Geometric Control of a Nonlinear Diffusion System with Time-Dependent Spatial Domain

International audienceA Stefan problem represents a distributed parameter system with a time-dependent spatial domain. This paper addresses the boundary control of the position of the moving liquid-solid interface in the case of nonlinear Stefan problem with Neumann actuation. The main idea consists in deriving an equivalent linear model by means of Cole-Hopf tangent transformation, i.e. under a certain physical assumption, the original nonlinear Stefan problem is converted to a linear one. Then, the geometric control law is deduced directly from that developed, by the authors of the present paper, for the linear Stefan problem. Based on the fact that the Cole-Hopf transformation is bijective, it is shown that the developed control law yields a stable closed-loop system. The performance of the controller is evaluated through numerical simulation in the case of stainless steel melting characterized by a temperature-dependent thermal conductivity, which is nonlinear. The objective is to control the position of the liquid-solid interface by manipulating a heat flux at the boundary

Comparison of model predictive control strategies for the simulated moving bed

International audienceThis work compares three ways of controlling the simulated moving bed (SMB), an efficient process for chromatographic separation. Linear model predictive control (MPC) is considered in this work. A comparison of two different sets of manipulated inputs is carried out: on one hand, the classical one often presented in the literature, which consists in manipulating directly different flow rates involved in the process and, on the other hand, an approach coming from other counter-current separation processes which consists in manipulating the ratios of flow rates of each SMB zone. A hybrid method using the inputs calculated for a true moving bed (TMB) and implemented on the SMB is also compared. The advantages and drawbacks of each control strategy are discussed. In all cases, results show clearly the interest of applying MPC to high complexity systems such as the SMB

Distributed feedback control of a fractional diffusion process

International audienceIn this paper, a control law that enforces an output tracking of a fractional diffusion process is developed. The dynamical behavior of the process is described by a space-fractional parabolic equation. The objective is to force a spatial weighted average output to track its specified output by manipulating a control variable assumed to be distributed in the spatial domain. The state feedback is designed in the framework of geometric control using the notion of the characteristic index. Then, under the assumption that the fractional diffusion process is a minimum phase system, it is shown that the developed control law guarantees exponential stability in L2 -norm for the resulting closed loop system. Numerical simulations are performed to show the tracking and disturbance rejection capabilities of the developed controller

Distributed feedback control of a fractional diffusion process

International audienceIn this paper, a control law that enforces an output tracking of a fractional diffusion process is developed. The dynamical behavior of the process is described by a space-fractional parabolic equation. The objective is to force a spatial weighted average output to track its specified output by manipulating a control variable assumed to be distributed in the spatial domain. The state feedback is designed in the framework of geometric control using the notion of the characteristic index. Then, under the assumption that the fractional diffusion process is a minimum phase system, it is shown that the developed control law guarantees exponential stability in L 2-norm for the resulting closed loop system. Numerical simulations are performed to show the tracking and disturbance rejection capabilities of the developed controller

Odile Goerg, Fantômas sous les tropiques : aller au cinéma en Afrique coloniale

Quelle histoire du cinéma pour des pays longtemps dépourvus de productions nationales ? Dans Fantômas sous les tropiques, Odile Goerg rappelle que la passion du continent africain pour le Septième Art débute bien avant la naissance d’une industrie cinématographique – quasi inexistante durant la période coloniale. Elle convie le lecteur à se mêler à la foule enthousiaste des spectateurs se pressant dans les cours, les cafés ou les salles de spectacle : commerçants libanais, colons européens, f..

Optimal nonlinear control of an industrial emulsion polymerization reactor

International audienceIn this paper, the modelling, dynamic optimization and nonlinear control of an industrial emulsion polymerization reactor producing poly-vinyl acetate (PVAc) are proposed. The reaction is modeled as a two-phase system composed of an aqueous phase and a particle phase according to the model described in our previous work (Gil et al., 2014). The case study corresponds to an industrial reactor operated at a chemical company in Bogotá (Colom-bia). An industrial scale reactor (11 m 3 of capacity) is simulated. Three different dynamic optimization problems are solved from the more simplistic (only one control variable: reactor temperature) to the more complex (three control variables: reactor temperature, initiator flow rate and monomer flow rate) in order to minimize the reaction time. The results show that it is possible to minimize the reaction time while some polymer desired qualities (conversion, molecular weight and solids content) satisfy defined constraints. The optimal temperature profile and optimal feed policies of the monomer and initiator, obtained in a dynamic optimization step, are used as optimal set points for reactor control. A nonlinear geometric controller based on input/output linearization is implemented for temperature control

The Return of the Victorian Mummy: Alex Kurtzman’s The Mummy (2017), A Modern Orientalist Tale

As part of the Dark Universe reboot of Universal Monsters, Alex Kurtzman’s movie, The Mummy (2017) was meant to give new life to the Victorian monsters that fascinated Hollywood in the 1940s and 1950s. As it happened, the film also gave new life to the ideological dynamics of Victorian and Edwardian mummy fiction by displacing them to reflect current global issues. Indeed, the anxieties and obsessions put forward by the authors of mummy fiction (Bram Stoker, Conan Doyle, etc.) within the genre of imperial Gothic are dramatised in Kurtzman’s film and brought up to date to resonate with contemporary issues. The original tales of the mummy constructed the female mummy as a terrifying as well as enthralling embodiment of an imperial Other who comes back to life to wreak revenge upon the transgressive male archaeologists who disturbed her rest. Therefore, the well-known motif of the mummy’s curse acts as a metaphor for imperial dynamics as well as an ominous projection of what may happen, should the Empire strike back. The gender of literary mummies also points to the fear of a patriarchal society confronted to the growing struggle of women for social and political empowerment. The political and gendered dimensions of mummy fiction were left out of the numerous film adaptations which only retain the monstrous character of a dead body come back to life to threaten the living. Alex Kurtzman’s film marks the return of the Victorian mummy as a female embodying radical Otherness and the threat of an Orient embroiled in an endless war with the West.Premier opus de la franchise destinée à redonner vie aux Universal Monsters des années 1940 et 1950 inspirés par la littérature britannique du XIXe siècle, The Mummy d’Alex Kurtzman (2017) redonne également vie aux dynamiques idéologiques qui sont celles de la littérature victorienne et édouardienne, qui a vu émerger la figure de la momie. Genre éminemment politique, la mummy fiction, telle qu’elle prend forme sous la plume d’auteurs tels que Bram Stoker ou Arthur Conan Doyle, se fait l’expression des angoisses et des obsessions liées à l’Empire britannique en déclin. Le film de Kurtzman, en plaçant le récit de la découverte de la momie à notre époque, offre un écho contemporain aux problématiques impériales de la fin du XIXe siècle. Les premiers récits de momie de la littérature populaire britannique ont construit la femme momifiée en tant que figure à la fois terrifiante et séduisante d’un Autre impérial revenu à la vie pour se venger de la transgression commise par l’archéologue qui l’aurait tirée de son sommeil. Ainsi, le célèbre motif de la malédiction de la momie peut être interprété comme une métaphore des dynamiques impériales et de la menace qui pèse sur la métropole, si l’Empire s’avisait de contre-attaquer. En outre, le genre des momies littéraires indique également la crainte d’une société patriarcale confrontée à une lutte pour l’autonomie politique et sociale de la femme en plein essor. Si les dimensions politique et genrée ont le plus souvent été oubliées dans les nombreuses adaptations cinématographiques des récits de momie, le film d’Alex Kurtzman marque le retour de la momie victorienne en tant qu’incarnation d’une altérité radicale et d’un Orient éternellement en guerre contre l’Occident

Feedback control of bilinear distributed parameter system by input-output linearization

International audienceIn this paper, a control law that enforces the tracking of a boundary controlled output for a bilinear distributed parameter system is developed in the framework of geometric control. The dynamic behavior of the system is described by two weakly coupled linear hyperbolic partial differential equations. The stability of the resulting closed-loop system is investigated based on eigenvalues of the spatial operator of a weakly coupled system of balance equations. It is shown that, under some reasonable assumptions, the stability condition is related to the choice of the tuning parameter of the control law. The performance of the developed control law is demonstrated, through numerical simulation, in the case of a co-current heat exchanger. The control objective is to control the outlet cold fluid temperature by manipulating its velocity. Both tracking and disturbance rejection problems are considered

Observer design for a nonlinear diffusion system based on the Kirchhoff transformation

International audienceThis paper deals with the state estimation for a nonlinear diffusion system. An observer that reconstructs the whole state, from the available measurements, is proposed based on an equivalent linear diffusion model obtained using the Kirchhoff tangent transformation. This bijective mapping allows to apply the available and powerful state estimation theory of linear distributed parameter systems and simplifies the observer design. Hence, an observer can be designed for the obtained equivalent linear diffusion system and by using the Kirchhoff transformation, the whole state of the original nonlinear diffusion system is recovered. The observability analysis of the nonlinear diffusion system and the convergence of the proposed observer are also investigated based on the equivalent linear diffusion system. The effectiveness of the proposed observer is shown, through numerical simulation runs, in the case of a heated steel rod by considering both an uniformly distributed and a punctual boundary sensing