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 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

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

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

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

Robust Control Strategy for a Conduction–Convection System Based on the Scenario Optimization

International audienceThis paper deals with the robust control of an uncertain conduction–convection system in the framework of probabilistic control design based on both the geometric control and the scenario optimization approach. Thus, a robust control strategy that copes with parameter uncertainties is proposed for a heated rod taken as an application example of a conduction–convection system. The design approach consists in two steps. In the first step, assuming a nominal model, a state feedback that yields a stable linear lumped parameter system, of first order, in closed loop is designed by means of geometric control theory. The stability of the resulting closed-loop system is demonstrated based on the perturbation theorem from semigroup theory. The second step consists in defining the input reference of the designed state feedback by a structured robust controller. The parameter tuning of the structured controller is formulated as a semi-infinite (or robust) optimization problem which is, then, relaxed using the scenario approach leading to a standard finite optimization problem. The solution of this scenario optimization problem is achieved using a genetic algorithm. The proposed control strategy is adopted to cope with parameter uncertainties in the problem of heating a steel rod. The effectiveness of the proposed robust control strategy is demonstrated by simulation

A fast response and recovery H2S gas sensor based on free-standing TiO2 nanotube array films prepared by one-step anodization method

International audienceThe free-standing TiO 2 nanotube (TiNT) array film was firstly synthesized by a one-step anodization method. The characterization results with SEM, TEM, XRD and EDX indicated that the main compound on the TiNT array film was titania with anatase phase, and the average inner diameter of the nanotube was around 110 nm with a wall thickness of 16 nm and a layer thickness of 3.8 µm. Subsequently, the TiNT-based gas sensor was fabricated and its sensing properties toward H 2 S were investigated. The results showed that, operating under the optimum temperature of 300 °C, the TiNT-based gas sensor not only had excellent reversibility, selectivity and stability, but also attained the response values 4.5-26.2 to the detected H 2 S gas at 1-50 ppm, and good linearity between the sensor response and H 2 S concentration could be observed. Meanwhile, the response and recovery time of the sensor to 50 ppm H 2 S gas were as low as 22 s and 6 s, respectively. In addition, the growth mechanism of the free-standing TiNT array film and the gas sensing mechanism of the TiNT-based gas sensor towards H 2 S were also given in the article. Lastly, the outstanding gas sensing properties and easy fabrication of the TiNT-based gas sensor presented the potential industrial applications in the future