Dirac structures and boundary control systems associated with skew-symmetric differential operators

Associated with a skew-symmetric linear operator on the spatial domain $[a,b]$ we define a Dirac structure which includes the port variables on the boundary of this spatial domain. This Dirac structure is a subspace of a Hilbert space. Naturally, associated to this Dirac structure is infinite dimensional system. We parameterize the boundary port variables for which the $C_{0}$-semigroup associated to this system is contractive or unitary. Furthermore, this parameterization is used to split the boundary port variables into inputs and outputs. Similarly, we define a linear port controlled Hamiltonian system associated with the previously defined Dirac structure and a symmetric positive operator defining the energy of the system. We illustrate this theory on the example of the Timoshenko Beam. \u

Boundary control for a class of dissipative differential operators including diffusion systems

In this paper we study a class of partial differential equations (PDE's), which includes Sturm-Liouville systems and diffusion equations. From this class of PDE's we define systems with control and observation through the boundary of the spatial domain. That is, we describe how to select boundary conditions, such that the resulting system has inputs and outputs acting through the boundary. Furthermore, these boundary conditions are chosen in a way that the resulting system has a nonincreasing energy.\u

Magnetic Shape Memory Alloys as smart materials for micro-positioning devices

In the field of microrobotics, actuators based on smart materials are predominant because of very good precision, integration capabilities and high compactness. This paper presents the main characteristics of Magnetic Shape Memory Alloys as new candidates for the design of micromechatronic devices. The thermo-magneto-mechanical energy conversion process is first presented followed by the adequate modeling procedure required to design actuators. Finally, some actuators prototypes realized at the Femto-ST institute are presented, including a push-pull bidirectional actuator. Some results on the control and performances of these devices conclude the paper

Dissipative boundary control systems with application to distributed parameters reactors

In this paper we consider distributed parameter physical systems composed of a reversible part associated with a skew-symmetric operator J as Hamiltonian systems and a symmetric operator associated with some irreversible phenomena. We will show how to use results obtained on reversible systems to parametrize the boundary conditions such that the solution of the associated PDE is contractive. The theoretical results are applied to the example of a tubular reactor with first order chemical reaction. The obtained parametrization is compared with the classical Dankwert conditions.\u

STABILIZATION OF NON ISOTHERMAL CHEMICAL REACTORS USING TWO THERMODYNAMIC LYAPUNOV FUNCTIONS

The main goal of this paper is to introduce a link between the thermodynamics and control systems theory. More precisely, the paper focuses on Lyapunov based control of process systems, specially the non isothermal Continuous Stirred Tank Reactors in a thermodynamic framework, using either the jacket temperature or the inlet molar flow rate as the only control input. As soon as the constraint on the total mass is considered and the reaction kinetics is a Lipschitz continuous function with respect to the temperature, it shows that the stabilization of thermal solicitations reciprocally entails the one of matter using La Salle’s invariance principle. As a consequence, these control problems can be solved if the closed loop Lyapunov functions are chosen to be proportional to the thermal part or material part of the so called thermodynamic availability function. Some numerical simulations for a first order chemical reaction with multiple steady states are given to validate our theoretical developments. The performance of the obtained nonlinear controllers with regard to the conversion rate is also discussed.The main goal of this paper is to introduce a link between the thermodynamics and control systems theory. More precisely, the paper focuses on Lyapunov based control of process systems, specially the non isothermal Continuous Stirred Tank Reactors in a thermodynamic framework, using either the jacket temperature or the inlet molar flow rate as the only control input. As soon as the constraint on the total mass is considered and the reaction kinetics is a Lipschitz continuous function with respect to the temperature, it shows that the stabilization of thermal solicitations reciprocally entails the one of matter using La Salle’s invariance principle. As a consequence, these control problems can be solved if the closed loop Lyapunov functions are chosen to be proportional to the thermal part or material part of the so called thermodynamic availability function. Some numerical simulations for a first order chemical reaction with multiple steady states are given to validate our theoretical developments. The performance of the obtained nonlinear controllers with regard to the conversion rate is also discussed

Boundary triplets for skew-symmetric operators and the generation of strongly continuous semigroups

We give a self-contained and streamlined exposition of a generation theorem for C0-semigroups based on the method of boundary triplets. We apply this theorem to port-Hamiltonian systems where we discuss recent results appearing in stability and control theory. We give detailed proofs and require only a basic knowledge of operator and semigroup theory.Comment: 19 page

Dynamic modeling of the reactive twin-screw co-rotating extrusion process: experimental validation by using inlet glass fibers injection response and application to polymers degassing

International audienceIn this paper is described an original dynamic model of a reactive co-rotating twinscrew extrusion (TSE) process operated by the Rhodia company for the Nylon-66 degassing finishing step. In order to validate the model, dynamic experiments have been performed on a small-scale pilot plant. These experiments consist in a temporary injection of glass fibers at the inlet of the extruder after it has reached a given operating point. The outlet glass fibers mass fraction time variation is then measured. This experiment does not lead to the RTD measurement. As a matter of fact, due to the high quantity of glass fibers that is introduced, the behavior of the flow through the extruder is perturbed so that the glass fibers cannot be considered as an inert tracer. The dynamic model that we have published elsewhere (Choulak et al., Ind. Eng. Chem. Res., 2004, 43(23), 7373-7382) is adapted to take into account this nonlinear behavior of the extruder with respect to the glass fibers injection and is favorably compared to experimental results. The description of the degassing operation is also included in the model. The model allows simulations of the complete dynamic behavior of the process. When the steady state is reached, the good position of the degassing vent with respect to the partially and fully filled zones positions can also be checked, thus illustrating the way the model can be used for design purposes

Induction machine control using robust eigenstructure assignment

International audienceControl of induction machines is well known to be difficult owing to the fact that the models of induction motor are highly nonlinear and time variant. In this paper, we propose a very simple approach based on linear eigenstructure assignment and eigenstructure projection to design an efficient control law. This is the first step to a more global approach using multimodel eigenstructure assignment and self-scheduling. The controller, which is proposed here, is not scheduled (with the rotor speed) but still has correct performance over the entire operating range of the induction motor. A Kalman filter is used to estimate the flux vector. The simulation is based on the non-linear model and the application is made on an experimental bench. (c) 2005 Elsevier Ltd. All rights reserved