Boussad Hamroun

Control by Interconnection and Energy-Shaping Methods of Port Hamiltonian Models. Application to the Shallow Water Equations

In this paper a control algorithm for the reduced port-Controlled Hamiltonian model (PCH) of the shallow water equations (PDEs) is developed. This control is developed using the Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) method on the reduced PCH model without the natural dissipation. It allows to assign desired structure and energy function to the closed loop system. The same control law is then derived using an energy shaping method based on Casimirs invariants, associated with a particular conservative interconnection between the boundary variables. This gives a physical interpretation for the designed controller. Finally, a stability analysis of the dissipative system in closed loop with the designed control is done using LaSalles invariance principle. Simulation results made on a micro-channel simulator are presented, showing the effectiveness of the control law.

Port-based modelling and geometric reduction for open channel irrigation systems

A port based model for the water flows and levels dynamics in open channel systems is derived. It is structured into dissipative and conservative sub-systems related through a symplectic geometric structure which expresses instantaneous power conservation. This model is equivalent to the classical Saint-Venant equations (nonlinear PDEs also called shallow water equations) but trivially exhibits some interesting properties (passivity, stability, stored energy, entropy production) which may be useful for analysis or control purposes. Therefore the paper then focuses on a reduction scheme which preserves the geometric symplectic structure of the infinite dimensional model. This reduction scheme leads to a reduced port-controlled Hamiltonian finite-dimensional system which is compared with the infinite dimensional model and with other classical reduced models both in terms of spectral and energetic properties.

Lattice Boltzmann Model for the Simulation of Flows in Open Channels with Application to Flows in a Submerged Sluice Gate

Numerical simulations of free-surface flows are important to provide a prediction tool for the optimal management of irrigation canals. Here, we consider an alternative to solving the shallow-water equations. We propose a free-surface model in which the vertical component of the water current is fully resolved. We believe that such a detailed description can be useful to model the flow around gates or in other situations where the vertical structure of the flow will be important such as in the case of sediment transport and deposition. Our approach is based on a two-fluid lattice Boltzmann model. We compare the predictions obtained from numerical simulation and experiments performed on a laboratory microcanal facility.

Passivity based control of a reduced port-controlled hamiltonian model for the shallow water equations

In this paper an extension of an existing reduced port-controlled hamiltonian (PCH) model for the shallow water equations (PDEs) is first proposed. It aims at a new definition for the passive boundary port-variables which allows the application of a passivity-based approach to control the water flows and levels profiles in irrigation channel reaches. Then a control law based on the Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) methodology is developed. It allows to assign desired structure and energy function to the closed loop system. Simulation results made on a micro-channel simulator are presented, showing the effectiveness of the control law.

Port Hamiltonian System in Descriptor Form for Balanced Reduction: Application to a Nanotweezer

Abstract This paper proposes a method of balanced model reduction for constrained linear port Hamiltonian systems. Constrained linear port Hamiltonian systems are first written in a canonical descriptor form such that the Hamiltonian structure is preserved. The computations of the controllability and observability Gramians are then used to derive the balanced port Hamiltonian representation of the system. The method of flow constraint is applied to reduce the system. Finally, numerical simulations for the reduction of a micro mechanical actuator model is given to illustrate the effectiveness of the proposed method.

Distributed port-Hamiltonian modelling for irreversible processes

ABSTRACT Infinite-dimensional port-Hamiltonian representation of irreversible processes accounting for the thermal energy domain is presented. Two examples are studied: the transmission line and a non-isothermal reaction diffusion process. The proposed approach uses thermodynamic variables in order to define the infinite-dimensional interconnection structure linking the different phenomena. A presentation is given for one-dimensional spatial domain. For the transmission line, the Hamiltonian is the total energy and for the reaction diffusion process it is the enthalpy or the opposite of entropy.

Reduced order LQG control design for port Hamiltonian systems

The aim of this paper is to propose a reduced order control design method for large scale port Hamiltonian systems. To this end, a structure preserving reduction method and a modified LQG control design are combined to derive a reduced order model suitable for control purposes. We first recall the structure preserving reduction method for port Hamiltonian systems called effort constraint method and characterize the error bound associated to this reduction method. We then give sufficient conditions for non-standard LQG design which allow to design a passive controller equivalent to the control by interconnection of port Hamiltonian systems. This LQG method allows to define an LQG balanced realization by computing the LQG Gramians, the effort-constraint method is then used to derive a reduced order port Hamiltonian system and to design a reduced order passive LQG controller. Finally, the method is illustrated in simulation on a mass–spring–damper system. The performances of the reduced order controller are compared to the results obtained with a full order passive LQG controller.

Hybrid Modeling of Phase Transition for Evaporators and Condensers in Chillers

Abstract A novel hybrid dynamic model for two-phase heat exchangers is described in this paper. This model is developed for dynamic modeling of chillers and heat pumps. It permits to represent over time the spatial distribution of the state variables such as the mass fraction, the mass density, the temperature and the pressure. A switching procedure between different regimes based on a phase stability test is applied to ensure the continuity of the system evolution. This switching is performed by matrix operations, which permit to achieve a global and very compact representation of the system. The manipulated matrices are analytically determined from a thermodynamic model of the refrigerant based on an equation of state. A simulation program is developed using the Matlab software. Simulation tests with step-type inputs are provided, which show the relevance of the model as well as its high flexibility since one can switch automatically from an evaporation situation to a condensation situation and vice-versa.

Availability based Stabilization of Tubular Chemical Reactors

Abstract This paper is concerned with the stabilization of tubular reactors by using the second law of Thermodynamics. The thermodynamic availability function is used as a Lyapunov function for the practical derivation of distributed control laws for the stabilization around a stationary profile of a fixed bed reactor. No assumption is made on the linearity of phenomenological law as for linear irreversible thermodynamics neither on the passivity of the considered system.

Energy shaping based control for open irrigation channel using a reduced port hamiltonian model

We present in this paper a control algorithm for the open irrigation channel using an obtained reduced port hamiltonian model of shallow water equations. This control is designed using the Casimirs invariant based energy shaping method associated with a particular conservative interconnection between the boundary variables. Some experimental results obtained on a micro canal show the effectiveness of the control.