Audrey Favache

Brief paper: Power-shaping control of reaction systems: The CSTR case

Power-shaping control is a recent approach for the control of nonlinear systems based on the physics of the dynamical system. It rests on the formulation of the dynamics in the Brayton-Moser form. One of the main obstacles for using the power-shaping approach is to write the dynamics in the required form, since a partial differential equation system submitted to sign constraints has to be solved. This work comes within the framework of control design approaches that could possibly generate a closer link between the notions of energy that are specific to reaction systems as derived from thermodynamics concepts, and the dynamic system stability theory. The objective of this paper is to address the design of power-shaping control to reaction systems, and more particularly the step of solving the partial differential equation system. In order to illustrate the approach, we have selected the classical yet complex continuous stirred tank reactor (CSTR) as a case study. We show how using the power-shaping approach leads to a global Lyapunov function for the unforced exothermic CSTR. This Lyapunov function is then reshaped by means of a controller in order to stabilize the process at a desired temperature.

Some Properties of Conservative Port Contact Systems

The dynamics of open irreversible thermodynamic systems, that is systems including both the balance equation of the energy and the entropy, has been formulated as contact vector fields with generating functions depending on some external (control) variable and called conservative port contact systems. In this paper we relate the dynamical properties of these systems (equilibrium points, asymptotic stability) to properties of the generating functions (the contact Hamiltonian functions). We show that the equilibrium points of the system satisfy certain conditions involving the contact Hamiltonian function. We also consider Lyapunovs first theorem to emphasize a stability criterion for the equilibrium points in terms of this contact Hamiltonian function and relate it to some thermodynamical properties. These results are then related to the physical phenomena that are taking place in the system.

Power-shaping control: Writing the system dynamics into the Brayton–Moser form

Power-shaping control is an extension of energy-balancing passivity-based control that is based on a particular form of the dynamics, the Brayton–Moser form. One of the main difficulties in this control approach is to write the dynamics in the suitable form since this requires the solution of a partial differential equation (PDE) system with an additional sign constraint. Here a general methodology is described for solving this partial differential equation system. The set of all solutions to the PDE system is given as the solution of a linear equation system. Furthermore a necessary condition is given so that a solution of the linear system which meets the sign condition exists. This methodology is illustrated on the case of a chemical reactor, where the physical knowledge of the system is used to find a suitable solution.

Power-Shaping Control of an Exothermic Continuous Stirred Tank Reactor (CSTR)

Abstract Abstract The exothermic continuous stirred tank reactor (CSTR) is a classical yet complex case study of nonlinear dynamical systems. Power-shaping control is a recent approach for the control of nonlinear systems based on the physics of the dynamical system. In this paper we present a general methodology to apply the power-shaping control approach to the exothermic CSTR study case. It results in a global Lyapunov function for the exothermic CSTR. This Lyapunov function is then reshaped by the means of a controller in order to stabilize the process at a desired temperature. Some considerations on the local and global convergence to the desired state are presented.

Analysis and control of the exothermic continuous stirred tank reactor: the power-shaping approach

The exothermic continuous stirred tank reactor (CSTR) is a classical yet complex case study of nonlinear dynamical systems. Power-shaping control is a recent approach for the control of nonlinear systems based on the physics of the dynamical system. In this paper we apply the power-shaping control approach to the exothermic CSTR study case. A global Lyapunov function is derived for the open-loop exothermic CSTR. This Lyapunov function is then reshaped by the means of a controller in order to stabilize the process at a desired temperature. Some considerations on the local and global convergence to the desired state are presented.

Towards power-shaping control of the CSTR: from thermodynamics to the Brayton-Moser formulation of the dynamics

Abstract The non-isothermal continuous stirred tank reactor (CSTR) is a classical yet complex case study of nonlinear dynamical systems. Power-shaping control is a recent approach for the control of nonlinear systems based on the physics of the dynamical system and it rests on the formulation of the dynamics in the Brayton-Moser form. The Brayton-Moser formulation of the non-isothermal continuous stirred tank reactor is investigated based on physical considerations on the system.

A PDE approach to the derivation of the Brayton-Moser form for power-shaping control

Power-shaping control is an extension of energy-balancing passivity-based control based on a particular form of the dynamics, the Brayton-Moser form. One of the main difficulties in this approach is to write the dynamics in the suitable form since it requires the solution of a partial differential equation (PDE) system with an additional sign constraint. Here a general methodology is described for solving this partial differential equation system. The set of all solutions to the PDE system is given as the solution of a linear equation system. A necessary condition is given so that a solution of the linear system which meets the sign condition exists. This methodology is illustrated on a chemical reactor example, where the physical knowledge of the system is used to find a suitable solution.