Lyapunov-based control of non isothermal continuous stirred tank reactors using irreversible thermodynamics.

International audienceIn this paper, the thermodynamic availability function is used as a Lyapunov function for the practical derivation of non linear control laws for the stabilization of a large class of CSTRs far from the equilibrium. The strict convexity of the availability function is guaranteed as long as one of the extensive variables is fixed. In this study, we consider liquid mixture with constant volume, the constraint on the volume being insured by perfect regulation of the outlet flow of the CSTR. Several control laws are then derived which insure global asymptotic stability, exponential stability or simple asymptotic stability. These control laws are discussed regarding the magnitude and the dynamic variations of the control variable. It is shown that the availability function can be split into two parts: one corresponds to the mixing term and depends on mole numbers only and the other depends on both temperature and mole numbers. The two parts are positive and the second one is chosen as a new Lyapunov function. The use of this new Lyapunov function insures smooth variations of the control variable. An exothermal, first order chemical reaction leading to multiple steady-state operating points of the CSTR illustrates the proposed theory

Control and optimization of a three-phase catalytic slurry intensified continuous chemical reactor

International audienceIntensified continuous mini-reactors working in high pressure and temperature conditions are particularly effective at coping with mass transfer limitations during three-phase catalytic reactions. They are highly non-linear, multivariable systems and behave differently from conventional batch, fed-batch or continuous non-intensified reactors. In this paper, the optimization and control of this new process are presented using a two-layer approach consisting of a hierarchical control structure with an optimization layer which calculates the set points for an advanced controller. The latter is based on the concavity of the entropy function and the use of thermodynamic availability as a Lyapunov function. The three-phase catalytic o-cresol hydrogenation performed under high pressure and temperature in a small-scale pilot of the RAPTOR® reactor designed by the French company AETGROUP SAS, is taken as a representative test example to illustrate the strategy. The performance of the control structure is illustrated by simulation

Passivity based control of irreversible port Hamiltonian Systems.

International audienceThe frameworks of thermodynamic availability function and irreversible port Hamiltonian systems are used to derive passivity based control strategies for irreversible thermodynamic systems. An energy based availability function is defined using as generating function the internal energy. This is a variation with respect to previous works where the total entropy usually corresponds to the generating function. The specific structure of irreversible port-Hamiltonian systems then permits to elegantly derive stability conditions for open and closed thermodynamic systems. The results are illustrated on two classical thermodynamic examples: The heat exchanger and the continuous stirred tank reactor

Modelling and control of multi-energy systems : An irreversible port-Hamiltonian approach.

International audienceIn recent work a class of quasi port Hamiltonian system expressing the first and second principle of thermodynamics as a structural property has been defined : Irreversible port-Hamiltonian system. These systems are very much like port-Hamiltonian systems but differ in that their structure matrices are modulated by a non-linear function that precisely expresses the irreversibility of the system. In a first instance irreversible port-Hamiltonian systems are extended to encompass coupled mechanical and thermodynamical systems, leading to the definition of reversible-irreversible port Hamiltonian systems. In a second instance, the formalism is used to suggest a class of passivity based controllers for thermodynamic systems based on interconnection and Casimir functions. However, the extension of the Casimir method to irreversible port-Hamiltonian systems is not so straightforward due to the "interconnection obstacle". The heat exchanger, a gas-piston system and the non-isothermal CSTR are used to illustrate the formalism

The Port Hamiltonian approach to modeling and control of Continuous Stirred Tank Reactors.

International audienceThis paper proposes a thermodynamical pseudo Hamiltonian formulation of Continuous Stirred Tank Reactor model in which takes place some chemical reaction. This is done both in the isothermal and non isothermal cases. It is shown that the Gibbs free energy and the opposite of entropy can be chosen as Hamiltonian function respectively. For the non isothermal case, the so called Interconnection and Damping Assignment Passivity Based Control method is applied to stabilize the system at a desired state. For this general reaction scheme, the control problem is shown to be easy to solve as soon as the closed loop Hamiltonian function is chosen to be proportional to the so called thermodynamic availability function. Simulation results based on a simple first order reaction and operating conditions leading to multiple steady states of the CSTR are given to validate the proposed control design procedure

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

Irreversible port-Hamiltonian systems : a general formulation of irreversible processes with application to the CSTR.

International audienceIn this paper we suggest a class of quasi-port Hamiltonian systems called Irreversible port Hamiltonian Systems, that expresses simultaneously the first and second principle of thermodynamics as a structural property. These quasi-port Hamiltonian systems are defined with respect to a structure matrix and a modulating function which depends on the thermodynamic relation between state and co-state variables of the system. This modulating function itself is the product of some positive function and the Poisson bracket of the entropy and the energy function. This construction guarantees that the Hamiltonian function is a conserved quantity and simultaneously that the entropy function satisfies a balance equation containing an irreversible entropy creation term. In the second part of the paper, we suggest a lift of the Irreversible Port Hamiltonian Systems to control contact systems defined on the Thermodynamic Phase Space which is canonically endowed with a contact structure associated with Gibbs' relation. For this class of systems we have suggested a lift which avoids any singularity of the contact Hamiltonian function and defines a control contact system on the complete Thermodynamic Phase Space, in contrast to the previously suggested lifts of such systems. Finally we derive the formulation of the balance equations of a CSTR model as an Irreversible Port Hamiltonian System and give two alternative lifts of the CSTR model to a control contact system defined on the complete Thermodynamic Phase Space

A systematic approach to plant-wide control based on thermodynamics

Abstract In this work, a systematic approach to plant-wide control design is proposed. The method combines ingredients from process networks, thermodynamics and systems theory to derive robust decentralized controllers that will ensure complete plant stability. As a first step, the considered process system is decomposed into abstract mass and energy inventory networks. In this framework, conceptual inventory control loops are then designed for the mass and energy layers to guarantee that the states of the plant, both in terms of extensive and intensive properties, will converge to a compact convex region defined by constant inventories. This result by itself does not ensure the convergence of intensive variables to a desired operation point as complex dynamic phenomena such as multiplicities may appear in the invariant set. In order to avoid these phenomena, thermodynamics naturally provides the designer, in these convex regions, with a legitimate storage or Lyapunov function candidate, the entropy, that can be employed to ensure global stability. Based on this, the control structure design procedure is completed with the realization of the conceptual inventory and intensive variable control loops over the available degrees of freedom in the system. To that purpose, both PI and feedback linearization control are employed. The different aspects of the proposed methodology will be illustrated on a non-isothermal chemical reaction network

Effect of Model Plant Mismatch in Model Predictive Controller Performance: Continuous Stirred Tank Reactor

Plant model is one of the important aspects in the design and implementation of Model Predictive Controller (MPC). The performance of MPC depends on the accuracy and quality of plant model. However, dynamic behaviour of a plant may change with time. Hence, plant model that are used for the design will no longer represent the plant current state after some time. In this dissertation, the effect of model plant mismatch on MPC performance will be shown by the researcher. During the conduct of this research, the researcher has developed a non-linear CSTR model by using SIMULINK. Manipulated variable and controlled variable for the CSTR model has been set by the researcher. Besides that, the researcher developed 3 different linear transfer function model using 3 different ranges. By using this 3 different transfer function model, the researcher designed 3 different MPC. The researcher has tested the plant model with 2 different tests. First, to understand the dynamic model of this CSTR, the researcher has done an open loop test to this CSTR model by adding few percentages of increment in step change to the plant input. The changes in controlled variable inside the reactor is then measured and analyzed. For the second test, the researcher done a closed loop test to measure the performance of MPC between the accurate plant models and mismatch plant models. This test is done by using MPC with plant model to control to a limit which is out of its range to represent the mismatch plant model. In the open loop test, when step change is added to the plant input, all output changes from its set point which clearly shows the non-linearity behaviour of the plant. For the MPC performance test, when mismatch is added, the controller becomes less stable and it took a longer time to reach the steady state and the new set point

Control of input-output contact systems.

International audienceControl input-output contact systems are the representation of open irreversible Thermodynamic systems whose geometric structure is defined by Gibbs' relation. These systems are called conservative if furthermore they leave invariant a particular Legendre submanifold defining their thermodynamic properties. In this paper we address the stabilization of controlled input-output contact systems. Firstly it is shown that it is not possible to achieve stability on the complete Thermodynamic Phase Space. As a consequence, the stabilization is addressed on some invariant Legendre submanifold of the closed-loop system. For structure preserving feedback of input-output contact systems, i.e., for the class of feedback that renders the closedloop system again a contact system, the closed-loop invariant Legendre submanifolds have been characterized. The stability of the closed-loop system has then been proved using Lyapunov's second method. The results are illustrated on the classical thermodynamic process of heat transfer between two compartments and an exterior control