(247e) Port Hamiltonian Approach to Modeling and Control of Coupled Chemical Reactors

Models of chemical processes alter in details from ordinary differential equations (ODEs) for

the modeling of a Continuous Stirred Tank Reactor (CSTR) to a large set of Partial Differential

Equations (PDEs) for tubular reactors. Usually, models of chemical reactors are developed

on the basis of the conservation of extensive quantities, namely balance of energy, mass,

momentum and entropy. Due to the coupling between reaction and transport phenomena,

these models usually exhibit very complex behavior.

Port Hamiltonian framework has been widely applied in finite-dimensional processes in

chemical, electrical, mechanical domains, e.g. CSTR (see [1]). Recently, Port Hamiltonian

theory was developed and generalized to infinite-dimensional systems, see [2] [3] [4]. In [4], it

is shown that many infinite-dimensional processes in chemical and mechanical domains falls

into the category of Port Hamiltonian systems, e.g. most of hyperbolic systems. Moreover,

under the Port Hamiltonian framework, the energy-based control approaches are investigated.

In this work, we propose a Port Hamiltonian representation of a distributed reactor for

control purpose. The Hamiltonian representation provides powerful analysis methods (e.g.

for stability), and it enables the use of Lyapunov-stability theory and passivity-based control.

In particular, Hamiltonian representation is powerful when addressing the boundary control

of distributed parameter systems. We discuss how the state variables are chosen in such a

way that geometric properties of the model are emphasized. The chemical reactors given in

[5] are studied in this work and the presentation of the considered reactors is given for one

dimensional spatial domain by utilizing the internal energy.

 [1] Hoang, H., Couenne, F., Jallut, C., and Le Gorrec, Y. (2011). The port Hamiltonian approach

to modeling and control of Continuous Stirred Tank Reactors. Journal of Process Control,

21(10), 1449--1458.

[2] Villegas, J. A., Zwart, H., Gorrec, Y. L., and Maschke, B. (2009). Exponential stability of a

class of boundary control systems. Automatic Control, IEEE Transactions on, 54(1), 142--147.

[3] Wu, Y. (2015). Passivity preserving balanced reduction for the nite and innite dimensional

port Hamiltonian systems (Doctoral dissertation, Universit Claude Bernard-Lyon I).

[4] Jacob, B., and Zwart, H. (2012). Linear port-Hamiltonian systems on innite-dimensional

spaces (Vol. 223). Springer Science & Business Media.

[5] Ramkrishna, D., and Amundson, N. R. (1974). Stirred pots, tubular reactors, and self-adjoint

operators. Chemical Engineering Science, 29(6), 1353--1361.