Passivity based control of reaction diffusion systems: Application to the vapor recovery reactor in carbothermic aluminum production

Stability analysis and passivity properties for a class of chemical reactors: Internal entropy production approach

“…For instance, Dammers and Tels (1974), based on the Brussels school of thermodynamics (Glansdorff and Prigogine, 1971), proposed a suitable potential function related to Prigogine's velocity potential to state a stability criteria in adiabatic stirred flow reactors, and Tarbell (1977) has proposed a Lyapunov function for continuous stirred tank reactor (CSTR) with a steady state near the equilibrium point, that resembled the thermodynamical entropy production function, while Georgakis (1986) suggested the use of extensive rather than intensive variables for process control purposes. More recently, Alonso, Ydstie and coworkers have explored this research area, that resulted in very insightful works on the control design of process ssystems (see e.g., Ydstie, 1996, 2001;Ydstie and Alonso, 1997;Coffey et al, 2000;Alonso et al, 2002;Ydstie, 2002;Balaji et al, 2010) to develop stabilizing mass and energy inventory controllers (Farschman et al, 1998) and to derive general structural stability conditions for chemical process networks (Hangos et al, 1999;Antelo et al, 2007;Baldea et al, 2013;Hioe et al, 2013). In addition to the concept of inventories, they have used a nonlinear extension of the curvature of the entropy function called availability as it has been proposed within the framework of passivity theory for processes.…”

“…In the particular case of reacting systems, continuous stirred tank reactors (CSTRs) have been the subject of a large number of stability and advanced control studies that can be taken into account by system theory: these systems are usually nonlinear and may exhibit multiple steady states. The features have been also taken into account to address the stability issue by using a number of thermodynamics based approaches (Dammers and Tels, 1974;Tarbell, 1977;Favache and Dochain, 2009;Balaji et al, 2010;Hoang et al, 2011bRamirez et al, 2013;; however, it appears that even for simple reactions, analysis and control issues using thermodynamic properties are still open problems . In this contribution, the stability an passivity properties of a class of chemical reactors are addressed by using the internal entropy production as a Lyapunov-candidate function when the reactor is isolated and as a storage function when the reactor interacts with the surroundings.…”