(613b) Economic Model Predictive Control of Transport-Reaction Processes

Recently, economic model predictive control (EMPC) has gained popularity within the chemical process control community because of its unique ability to merge dynamic economic optimization and control of chemical processes. Several theoretical results on EMPC [1]-[3] as well as numerous applications of EMPC [4]-[6] have been presented. However, no work has been done the application of EMPC to partial differential equation (PDE) systems arising in the modeling of transport-reaction processes even though they are prominent within chemical process industries.  Transport-reaction processes processes are typically modeled by quasi-linear parabolic PDEs whose spatial differential operators are typically characterized by a spectrum that can be partitioned into finite (possibly unstable) slow part and an infinite dimensional stable fast complement, thereby implying the presence of low-dimensional dominant dynamic behavior in parabolic PDE systems.

This work focuses on the development of economic model predictive control (EMPC) systems for transport-reaction processes described by quasi-linear parabolic PDEs and their application to a non-isothermal tubular reactor where a second-order chemical reaction takes place. The tubular reactor is modeled by two nonlinear parabolic PDEs. Galerkin's method is used to derive finite-dimensional systems that capture the dominant dynamics of the parabolic PDEs which are subsequently used for the EMPC design. The EMPC formulation uses the integral of the reaction rate along the length of the reactor as an economic cost function subject to constraints on the control action and states over an operation period. Closed-loop simulations are conducted of a low-order EMPC system, formulated with a constraint on the available reactant material over each operation period, applied to a high-order discretization of the PDEs and of a high-order EMPC system formulated with a specific state constraint and with the constraint on the available reactant material. Simulation results demonstrate that the EMPC operates the process in a time-varying fashion and improves the economic cost over steady-state operation using the same amount of reactant material over a fixed period of operation, as well as meeting state constraints. Furthermore, an output feedback implementation of the proposed EMPC schemes will also be presented.

References:

1. Diehl M, Amrit R, Rawlings JB. A Lyapunov function for economic optimizing model predictive control. IEEE Transactions on Automatic Control. 2011;56:703-707.
2. Huang R, Harinath E, Biegler LT. Lyapunov stability of economically oriented NMPC for cyclic processes. Journal of Process Control. 2011;21:501-509.
3. Heidarinejad M, Liu J, Christofides PD. State estimation-based economic model predictive control of nonlinear systems. Systems & Control Letters. 2012;61:926-935.
4. Lao L, Ellis M, Christofides PD. Economic model predictive control of transport-reaction processes. Industrial & Engineering Chemistry Research. submitted.
5. Idris EAN, Engell S. Economics-based NMPC strategies for the operation and control of a continuous catalytic distillation process. Journal of Process Control. 2012;22:1832-1843.
6. Ma J, Qin J, Salsbury T, Xu P. Demand reduction in building energy systems based on economic model predictive control. Chemical Engineering Science. 2012;67:92-100.