370146 Economic Model Predictive Control of Nonlinear Time-Delay Systems

Monday, November 17, 2014: 1:06 PM
404 - 405 (Hilton Atlanta)
Matthew Ellis1, Liangfeng Lao1 and Panagiotis D. Christofides2, (1)Chemical and Biomolecular Engineering, University of California, Los Angeles, Los Angeles, CA, (2)Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, Los Angeles, CA

Tightly integrating process economic optimization and process control has been a significant focus of research in the context of chemical process control for the last ten years. Recently, economic model predictive control (EMPC) has been proposed as a potential feedback control that merges economic optimization and control into a unified control methodology [1]-[4]. EMPC differs from standard tracking model predictive control in that it is formulated with a cost function or performance index that represents the process economics and not necessarily a quadratic cost function. Most of the theoretical work (e.g., rigorous closed-loop stability and performance analysis) on EMPC has been completed for systems described by finite-dimensional nonlinear ordinary differential equations (or finite-dimensional nonlinear discrete-time equations). While some work has been completed on formulating EMPC schemes for systems described by partial differential equations by reduced-order modeling (e.g., [4]), no work has been completed for applying EMPC to systems described by nonlinear difference differential equations (DDEs). To motivate the need for such work, it is important to point out that many chemical processes exhibit both nonlinearities due to complex reaction mechanisms and Arrhenius rate dependence and significant time delays due to transportation lags (e.g., flow through pipes), measurement delays, and control actuator delays. Moreover, to adequately capture both the delays and nonlinearities in the dynamic model used in the formulation of an EMPC a DDE model should be used.

In the present work, a two-mode EMPC is designed via Lyapunov-based techniques for systems described by nonlinear difference differential equations modeling state, control actuator, and measurement sensor delays (i.e., state, input, and output time-delays). First, the DDEs are written as an infinite-dimensional system in an appropriate Banach space and an explicit stabilizing controller is derived for system using a combination of Lyapunov-based and geometric techniques (e.g., [5]). Then, Lyapunov-based constraints are imposed in the EMPC problem which are based on the Lyapunov functional derived for the closed-loop DDE system under the explicit stabilizing controller. Under the first mode of operation, the EMPC may dictate a possibly time-varying operating policy, while under the second mode of operation, the computed input trajectory forces convergence of the closed-loop state to the desired set-point. Closed-loop stability under the proposed EMPC scheme is rigorously analyzed and conditions where closed-loop stability in the sense of boundedness of the closed-loop state trajectory (mode 1 operation of the EMPC) and convergence to the desired set-point (mode 2 operation of the EMPC) are given. Lastly, the EMPC scheme will be demonstrated using a chemical process example.

[1] Angeli D, Amrit R, Rawlings JB. On average performance and stability of economic model predictive control. IEEE Transactions on Automatic Control. 2012;57:1615-1626.
[2] Diehl M, Amrit R, Rawlings JB. A Lyapunov function for economic optimizing model predictive control. IEEE Transactions on Automatic Control. 2011;56:703-707.
[3] Huang R, Harinath E, Biegler LT. Lyapunov stability of economically oriented NMPC for cyclic processes. Journal of Process Control. 2011;21:501-509.
[4] Heidarinejad M, Liu J, Christofides PD. Economic model predictive control of nonlinear process systems using Lyapunov techniques. AIChE Journal. 2012;58:855-870.
[5] Lao L, Ellis M, Christofides PD. Economic model predictive control of transport-reaction processes. Industrial \& Engineering Chemistry Research, in press.
[6] Antoiades C, Christofides PD. Feedback control of nonlinear differential difference equation systems. Chemical Engineering Science. 1999;54:5677-5709.

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