(207d) Moving Horizon Estimation for Diffusion-Transport-Reaction Systems: A Late-Lumping Approach | AIChE

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(207d) Moving Horizon Estimation for Diffusion-Transport-Reaction Systems: A Late-Lumping Approach

Authors 

Xie, J. - Presenter, University of Alberta
Huang, B., University of Alberta
Dubljevic, S., University of Alberta
Diffusion-transport-reaction systems are widely present in chemical engineering practice, e.g., chemical tubular reactors, fluid transportation systems, heat transfer processes, and so on [1-2]. These types of systems, often known as distributed parameter systems (DPS), naturally have spatial-temporal dynamics, and the corresponding modeling, estimation, control, and regulation are theoretically challenging and practically complex. Based on a reasonable understanding of the first principle behind such systems, such as mass, momentum, and energy balance laws, their governing equations can be derived in the form of partial differential equations (PDE) or partial integral differential equations (PIDE). Compared to lumped parameter systems modeled by ordinary differential equations (ODE), the state and output estimation of DPS are often more demanding since spatially distributed sensors are prohibitively expensive and sometimes even impossible to install (e.g., implementing a spatially distributed concentration analyzer when a chemical tubular reactor is installed and being operated). Furthermore, the infinite-dimensionality nature of DPS makes the corresponding estimator algorithms design mathematically difficult.

The fundamental state reconstruction and estimation techniques can be mainly traced back to two categories, namely, the Luenberger observer and Kalman filter, depending on that if the considered underlying dynamical model is deterministic or stochastic [3]. However, in practice, the ubiquitous physical constraints in chemical engineering processes make the classic Luenberger observer and Kalman filter not directly applicable to state estimation. On the other hand, moving horizon estimation, as an optimization-based technique, has been actively studied and applied over the past decades, especially for lumped parameter systems [4-6]. Technically, direct extension of MHE to DPS is not straightforward due to the spatial-temporal dynamics nature of DPS. Most existing works that addressed MHE design for DPS are based on spatial discretization or order reduction, which belongs to the early lumping design and might face stability inconsistency issues when implementing the estimation results back to the original distributed parameter system. To address this issue, we propose a late lumping approach for the MHE design of state and output estimation of diffusion-transport-reaction systems. The proposed design relies on a novel model time-discretization approach which does not perform any spatial discretization nor model-order reduction [7-8]. In this presentation, we show that the important system properties including approximate observability are invariant under the transformation. Based on that, the optimality and stability analyses of the proposed design are presented. Finally, we provide several typical diffusion-transport-reaction examples to verify the effectiveness and applicability of the proposed design. The proposed theoretical results can be applicable to other classes of distributed parameter systems in chemical, mechanical, and energy systems.

References

[1]. W. H. Ray, Advanced Process Control, McGraw-Hill, New York 1981.

[2]. Christofides, P.D. and Chow, J., 2002. Nonlinear and robust control of PDE systems: Methods and applications to transport-reaction processes. Appl. Mech. Rev., 55(2), pp.B29-B30.

[3]. D. Simon, 2006. Optimal state estimation: Kalman, H infinity, and nonlinear approaches. John Wiley & Sons.

[4]. C. V. Rao, J. B. Rawlings, and J. H. Lee, Constrained linear state estimation—A moving horizon approach, Automatica, vol. 37, no. 10, 614 pp. 1619-1628, 2001.

[5]. C. V. Rao, J. B. Rawlings, and D. Q. Mayne, Constrained state estimation for nonlinear discrete-time systems: Stability and moving horizon approximations, IEEE Trans. Autom. Control, vol. 48, no. 2, pp. 246-258, 618 Feb. 2003.

[6]. A. Alessandri, M. Baglietto, and G. Battistelli, Moving-horizon state estimation for nonlinear discrete-time systems: New stability results and approximation schemes, Automatica, vol. 44, no. 7, pp. 1753-1765, 2008.

[7]. V. Havu and J. Malinen, The Cayley transform as a time discretization 640 scheme, Numer. Funct. Anal. Opt., vol. 28, no. 7-8, pp. 825-851, 2007.

[8]. J. Xie, J.P. Humaloja, C.R. Koch, and S. Dubljevic, 2022. Constrained Receding Horizon Output Estimation of Linear Distributed Parameter Systems. IEEE Trans. Autom. Control. 1-8.

Topics 

Process Automation & Control
Transport Phenomena
Energy

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