(149f) Dynamic Analysis and Model Predictive Control of a Biochemical Reactor Under Delayed Uncertain Measurement and Multi-Rate Actuation/Sampling | AIChE

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(149f) Dynamic Analysis and Model Predictive Control of a Biochemical Reactor Under Delayed Uncertain Measurement and Multi-Rate Actuation/Sampling

Authors 

Ozorio Cassol, G. Sr. - Presenter, University of Alberta
Dubljevic, S., University of Alberta
Different types of (bio)chemical processes are modeled by partial differential equations, generally known as distributed parameter systems. Axial dispersion reactors, separation columns, and the flow inside a pipeline are a few examples. In this contribution, a tubular biochemical reactor nonlinear model is initially considered. This dynamical model can describe a large class of bioprocesses, such as in wastewater treatment [1] or water treatment [2].

First, the possible existence of different equilibrium profiles is shown in the dynamic analysis of the non-linear model [3]. Then, the control and state estimation problems are considered for a linearized version of the system around a desired equilibrium profile. It is considered that the system is under output delay due to the necessary analysis that needs to be carried out in the output of a biochemical process. In the same line, the output is also considered to present measurement uncertainties. Furthermore, the system is considered multi-rate for the actuation and sampling times.

When it comes to the stabilization of distributed systems, the complexity associated with the infinite-dimensional nature of the system has been addressed with the application of different methodologies, for example, backstepping [4], the linear quadratic regulator [5], and inertial manifolds [6].

Here, we consider an extension of the model predictive control for linear systems developed in previous contributions [7, 8]. As the controller requires state feedback, a Kalman filter is developed for state reconstruction based on the delayed output [9]. Finally, the difference in the actuation and sampling time also needs to be considered in the controller design.

[1] O. Schoefs, D. Dochain, H. Fibrianto and J.P. Steyer. Modelling and identification of a partial differential equation model for an anaerobic wastewater treatment process. Proc. 10th World Congress on Anaero bic Digestion (AD10-2004), Montreal, Canada, 2004.

[2] S. Bourrel, D. Dochain, J.P. Babary and I. Queinnec. Modelling, iden tification and control of a denitrifying biofilter. Journal of Process Control, 10, 73-91, 2000.

[3] S. Bourrel, D. Dochain. Stability analysis of two linear distributed parameter bioprocess models. Mathematical and Computer Modelling of Dynamical Systems, 6(3), 267-281, 2000 .
[4] M. Krstic and A. Smyshlyaev, Boundary Control of PDEs: A course on backstepping designs. Philadelphia: SIAM, 2008.
[5] I. Aksikas, J. J. Winkin, and D. Dochain, “Optimal LQ-feedback regulation of a nonisothermal plug flow reactor model by spectral factorization,” IEEE Transactions on Automatic Control, vol. 52, no. 7, pp. 1179–1193, 2007.
[6] P. Christofides and P. Daoutidis, “Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds,” Journal of Mathematical Analysis and Applications, vol. 216, no. 2, pp. 398–420, 1997.
[7] K. Muske and J. Rawlings. Model predictive control with linear models. AIChE Journal. 1993; 39(2):262–287.
[8] Q. Xu and S. Dubljevic. Linear Model Predictive Control for Transport-Reaction Processes. AIChE Journal. 2017;63 (7).
[9] J. Xie, Q. Xu, D. Ni and S. Dubljevic. Observer and filter design for linear transport-reaction systems, European Journal of Control, 2019;

Topics 

Process Automation & Control
Biochemical Processes

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