(216h) Robust Nonlinear Model Predictive Control for a Reactor with Runaway Conditions

In this work, we introduce a nonlinear model predictive controller (NMPC) for the safe operation of an open-loop unstable process with nonlinear dynamics and grade transitions. The nominal stability of the reactor is achieved through inclusion of terminal region constraints and terminal penalty. However, a path constraint is added to provide a safe backed-off operation point that reduces chances for reactor runaway or extinction due to disturbances and also provides safe process transitions in case of changing operation points.

The case study considered is a reactor with an exothermic chemical reaction, which exhibits multiplicity behaviour, and as in some cases, the economically desirable operation point is usually one of the unstable steady states (Flores-Tlacuahuac, Biegler et al. 2005). This is due to the elevated temperature level and conversion in comparison to stable steady states at low temperatures. However, the stable steady states at high temperatures are unattractive because side or decomposition reactions can take place, which affect the final product quality negatively. Moreover, despite being economically optimal, the nonlinearities of the chemical reaction have pronounced effects at the unstable steady states and are prone to ignition/extinction behaviour leading to critical system states and long process transitions in case of occurrence or even plant shutdown. Therefore, control schemes need to stabilize the process at the unstable operation point, while being robust against disturbances by complying with safety margins so as to avoid both runaway and extinguishing of the reaction.

This presentation therefore covers the experimental validation of the proposed NMPC control scheme using a laboratory CSTR process. Because nonlinear dynamics and constraints can be directly addressed, NMPC is an attractive approach for this problem.

For the validation of the proposed NMPC approach, an experimental setup has been implemented which makes use of a mixed-reality approach to provide a feasible possibility of comprehensive control algorithm tests. Kershenbaum introduced a similar approach which showed a good approximation of real process behaviour (Kershenbaum 2000; Santos, Afonso et al. 2001). In this work, the first order chemical reaction is irreversible and the heat of reaction is transported over the reactor wall using a coolant recycle through the jacket. Before entering the jacket, a heat exchanger with fresh cooling water is used to manipulate the jacket makeup temperature. The mimicked reactor exhibits multiplicity behaviour with respect to the jacket inlet temperature, which results in two stable steady states and one unstable steady state. The latter one is the desired operation point because of a higher conversion with still negligible side reactions. However, the reactor exhibits runaway or extinction behaviour, once the coolant temperature deviates from the corresponding steady state value.

To stabilize the system at the unstable steady state, the optimal control problem is formulated as a quasi-infinite horizon control QIH-NMPC (Findeisen and Allgöwer 2003). Therein, the inherent stability property of the infeasible infinite horizon control scheme is adopted using both terminal region constraints and a terminal cost function (Mayne, Rawlings et al. 2000). However, for large deviations from the set-point (e.g. because of a set-point change), the terminal region may be unfeasible with a finite prediction horizon. In this case, the optimal solution may lead to unstable results because of the single shooting properties (Binder, Blank et al. 2001) resulting in runaway or reaction extinction. Therefore, a path constraint is introduced into the optimal control problem that consists of a dynamic version of a runaway/extinction limit (Berty, Berty et al. 1989). This constraint thereby limits the feasible trajectories to a space of safe dynamic operation that prevents the undesired behaviour. The solution of the optimal control problem is obtained using a sequential approach to parameterize the control vector over the prediction horizon. It is well known, that such a feasible path approach has single shooting properties and is sensitive for instability of the controlled system. This stems from the corresponding strong nonlinearities of the objective function for longer prediction horizons and the dependency of the initial guesses for the control vector (Ascher and Petzold 1998; Diehl, Bock et al. 2002; Zavala, Laird et al. 2008).

This work will cover the introduction of the proposed control algorithm and solution strategy of the optimal control problem. Experimental results will be presented to validate the approach and provide a comparison to common control schemes. Furthermore, within this scope, aspects of infeasibility (e.g. infeasible initial values) and performance of the solution of the optimal control problem will also be discussed.

References:

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Binder, T., C. Blank, et al. (2001). Introduction to Model Based Optimization of Chemical Processes on Moving Horizons. Online Optimization of Large Scale Systems: State of the Art. M. Grötschel, S. O. Krumke and J. Rambau. Heidelberg, Springer-Verlag Berlin: 295-340.

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Findeisen, R. and F. Allgöwer (2003). The quasi-infinite horizon approach to nonlinear model predictive control: 89-108.

Flores-Tlacuahuac, A., L. T. Biegler, et al. (2005). "Dynamic Optimization of HIPS Open-Loop Unstable Polymerization Reactors." Industrial \& Engineering Chemistry Research 44(8): 2659-2674.

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Santos, L. O., P. A. F. N. A. Afonso, et al. (2001). "On-line implementation of nonlinear MPC: an experimental case study." Control Engineering Practice 9(8): 847-857.

Zavala, V., C. Laird, et al. (2008). "Fast implementations and rigorous models: Can both be accommodated in NMPC?" International Journal of Robust and Nonlinear Control 18(8): 800-815.