(557c) Application of a Lyapunov-Based Nonlinear Controller to a Reactor with Highly Exothermic Reactions

Keywords - Nonlinear Control, Robust Control, Lyapunov Theory, Chemical reactors, Experimental results

This work examines improved methods of controlling a class of chemical reactors in which a highly exothermic reaction takes place, and gives relevance to the controller's experimental performance in a real application equivalent to what is encountered in industry. The control objective is to maintain the temperature inside the reactor by manipulating two variables. Several options are available; in this work, we consider as controls the cooling supplied by the jacket and the inlet concentration of one reactant (or, alternatively, the concentration of a homogenous catalyst or promoter of the flow rate of a diluent). These variables are most easily adjusted in the experimental set-up used to test the performance of the Lyapunov-based nonlinear robust controller developed previously [1 and 2].

Making use of Lyapunov theory it is possible to prove the capability of a simple mathematical algorithm in globally stabilising a closed loop chemical reactor system where a strongly exothermic reaction takes place. The mathematical algorithm can be interpreted as an integrator of the error between the set-point and the actual value of the controlled variable. Moreover, a feature to explicitly deal with input constraints has been added to cope with discontinuous nonlinearities [3], which are present in all chemical processes. The resulting regulator (eq. 1) is non-model based, therefore robust against poor knowledge of the system parameters (only used for simulation purposes), and it only makes use of the output of the system avoiding the difficult-to-quantify controller performance degradation resulting from the introduction of a state observer.

                    eq. 1

I, O, and G stand for input, output and controller gain of the closed loop system respectively. The dot represents the variable derivative with respect to time. The superscripts min and max indicate the minimum and maximum values input can take and SP is the output set-point.

Lyapunov based controllers are attractive because of their recognised ability to globally stabilise a system. These controllers are mainly used when the model description is poor or inaccurate; model based solutions are preferred otherwise. A simple mathematical formulation, like the one employed in this work, was proposed [4, 5 and 6] to stabilise the temperature in a CSTR, in spite of uncertainties in the reaction kinetics and input saturations. The authors focused on an irreversible exothermic reaction taking place in a CSTR (control problem frequently found in the literature). In line with this work, [2] utilises the same type of nonlinear controller; extensively examines chemical reactors stability in the sense of Lyapunov and presents some experimental results for biological systems [7].

Recently, there has been an interest to incorporate several techniques for nonlinear systems in the same control strategy [8, 9, and 10]. The importance of Lyapunov-based strategies in global stabilisation of chemical systems is acknowledged and the benefits of optimality brought by model based control strategies are grasped. These control strategies also known as hybrid controllers, involve the switching between bounded control (essentially robust) and MPC in well-characterised regions of the state space (essentially optimal).

However it is difficult to find in the literature examples of experimental applications of the numerous different nonlinear controller proposals (and modified versions) to relevant real life situations. This work provides a solid set of experimental results, which were obtained in a pilot plant CSTR.

The PARSEX (PARtially Simulated EXothermic) reactor [11] is a pilot plant among the facilities in the laboratories at Imperial College, London. The reactor was designed to safely implementing and testing the performance of control algorithms like the one devised here. One great advantage of the PARSEX system is that proposed controllers can be implemented by testing them on a range of reaction systems, which are subject to potential control problems because of their exothermicity [12]. Among these are bulk polymerisations, hydrogenations, and partial oxidations. The experimental system was shown to be perfectly suitable for the generation of industrially similar results, as all measurements normally available in industry are also accessible when operating the PARSEX.

The experiments carried out include parameter uncertainty, namely changes in the heat transfer coefficient between the reactor and the jacket (simulation of scaling) and in the rate of reaction (simulation of catalyst deactivation). Work on disturbance rejection has also been executed.

The results obtained strongly suggest the ability of the proposed controller to globally stabilise the closed loop system and to achieve the desired set-point(s) as long as the control problem is feasible within the available bounded inputs. It is also clear from the parameter change experiments that the controller is robust.

References:

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