Modelling and controller design for distributed parameter systems via residence time distribution

Abstract

For chemical reactors with non-linear fluid dynamics, a linear model realisation is proposed. The inputs are the ingoing concentration of a certain component in the fluid, and the reaction rate. The output is the outgoing concentration. The realisation makes use of a first-order reaction equation, and the residence time distribution of the fluid particles inside the reactor. Also dead time is incorporated in the modelling. The method is tested on two non-linear models for which the residence time distributions are known analytically. The first model is a series of mixed tanks, and it is shown by simulation that the method gives an accurate approximation of the original model. The second model is a UV disinfection reactor, which has a dead time. For this model, the residence time distribution is first fitted by a form that is suitable for our realisation method. Simulations show that for realistic disturbances a high-performance linear controller can be designed. After that, the residence time distribution of a real life UV reactor (for which we have no model) is fitted by a suitable form. The fit is of the same quality as for the UV reactor model. This indicates that also for the real life UV reactor a high-performance controller can be designed.

Keywords:

• control design
• UV disinfection
• residence time distribution

Acknowledgements

This work was supported by the Technology Foundation STW under project number WWI.6345. We are grateful to Dr Nico Enthoven of Priva BV for providing us with experimental test results.