Stabilisation of nonlinear chemical processes via dynamic power-shaping passivity-based control

Abstract

It is well known that energy-balancing passivity-based control is stymied by the presence of pervasive dissipation. To overcome this problem in electrical circuits, some authors have used power-shaping techniques, where stabilisation is achieved by shaping a function akin to power instead of energy. Some extensions of the techniques to general nonlinear systems, yielding static state-feedback control laws, have also been reported. In this article, we extend these techniques to dynamic feedback control and apply them to nonlinear chemical processes. The stability analysis is carried out using the shaped power function as Lyapunov function. The proposed technique is illustrated with two nonlinear chemical process examples.

Keywords:

• power-shaping control
• passivity
• dynamic feedback control
• nonlinear chemical processes

Acknowledgements

This work is supported by the National Creative Research Groups Science Foundation of China (NCRGSFC: 60721062) and National Basic Research Program of China (973 Program 2007CB714006).

Notes

Notes

1. We refer the reader to Spivak (1990) for the Poincaré lemma in the differential form language, and to the recent work Yap 2009) for an inductive development using PDEs.

2. With some abuse of notation the symbols χ and (x, ξ) are sometimes mixed in the functions.