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

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.

[1]  Sten Bay Jørgensen,et al.  Nonlinear analysis and control of a continuous fermentation process , 2002 .

[2]  Romeo Ortega,et al.  Putting energy back in control , 2001 .

[3]  Arjan van der Schaft,et al.  Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems , 2002, Autom..

[4]  C. Kravaris,et al.  Robust nonlinear state feedback under structured uncertainty , 1988 .

[5]  Alessandro Astolfi,et al.  Dynamic extension is unnecessary for stabilization via interconnection and damping assignment passivity-based control , 2009, Syst. Control. Lett..

[6]  Daniel Sbarbaro,et al.  Corrigendum to “On the control of non-linear processes: An IDA-PBC approach” (H. Ramírez et al., Journal of Process Control 19 (1) (2009) 405–414) , 2010 .

[7]  Denis Dochain,et al.  Analysis and control of the exothermic continuous stirred tank reactor: the power-shaping approach , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[8]  M. Spivak.  A comprehensive introduction to differential geometry , 1979 .

[9]  Dimitri Jeltsema,et al.  An Energy-Balancing Perspective of Interconnection and Damping Assignment Control of Nonlinear Systems , 2003 .

[10]  Wei Lin,et al.  Global asymptotic stabilization of general nonlinear systems with stable free dynamics via passivity and bounded feedback , 1996, Autom..

[11]  Romeo Ortega,et al.  On the control of non-linear processes: An IDA–PBC approach , 2009 .

[12]  Jacquelien M. A. Scherpen,et al.  Power-based control of physical systems , 2010, Autom..

[13]  Jacquelien M. A. Scherpen,et al.  Power shaping: a new paradigm for stabilization of nonlinear RLC circuits , 2003, IEEE Trans. Autom. Control..

[14]  Romeo Ortega,et al.  Passivity-based Control of Euler-Lagrange Systems , 1998 .

[15]  Arjan van der Schaft,et al.  Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems , 2008, IEEE Transactions on Automatic Control.

[16]  Jacquelien M. A. Scherpen,et al.  An energy-balancing perspective of interconnection and damping assignment control of nonlinear systems , 2003, Autom..

[17]  Dimitri Jeltsema,et al.  Power Shaping Control of Nonlinear Systems: A Benchmark Example , 2006 .

[18]  Shirley Llamado Yap,et al.  The Poincaré Lemma and an Elementary Construction of Vector Potentials , 2009, Am. Math. Mon..

[19]  Romeo Ortega,et al.  Adaptive motion control of rigid robots: a tutorial , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[20]  Peter L. Lee,et al.  Process Control: The Passive Systems Approach , 2010 .

[21]  J.M.A. Scherpen,et al.  Multidomain modeling of nonlinear networks and systems , 2009, IEEE Control Systems.

[22]  J. K. Moser,et al.  A theory of nonlinear networks. I , 1964 .

[23]  A. Isidori,et al.  Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems , 1991 .