A UNIFIED PORT-HAMILTONIAN APPROACH FOR MODELLING AND STABILIZING CONTROL OF ENGINEERING SYSTEMS

Ha Ngoc Hoang, Quyen Phuong Le, Thuan Chi Nguyen

Abstract


This work deals with systems whose dynamics are affine in the control input. Such dynamics are considered to be significantly differentially expressed in a canonical form, namely the quadratic (pseudo) port-Hamiltonian representation, in order to explore further some structural properties usable for the tracking-error passivity-based control design. Different kinds of linear and nonlinear engineering systems including an open isothermal homogeneous system and a continuous biochemical fermenter are used to illustrate the approach.

Keywords


Engineering systems, Quadratic port-Hamiltonian representation, Passivity, Tracking-error control.

Full Text:

PDF

References


H.K. Khalil, Nonlinear systems, Prentice Hall, Upper Saddle River, 3rd edition, 2002.

R. Ortega, A. Loría, P.J. Nicklasson, H. Sira – Ramírez, Passivity Passivity-based control of Euler-Lagrange systems Mechanical, electrical and electromechanical applications Springer London, 1st edition, 1998.

F. Dörfler, J.K. Johnsen, F. Allgöwer, introduction to interconnection and damping assignment passivity-based control in process engineering, Journal of Process engineering, Journal of Process Control, 19(9), pp. 1413–1426, 2009.

A. Favache, D. Dochain, Power-shaping control of reaction systems: The CSTR case, Automatica, 46(11), pp. 1877–1883, 2010.

H. Ramírez, B. Maschke, D. Sbarbaro, Irreversible port-Hamiltonian systems: A general formulation of irreversible processes with application to the CSTR, Chemical Engineering Science, 89, pp. 223–234, 2013.

F. Couenne, C. Jallut, B. Maschke, P. Breedveld, M. Tayakout, Bond graph modelling for chemical reactors, Mathematical and Computer Modelling of Dynamical Systems, 12(2-3), pp. 159–174, 2006.

D. Eberard, B. Maschke, A. Van der Schaft, An extension of Hamiltonian systems to the thermodynamic phase space: Towards a geometry of nonreversible processes, Reports on Mathematical Physics, 60(2), pp. 175–198, 2007.

B. Maschke, R. Ortega, A. Van der Schaft, Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation, IEEE Transactions on Automatic Control, 45(8), pp. 1498–1502, 2000.

A. Van der Schaft, Port-controlled Hamiltonian systems: Towards a theory for control and design of nonlinear physical systems, SICE journal, 39(2), pp. 91–98, 2000.

R. Ortega, A. Van der Schaft, B. Maschke, G. Escobar, Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems, Automatica, 38(4), pp. 585–596, 2002.

R. Ortega, A. Van der Schaft, F. Castanos, A. Astolfi, Control by interconnection and standard passivity-based control of port-Hamiltonian systems, IEEE Transactions on Automatic Control, 53(11), pp. 2527–2542, 2008.

N. Monshizadeh, P. Monshizadeh, R. Ortega, A. Van der Schaft, Conditions on shifted passivity of port-Hamiltonian systems, Systems & Control Letters, 123, pp. 55–61, 2019.

M. Chidambaram, G.P. Reddy, Nonlinear control of systems with input and output multiplicities, Computers & Chemical Engineering, 20(3), pp. 295–299, 1996.

M. Guay, N. Hudon, Stabilization of nonlinear systems via potential-based realization, IEEE Transactions on Automatic Control, 61(4), pp. 1075–1080, 2016.

A. Favache, D. Dochain, J.J. Winkin, Power-shaping control: Writing the system dynamics into the Brayton-Moser form, Systems Control Letters, 60(8), pp. 618–624, 2011.

H. Hoang, D. Dochain, F. Couenne, Y. Le Gorrec, Dissipative pseudo-Hamiltonian realization of chemical systems using irreversible thermodynamics, Mathematical and Computer Modelling of Dynamical Systems, 23(2), pp.135–155, 2017.

A. Van der Schaft, L2-gain and passivity techniques in nonlinear control, Springer, 3rd edition, 2017.

T.S. Nguyen, N.H. Hoang, M.A. Hussain, Feedback passivation plus tracking-error-based multivariable control for a class of free-radical polymerization reactors, International Journal of Control, 92(9), pp. 1970–1984, 2019.

C. Batlle, Passive control theory I and II, The 2nd EURON/GEOPLEX Summer School on Modeling and Control of Complex Dynamical Systems, July 18-22, 2005, Bertinoro, Italy.

I.D. Mayergoyz, W. Lawson, Basic electric circuit theory: A one-semester text, Academic Press, 1st edition, 2012. ISBN: 9780124808652.

M.W. McCall, Classical mechanics: From Newton to Einstein - A modern introduction, Wiley, 2nd edition, 2010. ISBN: 9780470715741.

M.P. Niemiec, C. Kravaris, Nonlinear model-state feedback control for nonminimum-phase processes, Automatica, 39(7), pp. 1295–1302, 2003.

R. Antonelli, A. Astolfi, Continuous stirred tank reactors: easy to stabilise?, Automatica, 39(10), pp. 1817–1827, 2003.

H. Ramírez, D. Sbarbaro, R. Ortega, On the control of non-linear processes: An IDA-PBC approach, Journal of Process Control, 19(3), pp. 405–414, 2009.

C.A. Farschman, K.P. Viswanath, B.E. Ydstie, Process systems and inventory control, AIChE Journal, 44(8), pp. 1841–1857, 1998.




DOI: https://doi.org/10.15625/2525-2518/59/1/15238 Display counter: Abstract : 35 views. PDF : 15 views.

Refbacks

  • There are currently no refbacks.


budidaya tani

Index: Google Scholar; Crossref; VCGate; Asean Citation Index

Published by Vietnam Academy of Science and Technology