Abstract
This chapter is devoted to the development of a decentralised model predictive control (MPC) strategy for splitting parallel systems that have time-varying and unknown splitting ratios. The large-scale system in consideration consists of several dynamically-coupled modular subsystems. Each subsystem is regulated by a dedicated multivariable controller employing the open-loop MPC algorithms in conjunction with stability constraints. The connection topology of the large-scale systems includes serial, parallel and recirculated configurations. The solution to splitting parallel systems in this chapter is not only an alternative to the hybrid approach for duty-standby modes, but also a novel approach that accommodates the concurrent operations of splitting parallel systems. The effectiveness of this approach rests on the newly introduced asymptotically positive real constraint (APRC) which prescribes an approaching characteristic towards a positive real property of the system under control. The asymptotic attribute of APRC smooths out all significant wind-up actions in the control trajectories. The APRCs are developed into a one-time-step quadratic constraint on the local control vectors, which plays the role of a stability constraint for the decentralised MPC. The recursive feasibility is assured by characterizing the APRC with dynamic multiplier matrices. Numerical simulations for two typical modular systems in an alumina refinery are provided to illustrate the theoretical results.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Apkarian P, Adams R (2000) Advanced gian-scheduling techniques for uncertain systems. In: Ghaoui L El, Niculescu S (eds) Advanced in linear matrix inequality methods in control. SIAM, Philadelphia, pp 971–981
Apkarian P, Noll D (2006) IQC analysis and synthesis via nonsmooth optimization. Syst Contr Lett 55(12):971–981
Apkarian P, Pellanda P, Tuan H (2000) Mixed h 2 ∕ h ∞ multi-channel linear parameter-varying control in discrete time. Syst Contr Lett 41:333–346
Apkarian P, Tuan HD (2003) Parameterized linear matrix inequalities in control theory. SIAM J Contr Optim 38(4):1241–1264
Bao L, Nguyen AV (2010) Developing a physically consistent model for gibbsite leaching kinetics. Hydrometallurgy 104:86–98
Brogliato B, Lozano R, Maschke B, Egeland O (2006) Dissipative systems analysis and control: theory and applications. Springer, London
El Ghaoui L, Niculescu S (2000) Advances in linear matrix inequality methods in control. Society for Industrial and Applied Mathematic, Philadelphia, PA, USA
Hangos KM, Cameron IT (2001) Process modelling and model analysis. Academic Process, London
Harder J (2010) Trends in the extraction of bauxite and alumina. Aufbereitungs-Technik/Mineral Processing 51(5):44–57
Henrickson L (2010) The need for energy efficiency in Bayer refining. In: Proceedings of TMS annual meeting - light metals’10, Seattle pp 173–178
Hodouin D, Jämsä-Jounela SL, Carvalhoc MT, Bergh L (2001) State of the art and challenges in mineral processing control. Contr Eng Pract 9(1):995–1005
Hoffman T, Hutchinson HP (1975) The simulation of the Bayer process for extracting alumina from bauxite ore. In: Proceedings of symposium on computer design and erection of chemical plants, Czechoslovakia, pp 451–485
Jämsä-Jounela SL (2007) Future trends in process automation. Annu Rev Contr 31:211–220
Köroubreve{g}lu H, Scherer CW (2007) Robust performance analysis for structured linear time-varying perturbations with bounded rates-of-variation. IEEE Trans Automat Contr 52(3):197–211
Leslie RA, Blair JR (1975) The dynamic modelling of caustic concentration in the Bayer process. In: Proceedings of APCOM symposium 5, pp 137–14
Lunze J (1992) Feedback control of large scale systems. Prentice Hall, London
Maciejowski JM (2002) Predictive control with constraints. Prentice Hall, Harlow
Mahmoud MS (2010) Decentralized control and filtering in interconnected dynamical systems. CRC Press, New York
Megretski A, Rantzer A (1997) System analysis via integral quadratic constraints. IEEE Trans Automat Contr 42(6):819–830
Ouellet V, Bergeron S, Verville D (2007) Bayer process control at Alcan Vaudreuil works. In: Proceedings of 12th IFAC symposium on automation in mining, mineral and metal processing 12(1):Quebec
Rawlings JB, Stewart BT (2008) Coordinating multiple optimization-based controllers: New opportunities and challenges. J Process Control 18:839–845
Rotkowitz M, Lall S (2006) A characterization of convex problems in decentralized control. IEEE Trans Automat Contr 51:274–286
Scattolini R (2009) Architectures for distributed and hierarchical model predictive control - A Review. J Process Control 19:723–731
Schooman ML (2001) Reliability of computer systems and networks: fault tolerance, analysis and design. Wiley-Interscience, New York
Seborg DE, Edgar TF, Mellichamp DA, III FJD (2010) Process dynamics and control, 3rd edn. Wiley, NewYork
Sidrak YL (2001) Dynamic simulation and control of the Bayer process—a review. Ind Eng Chem Res 40:1146–1156
Siljak DD (1991) Decentralized control of complex systems. Academic, New York
Sourlas DD, Manousiouthakis V (2003) Best achievable decentralized performance. IEEE Trans Automat Contr 40(11):1858–1871
Tran T (2010) Overriding control for stability with manifest variables.In: Proceedings of IEEE international conference on control, automation, robotics and vision ICARCV’10, pp 236–241
Tran T, Nguyen HT, Ha QP (2010) Stability of complex systems with mixed connection configurations under shared control. In: Proceedings of IEEE international conference on control, automation, robotics and vision ICARCV’10, pp 513–517
Tran T, Tuan HD, Ha QP, Nguyen HT (2011) Toward plant-wide control of reticulated systems arising in alumina refineries with online stabilisation. In: Proceedings of the 18th IFAC World Congress, Milano, Italy
Tran T, Tuan HD, Ha QP, Nguyen HT (2011) Stabilising agent design for the control of interconnected systems. Int J Contr 84:1140–1156
Tuan HD, Apkarian P, Narikyio T, Yamamoto Y (2001) Parametrized linear matrix inequalities in fuzzy control system design. IEEE Trans Fuzzy Syst 9:324–332
Tuan HD, Apkarian P, Narikyio T, Kanota M (2004) New fuzzy control model and dynamic output feedback parallel distributed compensation. IEEE Trans Fuzzy Syst 12:13–21
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Tran, T., Tuan, H.D., Ha, Q.P., Nguyen, H.T. (2012). Decentralised Model Predictive Control of Time-Varying Splitting Parallel Systems. In: Mohammadpour, J., Scherer, C. (eds) Control of Linear Parameter Varying Systems with Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1833-7_9
Download citation
DOI: https://doi.org/10.1007/978-1-4614-1833-7_9
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-1832-0
Online ISBN: 978-1-4614-1833-7
eBook Packages: EngineeringEngineering (R0)