Abstract
This work deals with the modeling and the control of hybrid systems by using Mixed Logical Dynamical (MLD) system framework described by interdependent physical laws, logic rules, and operating constraints. These are describe by linear dynamic equations subject to linear inequalities involving real and integer variables. The changes which may appear over such dynamics, are modeled by using the auxiliary variables which take into account the interconnections effects. The MLD model is used to synthesize the model predictive control law (MPC). The discrete-time equivalent of the model predicts the hybrid system behavior over a prediction horizon. The controller requires solution of on line mixed integer quadratic or linear program to solve an optimization problem. Simulation was performed using HYSDEL compiler and APROS software to illustrate performances and efficiently of these tools using the model of a three-tank COSY benchmark.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Apros—Dynamic Process Simulation Software. http://www.apros.fi
Bemporad A, Morari M (1999) Control of systems integrating logic, dynamics and constraints. Automatica 35:407–427
Bemporad A, Mignone D, Morari M (1999) Moving horizon estimation for hybrid systems and fault detection. In: International proceedings of the american control conference, SanDiego
Camacho EF, Bordons C (2007) Model predictive control. Springer, London
Cavalier TM, Pardalos PM, Soyster AL (1990) Modeling and integer programming techniques applied to propositional calculus. J Oper Res 17:561–570 (Pergamon Press)
Clarke DW, Mohtadi C, Tuffs PS (1987) Generalized predictive control—part I. and II. Automatica 23:137–160 (Pergamon Journal)
De Schutter B, de Moor B (1999) The extended linear complementarity problem and the modeling and analysis of hybrid systems. In: Antsaklis P, Kohn W, Lemmon M, Nerode A, Sastry S (eds) Hybrid systems. Volume 1567 of lecture notes in computer science, pp 70–85. Springer, Berlin
De Schutter B, van den Boom T (2000) On model predictive control for maxmin-plus-scaling discrete event systems. Technical Report, The Netherlands
Fletcher R, Leyffer S (1995) Numerical experience with lower bounds for MIQP branch and bound. Technical report, department of mathematics, University of Dundee, Scotland
Levis AH et al (1987) Challenges to control: a collective view. IEEE Trans Autom Control AC-32:275–285
Heemels WPMH (1999) Linear complementarity Systems: A Study in hybrid dynamics. Ph.D. thesis, Department of Electrical Engineering, Eindhoven University of Technology, The Netherlands
Leenaerts DMW, van Bokhoven WMG (1998) Piecewise linear modeling and analysis. Kluwer Academic Publishers, Dordrecht (Springer science)
Mignone D (2002) Control and estimation of hybrid systems with mathematical optimization. Swiss federal institute of technology (ETH), thesis for the degree of Dr. Science, Italy
Nareshkumar NN (2009) A Multiple model approch for modeling, identification and control of nonlinear hybrid systems. Indian Institute of technology Bombay
Raman R, Grossmann IE (1992) Integration of logic and heuristic knowledge in MINLP optimization for process synthesis. Comput Chem Eng 16:155–171
Richalet J, Rault A, Testud JL, Papon J (1978) Model predictive heuristic control: applications to industrial processes. Automatica 14:413–428
Riedinger P (2000) Contribution à la commande optimale des systèmes dynamiques hybrides. PhD thesis, Centre de recherche en Automatique de Nancy & Institut National Polytechnique de Lorraine, France
Thomas J (2004) Estimation et commande prédictive à horizon glissant de systèmes hybrides. Ph.D. thesis, University Paris XI Orsay, Supelec
Torrisi FD, Bemporad A (2004) HYSDEL—a tool for generating computational hybrid models for analysis and synthesis problems. IEEE Trans Control Syst Technol 12:235–249
Villa JL, Duque M, Gauthier A, Rakoto-Ravalontsalama N (2003) MLD control of hybrid systems: application to the three-tank benchmark problem. In: IEEE International, conference on systems, man & cybernetics (SMC2003), USA, pp 666–671. Accessed 5–8 Oct 2003
Williams HP (2013) Model building in mathematical programming. 3rd edn. Wiley, New York
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Halbaoui, K., Belazreg, M.F., Boukhetala, D., Belhouchat, M.H. (2016). Modeling and Predictive Control of Nonlinear Hybrid Systems Using Mixed Logical Dynamical Formalism. In: Vaidyanathan, S., Volos, C. (eds) Advances and Applications in Nonlinear Control Systems. Studies in Computational Intelligence, vol 635. Springer, Cham. https://doi.org/10.1007/978-3-319-30169-3_19
Download citation
DOI: https://doi.org/10.1007/978-3-319-30169-3_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-30167-9
Online ISBN: 978-3-319-30169-3
eBook Packages: EngineeringEngineering (R0)