{"title":"Modeling Hybrid Systems with MLD Approach and Analysis of the Model Size and Complexity","authors":"H. Mahboubi, B. Moshiri, A. Khaki Seddigh","volume":11,"journal":"International Journal of Mechanical and Mechatronics Engineering","pagesStart":3687,"pagesEnd":3694,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/748","abstract":"Recently, a great amount of interest has been shown\nin the field of modeling and controlling hybrid systems. One of the\nefficient and common methods in this area utilizes the mixed logicaldynamical\n(MLD) systems in the modeling. In this method, the\nsystem constraints are transformed into mixed-integer inequalities by\ndefining some logic statements. In this paper, a system containing\nthree tanks is modeled as a nonlinear switched system by using the\nMLD framework. Comparing the model size of the three-tank system\nwith that of a two-tank system, it is deduced that the number of\nbinary variables, the size of the system and its complexity\ntremendously increases with the number of tanks, which makes the\ncontrol of the system more difficult. Therefore, methods should be\nfound which result in fewer mixed-integer inequalities.","references":"[1] A. Bemporad and M. Morari, \"Control of systems integrating logic,\ndynamic and constraints,\" Automatica, vol. 35, no. 3, Mar. 1999, pp.\n407-427.\n[2] W. P. M. H. Heemels, J. M. Schumacher, \"Linear Complementarity\nsystems,\" SIAM J. Appl. Math., vol. 60, no. 4, pp. 1234-1269,2000.\n[3] B. D. Schutter and T. van den Boom, \"Model predictive control for maxplus-\nlinear discrete event systems,\" Automatica, vol. 37, no. 7, pp. 1049-\n1056, 2001.\n[4] E. D. Sontag, \"Nonlinear regulation: the piecewise linear approach,\"\nIEEE Trans. Automat. Contr., 26(2), pp. 346-358, Apr.1981.\n[5] B. De Schutter and B. De Moor,\" The extended linear complementarity\nproblem and the modeling and analysis of hybrid systems,\" in Haybrid\nSystems V, P. Antsaklis, W.Kohn, M. Lemmon, A. Nerode, and S.\nSastry, Eds. New York: Spring- verlag, vol. 1567, Lecture Notes in\nComputer Science, pp. 70-85,1999.\n[6] W. P. Maurice H. Heemles and Bart De Schutter and Alberto Bemporad,\n\"Equivalence of hybrid dynamical models,\" Automatica, vol. 37, no. 7,\npp. 1085-1091, July 2001.\n[7] Domenico Mignone \"Control and Estimation of Hybrid Systems with\nmathematical Optimization\", PhD Thesis, Swiss Federal Institute of\nTechnology, Zurich, 2002.\n[8] O. Stursberg and S. Engell, \"Optimal Control of Switched Continues\nSystems using Mixed-Integer Programing,\" in Proc. 42nd IEEE\nConference on Decision and Control, Hawaii USA, 2003, pp. 640-645.\n[9] J. Till, S. Engell, S. Panek and Olaf Stursberg , \"Applied hybrid system\noptimization: an empirical investigation of complexity,\" Control\nEngineering Practice, vol. 12, pp. 1291-1303,2004.\n[10] M. Morari, Mato Baotic and Francesco Borrelli, \"Hybrid system\nmodeling and control,\" Europian Journal of Control, 2003.\n[11] http:\/\/www.AMPL.com\n[12] J. Habibi, B. Moshiri and A. Khaki Seddigh, \"Hybrid Modeling and\nPredictive Control of a Multi-Tank System: A Mixed Logical Dynamical\nApproach\" in Proc. IAWTIC-2005, Vienna Austria, 2005.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 11, 2007"}