طراحي و تحليل پايداري كنترل پيش بين انقباضي براي سيستم هاي هيبريد PWA

چكيده انگليسي :

Synthesis and Stability Analysis of Contractive Model Predictive Control for PWA Hybrid Systems Hadi Moghadas Dastjerdi h moghadas@ec iut ac ir 9th March 2011 Department of Electrical and Computer Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Languege Persian Yadollah Zakeri yzakeri@cc iut ac ir Javad Askari j askari@cc iut ac irAbstract The word Hybrid is used to refer to anything that is a mixture of other things especially two otherthings In Dynamical systems modeling theory Hybrid means a system its behavior is include the bothcontinuous and discontinuous dynamics Nowadays by the increasing use of computer controlledequipments new methodologies for the analysis and synthesis of hybrid systems are needed However ageneral model of hybrid systems although it can capture a lot of situations high modeling power composition of continuous and discontinuous dynamics usually leads to a high level of complexity withrespect to analysis and controller design techniques One of the most important resource of this complexityoriginates from the fact that the structure of particular classes of hybrid systems is not exploited Therefore in each choice of modeling formalism there is always the trade off between the modeling power and thecomplexity of the analysis That is why the research in hybrid systems also focuses on particular subclassesthat have a simpler representation and more structure but still include a wide range of industrially relevantprocesses Consequently in this study we focus on the piecewise affine PWA hybrid systems due to theiraccessible mathematical description on one hand and their ability to model a broad class of hybrid systemson the other hand Moreover the equivalence of PWA and other subclasses is proved possible under someadditional assumptions related to boundedness of input state output and auxiliary variables It is clear thattechniques facilitating combined analysis and synthesis of both discontinuous and ontinuous parts areindispensable to build more efficient controller design methods for hybrid systems In recent years theoptimal control and model predictive control MPC are the most significant methods which have been usedin hybrid systems In this study due to advantages such as ability of direct taking into account constraintsMPC has been chosen while applying contractive constraint of lyapunov function in order to guarantee closeloop stability is suggested Reducing complixity of synthesis procedure possible changing of computationload considering the problem restrictions and capability for effective impemantation make this approch moreuseful than common methods like final state equality constraint Since the systems in practice affected byperturbations robustness of contorl method is abselutly considerable Altoth it has been proven that applingcontractive constraint leads to exponentially stability but its has been shown that unlike classic systems exponentially stable discrete time PWA systems can have no robustness to arbitrarily small perturbations Inthis study Input to State Stability ISS and Input to State practical Stability ISpS for systems which arenot even continuous at the equilibrium point of suggested formulation has been presented Key WordsHybrid systems Piecewise affine systems Discrete time Input to State Stability Model predictive control contractive constraint of lyapunov function Robustness

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طراحي و تحليل پايداري كنترل پيش بين انقباضي براي سيستم هاي هيبريد PWA

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