شناسايي سيستم هاي خطي كسري تأخيري با استفاده از يك روش تركيبي

چكيده انگليسي :

Identification of linear delay fractional systems using a hybrid method Mahtab Manouchehri Naeini m manouchehri@math iut ac ir 2019 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Hamid Reza Marzban hmarzban@cc iut ac ir2000 MSC 93B30 26A33 34K37 34K28 Keywords Fractional systems Delay systems Parameter identification Block pulse functions Hybrid functions Abstract The concept of fractional calculus FC was initially proposed by Leibniz more than 300 years ago FC is concernedwith integrals and derivatives of arbitrary order It is demonstrated that the behavior of many complex systems arisingin various fields of science and engineering can be described more accurately by fractional differential equations orfractional integro differential equations with or without delay such as signal and image processing quantum evolutionof complex systems bioengineering viscoelastic flows biomedical control theory robotics finance and economics mechanics and dynamic systems modeling of polymers and proteins thermal diffusion in a wall transmission ofultrasound and active damping of flexible structures Time delays occur so often in almost every situation that toignore them is to ignore reality Indeed time delays have a fundamental impact on the stability of the system understudy As a result the existence of delay cannot be ignored Time delays arise in many physical and practical systemssuch as chemical processes power systems transportation systems climate models transmission lines robotics biological models nuclear reactors and population dynamics Recently much more attention has been paid on thesystem modeling using fractional order model in the community of control For example Podlubny et al proposedto model the heating furnace using fractional order model FOM Wang et al built a FOM for a thermal processin a boiler main steam system In a FOM was built to describe the behavior of a lead acid battery In a FOM for asolid core magnetic bearing was built These encourage research results revealed that FC provides us a power toolto build accurate model for a system which is very important for high performance controller design At present however FC has not an acceptable geometrical or physical interpretation and consequently there is a great difficultyto build FOM for a system based on mechanism analysis Therefore system identification have been reported infrequency domain and time domain It is noted that the existing works paid a little attention to the identification offractional order systems with time delays Time delay exists in various engineering systems such as chemical process long transmission lines in pneumatic systems nuclearreactor and rolling mill Fractional order systems with timedelays can also be found in practice For example the dynamic behavior of HIV infection of CD T cells and motioncontrol systems with actuator limitation can be well modeled using fractional systems with time delays Therefore itis significant to develop methods for the identification of fractional order systemswith time delays In this thesis twoapproximation methods are presented for parameter identification of linear fractional order systems with delay Thefoundation of the first method is based on block pulse functions The operational matrices of fractional integration anddelay associated with the block pulse functions are used to estimate the parameters of the system under consideration The Riemann Liouville integral operator is employed to derive the operational matrix of fractional integration forblock pulse functions The advantage of using operational matrix representation of fractional integral operator anddelay operator is that they transform an integral operation to an algebraic one As a concequence the computationalcomplexity is extremely reduced The foundation of the second approach is based on a hybrid of block pulse functionsand Legendre polynomials The op

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شناسايي سيستم هاي خطي كسري تأخيري با استفاده از يك روش تركيبي

شناسايي سيستم هاي خطي كسري , سيستم هاي تأخيري , ماتريس عملياتي انتگرال , چندجمله اي هاي لژاندر , توابع بلاك-پالس