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چكيده انگليسي :

A Hybrid Adaptive Observer for Frequency Estimation of Saturated Sinusoidal Signals Behnam Asadi Khashooei asadi behnam@gmail com February 19 2012 Department of Electrical and Computer Engineering Isfahan University of Technology 84156 83111 IranDegree M Sc Language FarsiSupervisors Dr Javad Askari j askari@cc iut ac ir Dr Mohsen Mojiri mohsen mojiri@cc iut ac irAbstractThe problem of estimating online the unknown parameters of systems and signals is of great interest inclassical control theory and appears in different forms in many practical applications To estimate theunknown parameters of a system we could use Adaptive Observers and for estimating the unknownparameters of a signal we could model the signal as a system and then apply adaptive observer for parameterestimation of the system and hence the signal Frequency estimation is a fundamental question in systemstheory that has many practical applications for instance in active noise and vibration control in helicopters disk drives and magnetic bearings It is also a challenging theoretical problem since the nonlineardependence on the unknown frequency stymies the application of standard well known techniques In somecases the measured signal may be deformed due to nonlinearities introduced by the sensor for example whenthe signal amplitude exceeds the sensor limits or leaves certain operative ranges in which the sensor operateslinearly Note that the latter case could be transformed into the former one if the signal is appositely cut offto eliminate the sensor distortions Common estimation algorithms such as Adaptive Notch Filter ANF donot provide suitable results in response to non sinusoidal periodic signals like saturated sinusoid In thisresearch we consider the problem of frequency estimation of saturated sinusoidal signals Since a saturatedsinusoid has two distinct dynamics over time we make use of the modeling structure in hybrid dynamicalsystems Firstly we model the saturated sinusoid as the output of a hybrid dynamical system in which theunknown frequency appears as a state and secondly we design a hybrid observer for estimating the states ofthe hybrid model and hence the unknown frequency of the saturated sinusoid In design of this hybridobserver we first explore the concept of the invariant manifold based reduced order observer in which aglobally convergent reduced order observer for general nonlinear systems is addressed The observerprovides asymptotic estimate of the unknown states by rendering attractive an appropriately selected invariant manifold in the extended state space Then we extend the nonlinear observer to estimate the statesin impulsive nonlinear systems and a class of hybrid systems with two operating modes Moreover wedesign the hybrid observer for the hybrid model of saturated signal Compared to the recently proposedmethod based on the hybrid observer concept the proposed method in this research has a simpleralgorithmic design simpler structure lesser number of state variables and better robustness to the variation inthe saturation level The validity of analytical studies are verified by several computer simulations On theother hand in this research the idea of combining hybrid systems and ANF in order to precisely estimate thefrequency of a saturated sinusoid has been explored This results in the introduction of a hybrid model ofANF HANF which is designed by taking into account the hybrid behavior of a saturated sinusoid andproviding a hybrid model of ANF to cope with this hybrid behavior Computer simulations demonstrate thatthe proposed HANF can provide accurate estimation without any bias and variance of the frequency of asaturated sinusoid Keywordsfrequency estimation saturated sinusoidal signal hybrid observer adaptive notch filter hybrid systems

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ارائه يك مشاهده گرهيبريد-وفقي براي تخمين فركانس سيگنال هاي سينوسي اشباع شده

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