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Synthesis And Engineering Application Of Uncertain Dynamic Systems Based On Parameter-Dependent Lyapunov Function

Posted on:2008-07-04Degree:MasterType:Thesis
Country:ChinaCandidate:B ZhouFull Text:PDF
GTID:2178360218952352Subject:Control Engineering
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In industrial process, aerospace, astronautics, it is usually difficult to characterize the dynamics of the controlled object exactly by a mathematical model, which renders inevitable error to exist between the derived mathematical model and the practical object. Thus, study on uncertain system has long drawn much attention from researchers working in systems and control areas. Robust control theory generally solves analysis and synthesis problems for parameter uncertain systems based on the notion of quadratic stability. Duo to its utilization of a common Lyapunov function for the entire uncertainty domain, quadratic stability has been well recognized to be conservative, which prevents robust control theory from further development and limits its applications in practical engineering to a great extent. This thesis, based on previous works others, systematically and deeply investigates the problems of state-feedback controller synthesis and filter design for polytopic uncertain systems based on parameter-dependent Lyapunov functions, and presents analysis and synthesis methodologies for uncertain dynamic systems in the unified parameter-dependent framework in order to reduce design conservatism. Part of the developed theories is applied to multi-objective control of vehicle active suspension systems and aerocraft.Chapters 1-2 first summarize and analyze the main results in the frontiers of parameter-dependent Lyapunov stability. A new result of parameter-dependent Lyapunov stability is introduced to robust multiobjective filtering, and robust L2-L∞filtering with pole constraint in a disk and robust full-order and reduced-order mixed l1/H∞filter for linear discrete systems will be used as the examples to systemic exhibit design procedures of robust multiobjective filtering based on parameter-dependent Lyapunov functions and to be compared with the quadratic stability results. It shows that the filter design procedures proposed in this thesis are much less conservative than earlier results. In chapter 3, the result of parameter-dependent Lyapunov stability is introduced to robust stabilization problem of time-delay systems in order to reduce design conservatism.Chapter 4 investigates the problem of robust L1 model reduction for the uncertain dynamic systems. For given stable continuous- and discrete-time uncertain linear systems, the purpose is respectively to construct reduced-order systems, such that the error system is asymptotically stable and has a guaranteed peak-to-peak performance. This problem is solved by using the Projection Lemma, and sufficient conditions are obtained for the existence of admissible reduced-order models in terms of LMIs plus matrix inverse constraints. Since these obtained conditions are not expressed as strict LMIs, the cone complementarity linearization (CCL) method is exploited to cast them into nonlinear minimization problems subject to LMIs constraints, which can be readily solved by standard numerical software.Chapter 5 applies the results developed to vibration control of vehicle active suspension systems. By analyzing the basic functions of vehicle active suspension, the vibration control for these systems is mathematically translated into a multi-objective control problem for polytopic uncertain systems. Considering that the parameterof body mass can be measured online, we propose state-feedback control strategy via parameter-dependent controllers. This part constitutes an attempt of applying the parameter-dependent Lyapunov stability idea to practical engineering problems, which extends the parameter-dependent Lyapunov stability theory and privides a design example for practical engineers' reference as well. Chapter 6 further applies the results developed to control of aerocraft. It is This technique has been significant in dealing with the problems of engineering application.
Keywords/Search Tags:parameter-dependent Lyapunov function, L1 performance, robust control and filtering, Model reduction, Vibration control for active suspension, Linear Matrix inequality
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