Analysis And Synthesis Of Several Classes Of Singularly Perturbed Systems

Singularly perturbed model is a class of mathematical models which can represent a lot of industrial systems.In the 1980s,singular perturbation theory had caught much attention from both practitioners and academics because of its advantages of order reduction and stiffness relief.There are a vast variety of nonlinear singularly perturbed models with high complexity.It is impossible to develop one method which can be used to analyze and control different models.Therefore,the analysis and control problems of three classical classes of nonlinear singularly perturbed systems are considered in this dissertation.The main results of the dissertation are summarized as follows:1.The robust absolute stability of a class of uncertain singularly perturbed Lur'e models is analyzed.By the construction of an ?-dependent Lur'e Lyapunov-Krasovskii functional,a stability criterion expressed in terms of ?-independent linear matrix inequalities(LMIs)is derived.Then,a method of designing a feedback controller is developed which can guarantee the absolute stability of the uncertain singularly perturbed Lur'e systems.A numerical example is given to show the effectiveness of the results.2.The optimal control problem of a class of singularly perturbed Bouyekhf models is studied.First of all,the high-order original system is decomposed into slow and fast subsystems.The optimal sub-controllers are designed separately for the two subsys-tems.Then a composite optimal controller is constructed based on the combination of the two sub-controllers.The composite optimal controller is compared to the original high-order optimal controller.It is proved that under some conditions the composite control input is O(?)close to the original control input.Two examples are utilized to verified the results obtained.3.For a class of singularly perturbed Bouyekhf models,a new composite opti-mal controller consisting of two sub-controllers is developed using the discrete state-dependent Riccati equation(D-SDRE).In this optimal control problem,the weight matrices in the cost function depend on the states.Therefore,the cost function is a more general case than the cost functions with constant weight matrices.It is proved that the equilibrium point of the original closed-loop system with the composite op-timal controller is locally asymptotically stable.Moreover,the region of attraction of the closed-loop system is estimated by using LMIs.4.The maximum power point tracking problem is considered for singularly per-turbed models of wind energy conversion systems with permanent magnet synchronous generators.The nonlinear wind energy conversion system is linearized at one opti-mal operating point,and the two-time-scale property is analyzed of the linearized model.Then the system is decoupled into slow and fast subsystems.Slow and fast sub-controllers based on model predictive control(MPC)method are synthesized(de-signed)separately and a composite MPC is obtained.The controller is tested upon a mathematical model and is validated with a wind turbine simulator.Via comparison with the existing controllers,the results indeed show improvements.5.The nonlinear singularly perturbed model of wind energy conversion systems is developed due to its two time scale property.A linear parameter varying(LPV)model is used to approximate the nonlinear singularly perturbed model.Robust stability of the open-loop LPV singularly perturbed system is analyzed using Lyapunov-Krasovskii functional and LMIs.An algorithm of designing a stabilizing H? controller for the nonlinear original model is proposed.The algorithm is validated with a wind turbine simulator,and the results show advantages over the existing result.