This dissertation studies the smooth switching LPV (Linear Parameter-Varying) system and control, as well as its applications in mechanical systems, aerospace systems to achieve the smooth transition between switching LPV controllers. Both state-feedback and dynamic output-feedback cases are addressed by the simultaneous design approach of smooth switching LPV control, and the proposed method has been applied to active vibration control of BWB (Blended-Wing-Body) aircraft flexible wing and the AMB (Active Magnetic Bearing) system. Moreover, a sequential design approach is developed to design smooth switching LPV controllers, where the high-dimensional optimization in the simultaneous design approach can be relaxed.In conventional switching LPV control, switching controllers are designed on each subregion while guaranteeing safe switching, but without considering the smoothness during switching events. The abruptly varying control signal can exceed actuator authority; moreover, abrupt changes in system responses caused by unsmooth controller gains will be harmful to system components and hardware. The simultaneous design of smooth switching LPV control minimizes a combined cost of system output H2 performance and smooth-switching index subject to H2 constraints on control inputs and Hinf constraint on bounded model uncertainty. These stability and performance criteria are then formulated using a set of Parametric Linear Matrix Inequalities (PLMIs). Besides, a tunable weighting coefficient is introduced to provide an optimal trade-off design between system H2 performance and switching smoothness. Simulation results with the AMB model and BWB aircraft wing model are provided to demonstrate the effectiveness of the proposed smooth switching control. In the above approach, switching controllers are synthesized by controller variables that simultaneously satisfy PLMIs on all subregions and switching stability conditions on all switching surfaces. When the number of subregions goes large, simultaneous design approach leads to a high-dimensional optimization problem, with a high number of LMI constraints, decision variables, online computational load, and memory requirement. As a result, these drawbacks make simultaneous design practically infeasible for high-order systems with many divided subregions. An innovative sequential design approach is proposed by introducing interpolated controller decision variables and formulating independent PLMI conditions on each subregion such that system performances on overlapped subregions are guaranteed as well. In this way, the switching controller synthesis conditions are formulated as independent optimization problems and can be well solved sequentially. Besides, this dissertation also utilizes the LPV framework to investigate optimal sensor placement to achieve optimal vibration suppression for a flexible BWB airplane wing. For a given flight speed range, vibration behaviors of the wing structure are evaluated by the guaranteed H2 performance with the H2 LPV controller. Candidate sensor locations are identified on each wing, and the optimal sensor placements can be found among these candidate sensor locations by the greedy algorithm. The searched optimal results are validated by globally searching through all possible combinations. With the LPV model of a flexible wing and H2 controller synthesisconditions, search results provide the optimal sensor locations, and besides, the trade-off between optimal system performance and the number of sensors can also be obtained.
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