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UBC Theses and Dissertations

Robust and optimal switching linear parameter-varying control Zhao, Pan


Linear parameter-varying (LPV) control is a systematic way for gain-scheduling control of a nonlinear or time-varying system that has parameter-dependent dynamics variations in its operating region. However, when the dynamics variations are large, LPV control may give the conservative performance. One way to reduce the conservatism is switching LPV (SLPV) control, in which we partition the operating region into sub-regions, design one local LPV controller for each sub-region, and switch among those local controllers according to some switching rules. On the one hand, this thesis makes three theoretical contributions to the SLPV control theory. Firstly, this thesis proposes a new approach to designing SLPV controllers with guaranteed stability and performance even when the scheduling parameters cannot be exactly measured. Secondly, this thesis presents two algorithms to optimize the switching surfaces (SSs) that can further improve the performance of an SLPV controller. One algorithm is based on sequentially optimizing the SSs and the SLPV controller for the state-feedback case. The other one is based on particle swarm optimization and can be used for both state-feedback and output-feedback cases. Finally, this thesis introduces a novel approach to designing SLPV controllers that could yield significantly improved local performance in some sub-regions without much sacrifice of the worst-case performance. This is different from the traditional approach that often leads to similar performance in all the sub-regions. On the other hand, this thesis addresses two practical problems using the theoretic approaches developed in this thesis. One is control of miniaturized optical image stabilizers with product variations. Specifically, multiple parameter-dependent robust (MPDR) controllers are designed to adapt to the product variations, while being robust against the uncertainties in measurement of the scheduling parameters that characterize the dynamics variation. Experimental results validate the advantages of the proposed MPDR controllers over a conventional robust mu-synthesis controller. The other application is control of a floating offshore wind turbine on a semi-submersible platform. SLPV controllers are designed for regulating the power and the generator speed and reducing the platform motion. The superior performance of the SLPV controllers is demonstrated in high-fidelity simulations.

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