Efficient, Structured Controller Synthesis for Linear Parameter-Varying Systems

A structured output-feedback controller synthesis in linear fractional transformation (LFT) formulation is derived. It is presented as a novel approach to the control of linear parameter-varying (LPV) systems. The LFT formulation leads to a controller synthesis with no approximation steps and it scales better than a gridded formulation when increasing the number of scheduling parameters. The proposed approach has better computational efficiency than a traditional output-feedback controller synthesis, as it solves two small semi-definite programs (SDP) in a two-step synthesis, rather than one large SDP posed by the traditional approach. This two-step synthesis also results in the controller’s fixed structure. The design process uses a recently proposed weighting scheme to impose unambiguous, tractable and physically interpretable closed-loop performance requirements; suitable for use on many aerospace applications. An exemplary spacecraft control problem demonstrates the computational superiority of the novel approach over standard output-feedback synthesis when using different scheduling parameters. There is also minimal loss in performance in the structured controller compared to the output-feedback controller.