Multi-objective Robust Control System Design Based on Finite Frequency KYP Lemma and Its Applications

点击翻译按钮获取中文摘要

The purpose of this research project is to develop a unified theory of control synthesis based on the analytical results on generalized KYP lemma, which is a finite frequency version of the original KYP lemma Especially, our main focus are on a systematic design method considering the more practical situations and on the design algorithms.The results on the synthesis theory are as follows:(1) PID controller synthesis based on the generalized KYP lemma.(2) A time-domain interpretation of the generalized KYP lemma, which includes an equivalence of positive-realness in frequency-domain and passivity in time-domain as a special case. It is a first step of the investigation for nonlinear systems.(3) An SoS (Sum of Squares) decomposition characterization of the generalized KYP lemma The result is useful for plant design from the view point of control.(4) A dual characterization of the generalized KYP lemma and its computational complexity analysis.A analysis/synthesis tool box has been developed based on our theoretical results. We also implemented primal-dual algorithms for solving the generalized KYP based optimization problems and compared the computational costs. The comparison shows that the positive semi-definite optimization problems derived from the generalized KYP lemma are very hard to solve in general. This motivates us to develop a new algorithm considering the structure.