Bode Integral: A Unifier of Control-Relevant Integral Relations. Issue 25 (2022)

• Record Type: Journal Article
• Authors: Ding, Yanling; Peng, Hui; Ma, Junqi; Hara, Shinji; Chen, Jie
• Is Part Of: IFAC-PapersOnLine. Volume 55:Issue 25(2022)
• Page Start: 97
• Page End: 102
• Publication Date: 2022
• Subjects: Conformal map -- Bode sensitivity integrals -- integral relations -- LTI feedback systems -- control performance limitation; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2022.09.330
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: Various frequency-domain integral formulas are available and can be used to characterize fundamental performance limitations and inherent performance tradeoffs in feedback systems design, and often they appear unrelated. The most exemplary result in this spirit is the Bode sensitivity integral relation. Yet in an interesting finding, in this paper we show that the Bode sensitivity integral can serve as a unifier to link all other integral formulas, including the complementary sensitivity integrals, the Poisson integrals, and the Bode gain-phase integrals, though traditionally they were derived in different ways and have been used for different performance objectives.