An Analytic Interpolation Approach to Stability Margins With Emphasis on Time Delay

• 成果类型: Article
• 署名作者: Ringh, Axel; Karlsson, Johan; Lindquist, Anders
• 署名单位: Hong Kong University of Science & Technology; Royal Institute of Technology; Shanghai Jiao Tong University; Royal Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3047336
• 发表日期: 2022
• 页码: 105-120
• 关键词: Control design; delay systems; H-infinity control; interpolation; Linear systems; robust stability; uncertain systems

摘要

Unlike the situation with gain and phase margins in robust stabilization, the problem to determine an exact maximum delay margin is still an open problem, although extensive work has been done to establish upper and lower bounds. The problem is that the corresponding constraints in the Nyquist plot are frequency dependent, and encircling the point s = -1 has to be done at sufficiently low frequencies, as the possibility to do so closes at higher frequencies. In this article, we present a new method for determining a sharper lower bound by introducing a frequency-dependent shift. The problem of finding such a bound simultaneously with gain and phase margin constraints is also considered. In all these problems, we take an analytic interpolation approach.