Design of observer-based feedback controller for multi-rate systems with various sampling periods using cyclic reformulation

Okajima, Hiroshi; Arinaga, Kenta; Hayashida, Atsuo

doi:10.51094/jxiv.409

##article.authors##

Okajima, Hiroshi Kumamoto University, Faculty of Advanced Science and Technology https://orcid.org/0000-0001-7621-7482 https://researchmap.jp/read0203288/
Arinaga, Kenta Kumamoto University, Graduate School of Science and Technology
Hayashida, Atsuo Kumamoto University, Graduate School of Science and Technology

DOI:

https://doi.org/10.51094/jxiv.409

キーワード:

Multi-rate system、 l2-induced norm、 LMI、 Cyclic reformulation、 State feedback control、 State observer

抄録

Signal sensing periods typically vary depending on the sensor used and may differ even within a single control system that involves multiple sensors. Likewise, input periods can vary based on the actuator used. This paper discusses the design of observer-based feedback controllers for linear, time-invariant, discrete-time systems operating in a multi-rate sensing and actuating environment. The observation and control periods of the sensors and actuators in the plant are assumed to have mutually rational ratios. First, we reduce the multi-rate system to a periodically time-varying system and provide a linear matrix inequality (LMI) condition for analyzing the l2 performance using cyclic reformulation, which is a type of time-invariant reformulation for periodic systems. Next, we extend the analysis method to design an observer-based feedback controller for the multi -rate system. This allows us to obtain multi-rate observer gains and feedback gains based on the l2-induced norm from disturbances to outputs. Finally, we present numerical results to demonstrate the effectiveness of the observer-based feedback system in the multi-rate environment.

利益相反に関する開示

The authors declare no conflicts of interest associated with this manuscript.

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