An Improved Equivalent-Input-Disturbance Approach for Repetitive Control System With State Delay and Disturbance

Pan Yu, Min Wu*, Jinhua She, Kang Zhi Liu, Yosuke Nakanishi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

71 Citations (Scopus)


An improved equivalent-input-disturbance (EID) approach is devised to enhance the disturbance-rejection performance for a strictly proper plant with a state delay in a modified repetitive-control system. A gain factor is introduced to construct an improved EID estimator. This increases the flexibility of system design and enables the adjustment of the dynamical performance of disturbance rejection. Moreover, the commutative condition, which is widely used for the conventional EID estimator, is avoided. Thus, it reduces the conservativeness of design by removing the constraints imposed by the commutative condition. The system is divided into two subsystems, and the separation theorem is applied to simplify the design. For one subsystem, the delay information on both the modified repetitive controller and the plant is used to reduce the conservativeness of stability condition. The resulting linear matrix inequality (LMI) is used to find the gain of the state-feedback controller. Another LMI is derived to design the gains of the state observer and the improved EID estimator for the other subsystem. A case study on a metal-cutting system validates the superiority of the developed method.

Original languageEnglish
Article number7951036
Pages (from-to)521-531
Number of pages11
JournalIEEE Transactions on Industrial Electronics
Issue number1
Publication statusPublished - 2018 Jan


  • Disturbance estimation
  • equivalent input disturbance (EID)
  • integral inequality
  • linear matrix inequality (LMI)
  • modified repetitive control
  • state delay

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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