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Research Papers

Design and Analysis for Uncertain Repetitive Control Systems With Unknown Disturbances

[+] Author and Article Information
R. Sakthivel

Department of Mathematics,
Bharathiar University,
Coimbatore 641046, India
e-mail: krsakthivel@yahoo.com

K. Raajananthini

Department of Mathematics,
Anna University-Regional Campus,
Coimbatore 641046, India
e-mail: rjnanthini@gmail.com

P. Selvaraj

Department of Mathematics,
Anna University-Regional Campus,
Coimbatore 641046, India
e-mail: selvamath89@gmail.com

Y. Ren

Department of Mathematics,
Anhui Normal University,
Wuhu 241000, China
e-mail: brightry@hotmail.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received April 15, 2017; final manuscript received June 20, 2018; published online July 23, 2018. Assoc. Editor: Ming Xin.

J. Dyn. Sys., Meas., Control 140(12), 121007 (Jul 23, 2018) (10 pages) Paper No: DS-17-1193; doi: 10.1115/1.4040663 History: Received April 15, 2017; Revised June 20, 2018

In this paper, the periodic tracking problem is considered for a class of continuous system with uncertainty, time-varying delay, and unknown bounded external disturbances. To be precise, in order to attenuate the unknown disturbance effectively, the equivalent-input-disturbance (EID) approach is incorporated into the developed algorithm. Then, the sufficient conditions that guarantee the asymptotic tracking performance of the system understudy are established based on the Lyapunov stability theorem. More precisely, Schur complement and free-weighting matrix approach are utilized to derive the main results. Moreover, the proposed EID-based modified repetitive controller (MRC) not only rejects the unknown external disturbance but also deals with the dead zone effect. Finally, two simulation examples are presented to verify the superiority of the proposed EID-based repetitive controller over the conventional repetitive controller.

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Figures

Grahic Jump Location
Fig. 1

Block diagram of the EID-based MRC system

Grahic Jump Location
Fig. 3

State responses for uncertain system in the presence of disturbance without EID: (a) tracking performance of closed-loop system (9) and (b) error

Grahic Jump Location
Fig. 4

State responses for uncertain system in the presence of disturbance with EID: (a) tracking performance of closed-loop system with EID (9) and (b) error

Grahic Jump Location
Fig. 5

Simulation results for uncertain system in the presence of dead-zone without EID: (a) tracking performance of closed-loop system (9) and (b) error

Grahic Jump Location
Fig. 6

Simulation results for uncertain system in the presence of dead-zone with EID: (a) tracking performance of closed-loop system (9) and (b) error

Grahic Jump Location
Fig. 7

Simulation result for different r(t) with T = 4

Grahic Jump Location
Fig. 8

Tracking error of the system with EID-based controller and disturbance observer based controller in Ref. [13]: (a) the output of the system y(t) with EID-based controller and disturbance observer based controller in Ref. [13], the reference input r(t) and (b) error

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