Research Papers

Adaptive Repetitive Control With Two Nonsynchronized Sampling

[+] Author and Article Information
Wu-Sung Yao

Department of Mechanical and
Automation Engineering,
National Kaohsiung First University
of Science and Technology,
No.1, University Road, Yanchao District,
Kaohsiung City 824, Taiwan
e-mail: wsyao@ nkfust.edu.tw

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 28, 2014; final manuscript received December 8, 2014; published online January 27, 2015. Assoc. Editor: Yongchun Fang.

J. Dyn. Sys., Meas., Control 137(6), 061003 (Jun 01, 2015) (8 pages) Paper No: DS-14-1094; doi: 10.1115/1.4029367 History: Received February 28, 2014; Revised December 08, 2014; Online January 27, 2015

Repetitive controllers have been shown to be effective for tracking periodic reference commands with known period. For a reference with fixed period, its implementation can be done with time fixed sampling where an integer number of samples in each period can be required. With variable periodic signal tracking with real-time realization, the number of samples per period may be a noninteger with a fixed sample rate. This paper presents an adaptive repetitive control scheme for reducing tracking errors due to variable periodic reference signals with two nonsynchronized sampling. Aside from time sampling, a position pulse signal generated by optical encoder is used to produce another fixed sampling. This technique can accommodate the variable periodic signal and variable samples per period for synchronization can be achieved by the position sampling. Experimental studies of a twin linear motor control system which comes up with variable periodic references are given. The experimental results illustrate the validity of the proposed implementation method in that adaptive repetitive control with two nonsynchronized sampling can effectively eliminate steady-state errors within a few cycles that are caused by variable periodic references.

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Fig. 1

The internal model of a periodic signal with period Td

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Fig. 2

Example of varying periodic signal: (a) time-domain function and (b) position-domain function

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Fig. 3

Modified repetitive control system

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Fig. 4

Recursive form of repetitive control system

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Fig. 5

Implementation of the repetitive control with variable periodic signal

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Fig. 6

(a) The position information and (b) synchronizing the time sampling and position sampling

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Fig. 7

Plot of equispaced angular position θ(t)

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Fig. 8

Twin-parallel linear servomotors with mechanical coupling

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Fig. 9

System model of the thrust command to the velocity output

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Fig. 10

System model from the thrust commands to velocity outputs with the mechanical coupling

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Fig. 11

Block diagram of the coupled system

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Fig. 12

Block diagram of disturbance rejection control system

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Fig. 13

Profile of the harmonic cam

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Fig. 14

Experiment results with the repetitive controller: (a) velocity cam profile input, and (b) position responses in position domain of the traditional (dashed line) and proposed (solid line) repetitive control

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Fig. 15

Experiment results with the repetitive controller: (a) velocity cam profile input, and (b) position responses in position domain of the traditional (dashed line) and proposed (solid line) repetitive control




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