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Research Papers

Prototype Angle-Domain Repetitive Control-Affine Parameterization Approach

[+] Author and Article Information
Perry Y. Li

Professor
Department of Mechanical Engineering,
University of Minnesota,
Minneapolis, MN 55455
e-mail: lixxx099@umn.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 6, 2015; final manuscript received September 8, 2015; published online October 1, 2015. Assoc. Editor: Douglas Bristow.

J. Dyn. Sys., Meas., Control 137(12), 121009 (Oct 01, 2015) (9 pages) Paper No: DS-15-1204; doi: 10.1115/1.4031577 History: Received May 06, 2015; Revised September 08, 2015

Angle-domain repetitive disturbances refer to disturbances that are periodic in a generic angle variable which is monotonically increasing with time but not uniformly. This paper extends the classical prototype repetitive control methodology for time periodic disturbances to this situation. Instead of using an internal model approach to derive the control, an affine parameterization approach is adopted which reduces the control design methodology to one of estimating and canceling the disturbance. While the resulting control architectures are similar to the classical time-domain periodic case, the stability conditions are different and depend on the choice of signal norm. This necessitates an alternate compensator design approach for the nonminimum phase terms. Robust stability is also considered in the L2 setting and an affine Q-filter concept is introduced to achieve robust stability.

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References

Figures

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Fig. 1

Angle-domain repetitive control problem

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Fig. 2

Affine parameterized control structure with innovation feedback

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Fig. 3

Relationship between output feedback and innovation feedback

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Fig. 4

Angle-domain repetitive control

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Fig. 5

Illustration of a time-domain signal that achieves maximum gain after going through an angle delay operator

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Fig. 6

Affine parameterized form of the angle-domain repetitive controller in Fig. 4 after look aheads are absorbed

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Fig. 7

Internal model implementation of the angle-domain repetitive controller in Fig. 6 with compensators satisfying Eqs. (23) and (24). Top: before absorbing the time-advance terms; bottom: after absorbing the time-advance terms.

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Fig. 8

Interaction of uncertainty with repetitive controller

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Fig. 9

Output feedback form of the repetitive controller with affine Q-filter. Top: before absorbing the time-advance terms; bottom: after absorbing the time-advance terms.

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Fig. 10

Angle-domain repetitive controller with kB̃o=1

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Fig. 11

Angular speed of unwound angle ω =θ˙

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Fig. 12

Angle-domain disturbance as a function of angle (top) and of time (bottom)

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Fig. 13

Output error with nominal controller

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Fig. 14

Actual and estimated disturbance (at output of Gi) with nominal controller

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Fig. 15

Frequency response of the 21 tap FIR affine Q-filter

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Fig. 16

Output error with controller and affine Q-filter

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Fig. 17

Actual and estimated disturbance (at output of Gi) with controller and affine Q-filter

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Fig. 18

Output error with simple controller in Fig. 10, n = 6 term series expansion, and affine Q-filter

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