0
Research Papers

A Simplified Method for Discrete-Time Repetitive Control Using Model-Less Finite Impulse Response Filter Inversion

[+] Author and Article Information
Yik R. Teo

Precision Mechatronics Lab,
School of Electrical Engineering and
Computer Science,
The University of Newcastle,
Callaghan, New South Wales 2308, Australia
e-mail: yik.teo@newcastle.edu.au

Andrew J. Fleming

Precision Mechatronics Lab,
School of Electrical Engineering and
Computer Science,
The University of Newcastle,
Callaghan, New South Wales 2308, Australia
e-mail: andrew.fleming@newcastle.edu.au

Arnfinn A. Eielsen

Department of Engineering Cybernetics,
Norwegian University of Science and Technology,
Trondheim NO-7491, Norway
e-mail: eielsen@itk.ntnu.no

J. Tommy Gravdahl

Department of Engineering Cybernetics,
Norwegian University of Science and Technology,
Trondheim NO-7491, Norway
e-mail: gravdahl@itk.ntnu.no

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 26, 2015; final manuscript received March 23, 2016; published online May 24, 2016. Assoc. Editor: Ming Xin.

J. Dyn. Sys., Meas., Control 138(8), 081002 (May 24, 2016) (13 pages) Paper No: DS-15-1346; doi: 10.1115/1.4033274 History: Received July 26, 2015; Revised March 23, 2016

Repetitive control (RC) achieves tracking and rejection of periodic exogenous signals by incorporating a model of a periodic signal in the feedback path. To improve the performance, an inverse plant response filter (IPRF) is used. To improve robustness, the periodic signal model is bandwidth-limited. This limitation is largely dependent on the accuracy of the IPRF. A new method is presented for synthesizing the IPRF for discrete-time RC. The method produces filters in a simpler and more consistent manner than existing best-practice methods available in the literature, as the only variable involved is the selection of a windowing function. It is also more efficient in terms of memory and computational complexity than existing methods. Experimental results for a nanopositioning stage show that the proposed method yields the same or better tracking performance compared to existing methods.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

A time delay with positive feedback with the appropriate initial function can model any periodic signal [1]

Grahic Jump Location
Fig. 2

Block diagram for a general RC system

Grahic Jump Location
Fig. 3

Equivalent description of sensitivity function

Grahic Jump Location
Fig. 4

Three-axis serial-kinematic nanopositioning platform [32]

Grahic Jump Location
Fig. 5

The ETFE for the nanopositioner along the x-axis (solid line) and the frequency response of a fifth order IIR model found using subspace identification (dashed line)

Grahic Jump Location
Fig. 6

The H2 -norm of the error between the ETFE and identified IIR models for model orders ranging from 1 to 50

Grahic Jump Location
Fig. 7

The number of nonminimum phase zeros (left y-axis) and the H2 -norm error of the ETFE and inverse of the ZPETC model response (right y-axis) for model order ranging from 1 to50

Grahic Jump Location
Fig. 8

The stability criterion plot of Eq. (4) for ZPETC inverse and low-pass filter H1(z−1) at cutoff frequency of 1 kHz for model orders ranging from 1 to 50 (left y-axis). The tracking performance for a 40 Hz triangular wave reference signal for model orders ranging from 1 to 50 (right y-axis).

Grahic Jump Location
Fig. 9

Frequency responses for the ETFE, the ZPETC inverse, and the product of the two, when using a with a fifth-order model

Grahic Jump Location
Fig. 10

The argument to the norms in the stability criteria (4), (5), and (6), when using a ZPETC inverse with a fifth-order model

Grahic Jump Location
Fig. 21

The measured output displacements

Grahic Jump Location
Fig. 22

The output displacement error

Grahic Jump Location
Fig. 20

The argument to the norms in the stability criteria (4), (5), and (6), when using a frequency sampling FIR filter (Hann window)

Grahic Jump Location
Fig. 16

The unit impulse response h3(n) when using a rectangular window and a Hann window

Grahic Jump Location
Fig. 15

Frequency sampling FIR filter inverse frequency responses, with rectangular and Hann windows

Grahic Jump Location
Fig. 13

The stability criterion plot of Eq. (4) for optimization-based FIR filter with error weighting (15) and low-pass filter H1(z−1) with cutoff frequency at 1 kHz for filter parameter p ranging from 1 to 50 (left y-axis). The tracking performance for a 40 Hz triangular wave reference signal (right) for the optimization-based FIR filter with error weighting (15) and filter parameter p ranging from 1 to 50 (right y-axis).

Grahic Jump Location
Fig. 12

Optimization-based FIR filter inverse frequency responses, with p = 30, q = 15, using the error weighting function (15)

Grahic Jump Location
Fig. 11

Optimization-based FIR filter inverse frequency responses, with p = 30, q = 15, using the error weighting function V(k) = 1

Grahic Jump Location
Fig. 14

The argument to the norms in the stability criteria (4), (5), and (6), when using an optimization-based FIR filter

Grahic Jump Location
Fig. 19

The average power of the error signal for frequency sampling FIR filter with different window functions

Grahic Jump Location
Fig. 18

The stability criterion plot of Eq. (4) for different window functions.

Grahic Jump Location
Fig. 17

Frequency sampling FIR filter inverse frequency responses, when using various Kaiser windows

Grahic Jump Location
Fig. 23

Computational complexity of each method, using asymptotic notation

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In