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Research Papers

Frequency-Weighted Variable-Length Controllers Using Anytime Control Strategies

[+] Author and Article Information
Bonnie H. Ferri

School of Electrical and Computer Engineering,
Georgia Tech,
Atlanta, GA 30332-0250
e-mail: bonnie.ferri@ece.gatech.edu

Aldo A. Ferri

School of Mechanical Engineering,
Georgia Tech,
Atlanta, GA 30332-0405
e-mail: al.ferri@me.gatech.edu

Gundula B. Runge

School of Mechanical Engineering,
Georgia Tech,
Atlanta, GA 30332-0405
e-mail: runge@match.uni-hannover.de

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 27, 2013; final manuscript received February 9, 2015; published online April 6, 2015. Assoc. Editor: YangQuan Chen.

J. Dyn. Sys., Meas., Control 137(8), 081001 (Aug 01, 2015) (10 pages) Paper No: DS-13-1174; doi: 10.1115/1.4029797 History: Received April 27, 2013; Revised February 09, 2015; Online April 06, 2015

This paper develops an optimal frequency-weighted strategy to design anytime controllers that can react to changing computational resources. The selection of the weighting function is driven by the expectation of the situations that would require anytime operation. For example, if the anytime operation is due to occasional and isolated missed deadlines, then the weighting on high frequencies should be larger than that for low frequencies. Low frequency components will have a smaller change over one sample time, so failing to update these components for one sample period will have less effect than with the high frequency components. Additional considerations explored in this paper are stability analyses, architectural issues, and transient management. Two examples are included that demonstrate the methodology.

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References

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Figures

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Fig. 3

Parallel anytime implementation for a compensator with four stages

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Fig. 2

Example of a digital controller implemented as three cascaded stages

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Fig. 1

Standard configuration for digital control of continuous- time systems where ZOH represents a zero-order hold

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Fig. 4

Frequency response of the first stage of the anytime compensator, K1D1(ω), compared to the full-order compensator for the case of (a) high frequency weighting optimization resulting in the HF Anytime Controller and (b) low frequency-weighting optimization resulting in the LF Anytime Controller

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Fig. 7

Average time responses of the tracking error and the corresponding standard deviations for different miss rates, d1 = 1%, 5%, and 9% for the series HF Anytime controller

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Fig. 8

Average time responses of the tracking error and the corresponding standard deviations for different miss rates, d1 = 1%, 5%, and 9% for the buffered controller

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Fig. 9

Average RMS controller deviation for three different sinusoidal excitations. Deviation is defined as e = θfoθro where θfo is the full-order response and θro is the output of the anytime or the buffered control system.

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Fig. 10

Average maximum controller deviations for three different sinusoidal excitations. Deviation is defined as e = θfo − θro where θfo is the full-order response and θro is the output of the anytime or the buffered control system.

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Fig. 5

Ensemble members with the worst case percent overshoot, (a) 46% for the buffered control and (b) 13% for the HF Anytime control; sampling period is T = 0.1 s

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Fig. 6

Average worst-case percent overshoot of response to two-cycle square wave reference signal, N = 300 runs, with bounds (vertical lines) showing one standard deviation. The standard deviation on the HF Anytime controller varies from 0.24% overshoot at 1% miss rate to 0.5% overshoot at miss rate of 9%.

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Fig. 11

Comparison of the standard deviations of the error signal for the parallel (a) HF Anytime controller and (b) LF Anytime controller. Simulation parameters are T = 0.1, N = 300, and d1 = 0% so stage 1 (gain alone) is always used.

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Fig. 14

Comparison of deviation from the full-order controller as measured by the average RMS deviation for the HF Anytime controller and the anytime controller from Ref. [7], d = [0, 10, 90]

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Fig. 12

Frequency response of the full-order compensator from Ref. [7] and HF Anytime controllers truncated to different stages from this paper

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Fig. 13

Sample responses to a square wave reference signal for (a) the HF Anytime controller and (b) anytime controller [7]

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