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Technical Briefs

Closed-Loop System Identification Based on Data Correlation

[+] Author and Article Information
Hassene Jammoussi

e-mail: hjammoussi@uh.edu

Karolos Grigoriadis

Department of Mechanical Engineering,
University of Houston,
Houston, TX 77204

Martin Books

Power Systems Controls,
Cummins Inc.,
Columbus, IN 47203

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 26, 2012; final manuscript received July 2, 2013; published online October 18, 2013. Assoc. Editor: Gregory Shaver.

J. Dyn. Sys., Meas., Control 136(1), 014507 (Oct 18, 2013) (10 pages) Paper No: DS-12-1319; doi: 10.1115/1.4025158 History: Received September 26, 2012; Revised July 02, 2013

A closed-loop system identification method is developed to estimate the parameters of a single input single output (SISO) linear time invariant system (LTI) operating within a feedback loop. The method uses the reference command in addition to the input–output data and establishes a correlation framework to structure the system. The correlation-based method is capable of delivering consistent estimates provided that the specific conditions on the signals are met. The method parallels the instrumental variables four step algorithm (IV4) and is comprised of three steps. First a model is estimated using cross correlation calculations between the reference input signal and the control and measured output signals. In the second step, a prefilter is identified to reduce estimation bias. In the final step, the prefilter, the instrumental variables and the measured signals are employed to estimate the final model. A consistency proof is provided for the proposed estimation process. The method is demonstrated on two examples. The first uses data collected from a diesel engine operation, and an open-loop model relating fueling to engine speed is sought. The identification process is complicated by the presence of nonmeasurable external torque disturbances and stochastic sensor noise. The second example uses data obtained from a time domain simulation of a closed-loop system where high levels of nonmeasured noise and disturbances were considered and a comparison with existing methods is made.

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Figures

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Fig. 1

Feedback control structure

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Fig. 2

Least squares estimation for G1 (q−1)

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Fig. 3

Estimation of filter F(q−1)

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Fig. 4

Estimation of the final model G2 (q−1)

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Fig. 5

Closed-loop engine system

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Fig. 6

Data collected from an off-highway Cummins-QSB engine

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Fig. 7

Predicted speed from proposed closed-loop identification versus measured speed

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Fig. 8

Evolution of the coefficients a1 and b1 in terms of the iterations

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Fig. 9

Collected data from the simulated closed-loop system

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Fig. 10

Predicted output from proposed closed-loop identification vs. other conventional methods

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Fig. 11

Bode plots of the exact model versus identified models from proposed IV3 algorithm and other conventional methods

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