An Instrumental Variable Method for Continuous-Time Transfer Function Model Identification With Application to Controller Auto-Tuning

[+] Author and Article Information
Patrick J. Cunningham

Ray W. Herrick Laboratories, Purdue University, 140 South Intramural Drive, West Lafayette, IN 47907-2031pjcunnin@purdue.edu

Matthew A. Franchek

 University of Houston, 4800 Calhoun Road, Houston, TX 77204-4792mfranchek@uh.edu

J. Dyn. Sys., Meas., Control 129(2), 154-162 (Jul 14, 2006) (9 pages) doi:10.1115/1.2432359 History: Received November 15, 2004; Revised July 14, 2006

An instrumental variable algorithm is presented that estimates the coefficients of a continuous transfer function model directly from sampled data. The algorithm is based on instrumental variables extracted from an auxiliary model and input and output signal derivatives estimated by filtered difference equations. As a result, this method does not require any prior knowledge of the output noise. To ensure the validity of the filtered derivative estimates, a criterion based on the Nyquist frequency and the system bandwidth is established. Then the concept of asymptotic consistency is applied to the proposed instrumental variable algorithm to identify the conditions for convergence of the model parameter estimates. Specifically, the asymptotic consistency conditions impose a continuous and persistent exciting constraint on the input signal. This is analogous to the persistent excitation condition for identification of discrete models. The proposed instrumental variable algorithm is demonstrated within an auto-tuning algorithm for feedback controllers based on plant inversion. In this application, the algorithm is only suitable for lower-order transfer functions that are minimum-phase and stable. These types of systems are common in industrial applications for manufacturing and process control. Here, the algorithm is experimentally validated for automatic tuning of the idle speed controller on a 4.6L Ford V-8 spark ignition engine.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

True continuous-time system with output noise

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Figure 2

True system with auxiliary model running in parallel

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Figure 3

Dependence of difference equation derivative estimates on sample rate (solid line—ideal f′, ▵—1Hzf′ estimate, ◻—10Hzf′ estimate, ◇—100Hzf′ estimate, 엯—3dB deviation points)

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Figure 4

Second-order model and measured FRF with coherence (solid line—measured FRF; dashed line—second-order model)

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Figure 5

(Top) Cross-correlation between input and residue; (middle) residue auto-correlation; (bottom) residue auto-correlation near τ=0

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Figure 6

Sequence of open-loop step responses

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Figure 7

Identified parameter evolution

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Figure 8

Controller performance



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