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TECHNICAL PAPERS

Estimating Model Uncertainty using Confidence Interval Networks: Applications to Robust Control

[+] Author and Article Information
Gregory D. Buckner

Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695greg̱buckner@ncsu.edu

Heeju Choi, Nathan S. Gibson

Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695

J. Dyn. Sys., Meas., Control 128(3), 626-635 (Jul 20, 2005) (10 pages) doi:10.1115/1.2199855 History: Received October 10, 2003; Revised July 20, 2005

Robust control techniques require a dynamic model of the plant and bounds on model uncertainty to formulate control laws with guaranteed stability. Although techniques for modeling dynamic systems and estimating model parameters are well established, very few procedures exist for estimating uncertainty bounds. In the case of H control synthesis, a conservative weighting function for model uncertainty is usually chosen to ensure closed-loop stability over the entire operating space. The primary drawback of this conservative, “hard computing” approach is reduced performance. This paper demonstrates a novel “soft computing” approach to estimate bounds of model uncertainty resulting from parameter variations, unmodeled dynamics, and nondeterministic processes in dynamic plants. This approach uses confidence interval networks (CINs), radial basis function networks trained using asymmetric bilinear error cost functions, to estimate confidence intervals associated with nominal models for robust control synthesis. This research couples the “hard computing” features of H control with the “soft computing” characteristics of intelligent system identification, and realizes the combined advantages of both. Simulations and experimental demonstrations conducted on an active magnetic bearing test rig confirm these capabilities.

Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

The combat hybrid power system (CHPS) flywheel alternator, with “inside out” AMB

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Figure 2

Single-input, single-output AMB test rig

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Figure 3

Schematic of AMB test rig

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Figure 4

Control and system identification diagram

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Figure 5

Bode plot of identified 2nd-order model, with 99.9% confidence intervals

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Figure 6

Model validation results: Measured and K-step ahead predicted rotor displacements

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Figure 7

Additive (top) and multiplicative (bottom) model uncertainty

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Figure 8

H∞ control diagram, with weighting functions

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Figure 9

Weighing functions for nominal H∞ controller synthesis

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Figure 10

Tracking performance for nominal H∞ controller

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Figure 11

Position-normalized tracking performance for nominal H∞ controller versus setpoint

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Figure 12

Position-normalized tracking performance for nominal H∞ controller versus frequency

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Figure 13

Control and model error modeling diagram

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Figure 14

Model error model, with 99.9% confidence intervals

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Figure 15

Intelligent model error identification using a nonrecurrent RBFN

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Figure 16

RBFN estimate of average model error magnitude

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Figure 17

CIN estimate of uncertainty bound (99.9% confidence interval of model error magnitude)

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Figure 18

Uncertainty bound derived from MEM and CIN confidence intervals

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Figure 19

Frequency responses of nominal and identified controllers

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Figure 20

Tracking performance for nominal and identified H∞ controllers: 2.0×10−3m setpoint

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Figure 21

Tracking performance for nominal and identified H∞ controllers: 2.5×10−3m setpoint

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Figure 22

Tracking performance for nominal and identified H∞ controllers 1.5×10−3m setpoint

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