This work uses a new method of determining a parameterization, resampling, and dimension search of an uncertainty model that can be used for efficient engineering models in control design. An algorithm using the Cayley–Menger determinant as a measure of the dimension test geometry (volume/area/length) of the parametric data points is presented to search for a reduced number of dimensions that can be used to represent the parameters of a model that captures the uncertainty in a dynamic system (uncertainty model). A genetic algorithm (GA) is utilized to solve the nonconvex problem of finding the coefficients of a parameterization of the uncertainty model. A resampling approach for the uncertainty model is also presented. The methods presented here are demonstrated on an electrohydraulic valve control system problem. This demonstration includes consideration of the dimensional search, data resampling, and parameterizing of an uncertainty class determined from test data for 30 replications of an electrohydraulic flow control valve which were experimentally modeled in the lab. The suggested resampling method and the parameterization of the uncertainty are used to analyze the robust stability of a control system for the class of valves using both frequency domain h-infinity methods and analysis of closed-loop poles for the resampled uncertainty model.

References

References
1.
Skogestad
,
S.
, and
Postlethwaite
,
I.
,
2005
,
Multivariable Feedback Control
,
Wiley
,
West Sussex, UK
.
2.
Carpenter
,
R.
, and
Fales
,
R.
,
2012
, “
Mixed Sensitivity H-Infinity Control Design With Frequency Domain Uncertainty Modeling for a Pilot Operated Proportional Control Valve
,”
ASME
Paper No. DSCC2012-MOVIC2012-8845.
3.
Sepasi
,
M.
,
Sassani
,
F.
, and
Nagamune
,
R.
,
2010
, “
Parameter Uncertainty Modeling Using the Multidimensional Principal Curves
,”
ASME J. Dyn. Syst., Meas., Control
,
132
(
5
), p.
054501
.
4.
Conway
,
R.
,
Felix
,
S.
, and
Horowitz
,
R.
,
2007
, “
Model Reduction and Parametric Uncertainty Identification for Robust H 2 Control Synthesis for Dual-Stage Hard Disk Drives
,”
IEEE Trans. Magn.
,
43
(
9
), pp.
3763
3768
.
5.
Yazdi
,
E. A.
,
Sepasi
,
M.
,
Sassani
,
F.
, and
Nagamune
,
R.
,
2011
, “
Automated Multiple Robust Track-Following Control System Design in Hard Disk Drives
,”
IEEE Trans. Control, Syst. Technol.
,
19
(
4
), pp.
920
928
.
6.
Sandu
,
A.
,
Sandu
,
C.
, and
Ahmadian
,
M.
,
2006
, “
Modeling Multibody Systems With Uncertainties. Part I: Theoretical and Computational Aspects
,”
Multibody Syst. Dyn.
,
15
(
4
), pp.
369
391
.
7.
Micó
,
M. L.
,
Oncina
,
J.
, and
Vidal
,
E.
,
1994
, “
A New Version of the Nearest-Neighbour Approximating and Eliminating Search Algorithm (AESA) With Linear Preprocessing Time and Memory Requirements
,”
Pattern Recognit. Lett.
,
15
(
1
), pp.
9
17
.
8.
Nene
,
S. A.
, and
Nayar
,
S. K.
,
1997
, “
A Simple Algorithm for Nearest Neighbor Search in High Dimensions
,”
IEEE Trans. Pattern Anal. Mach. Intell.
,
19
(
9
), pp.
989
1003
.
9.
Rizvi
,
S. Z.
,
Mohammadpour
,
J.
,
Tóth
,
R.
, and
Meskin
,
N.
,
2016
, “
A Kernel-Based PCA Approach to Model Reduction of Linear Parameter-Varying Systems
,”
IEEE Trans. Control Syst. Technol.
,
24
(
5
), pp.
1883
1891
.
10.
Kang
,
Z.
,
Kazem
,
B. I.
, and
Fales
,
R. C.
, 2015, “
Parameterized Uncertainty Model Using a Genetic Algorithm With Application to an Electro-Hydraulic Valve Control System
,”
ASME
Paper No. DSCC2015-9994.
11.
Sippl
,
M. J.
, and
Scheraga
,
H. A.
,
1986
, “
Cayley-Menger Coordinates
,”
Proc. Natl. Acad. Sci.
,
83
(
8
), pp.
2283
2287
.
12.
Clegg
,
J.
,
Dawson
,
J. F.
,
Porter
,
S. J.
, and
Barley
,
M. H.
,
2005, “
The Use of a Genetic Algorithm to Optimize the Functional Form of a Multi-Dimensional Polynomial Fit to Experimental Data
,”
IEEE
Congress on Evolutionary Computation,
Edinburgh, Scotland, Sept. 2–5, pp.
928
934.
13.
Gulsen
,
M.
,
Smith
,
A.
, and
Tate
,
D.
,
1995
, “
A Genetic Algorithm Approach to Curve Fitting
,”
Int. J. Prod. Res.
,
33
(
7
), pp.
1911
1923
.
14.
Carpenter
,
R.
, and
Fales
,
R.
,
2012
, “
Proportional Control System Design and Probability of Stability for a Pilot Operated Proportional Valve With Parametric Uncertainty
,”
Symposium on Fluid Power and Motion Control, Bath
, UK, pp. 347–362.
15.
Bowman
,
A. W.
, and
Azzalini
,
A.
,
1997
,
Applied Smoothing Techniques for Data Analysis: The Kernel Approach With S-plus Illustrations
,
Oxford Science Publications
,
Oxford, UK
.
16.
Wolfram
,
2018
, “
SmoothKernelDistribution
,” Mathematica, Champaign, IL, accessed, June 10, 2018, http://reference.wolfram.com/language/ref/SmoothKernelDistribution.html
17.
Fales
,
R.
,
2010
, “
Uncertainty Modeling and Predicting the Probability of Stability and Performance in the Manufacture of Dynamic Systems
,”
ISA Trans.
,
49
(
4
), pp.
528
534
.
You do not currently have access to this content.