A basic problem in the design of control systems is the lack of simple effective methods for designing decentralized control systems that are robust with respect to certain types of structural uncertainties. Here, we present one such design methodology that is based upon the Kalman–Yakubovich–Popov Lemma. Advantages of this approach include the ease with which output feedback controllers can be designed, and the fact that the design methodology and uncertainties are expressed using classical frequency domain notions. We use our design technique to obtain an integrated chassis controller for application to automotive dynamics.

Issue Section:
Research Papers
Keywords:
automobiles, control system synthesis, decentralised control, feedback, uncertain systems, vehicle dynamics, decentralized control, vehicle emulator, integrated chassis control, control system design methodology, robust control, Kalman-Yakubovich-Popov lemma, passivity, D-K iteration, block diagonal stability
Topics:
Control equipment, Design, Design methodology, Dynamics (Mechanics), Feedback, Stability, Vehicle dynamics, Vehicles, Control systems, Transfer functions

References

1.
Singh
,
M.
,
Decentralised Control
(
North-Holland
,
Amsterdam
, 1981).
2.
Shorten
,
R. N.
, and
Narendra
,
K. S.
, 2006, “
Strict Positive Realness and the Existence of Diagonal Lyapunov Functions
,”
45th IEEE Conference on Decision and Control
, pp.
2918
–
2923
.
3.
Solmaz
,
S.
, 2007, “
Topics in Automotive Rollover Prevention: Robust and Adaptive Switching Strategies for Estimation and Control
,” Ph.D. dissertation, NUI Maynooth, Ireland.
4.
Åström
,
K.
, and
Wittenmark
,
B.
, 1994,
Adaptive Control
,
Addison-Wesley Longman Publishing Co
,
Boston
.
5.
Safonov
,
M.
,
Ly
,
J.
, and
Chiang
,
R.
, 1993, “
μ-Synthesis Robust Control: What’s Wrong and How to Fix It?
,”
Proceedings of the 1993 IEEE Conference on Aerospace Control Systems
, CA.
6.
Villegas
,
C.
, 2009, Topics on Integrated Chassis Control, Ph.D. dissertation, NUI Maynooth, Ireland.
7.
Villegas
,
C.
,
Corless
,
M.
,
Shorten
,
R.
,
Readman
,
M.
, and
Solmaz
,
S.
, 2008, “
Decentralised Control Design of Lateral and Vertical Vehicle Dynamics Using Passivity
,”
79th Annual Meeting of the International Association of Applied Mathematics and Mechanics
, Bremen, Germany.
8.
Van de Vegte
,
J.
,
Feedback Control Systems
(
Prentice Hall
,
Englewoods Cliffs, NJ
, 1986).
9.
Shorten
,
R.
,
Curran
,
P.
,
Wulff
,
K.
, and
Zeheb
,
E.
, 2008, “
A Note on Spectral Conditions for Positive Realness of Transfer Function Matrices
,”
IEEE Trans. Autom. Control
,
53
(
5
), pp.
1258
–
1261
.
Crossref
Search ADS
 
10.
Villegas
,
C.
,
Readman
,
M.
,
Akar
,
M.
, and
Shorten
,
R.
, 2007,
Deliverable 21:Integrated Chassis Control
, CEmACS Project Final Report.
11.
Marriott
,
A. T.
,
Griffin
,
D. C.
, and
Lee
,
A. Y.
, 1995, “
A Variable Stability Test Vehicle for ITS Applications
,”
Future Transportation Technology Conference
, Vancouver, Canada, SAE Paper No. 961685.
12.
Ammon
,
D.
, 2004,
Künftige Fahrdynamik- und Assistenzsysteme — eine Vielzahl von Möglichkeiten und regelungstechnischen Herausforderungen, Steuerung und Regelung von Fahrzeugen und Motoren — AUTOREG 2004
,
Düsseldorf, Germany
.
13.
Lee
,
A. Y.
,
Marriott
,
A. T.
, and
Le
,
N. T.
, 1997, “
Variable Dynamic Testbed Vehicle: Dynamic Analysis
,
Proceedings of the 1997 SAE International Congress and Exposition
, SAE Paper No. 970560.
14.
Marriott
,
A. T.
, 1995, “
The Variable Dynamic Testbed Vehicle
,”
Proceedings of the 1995 SAE International Congress and Exposition
, SAE Paper No. 950032.
15.
Duplitzer
,
E.
, 1996,
Identifikation und Validierung einers Modells für ein Fahrzeug mit aktivem Fahrwerk
, Studienarbeit,
Universität Stuttgart/DaimlerBenz
.
16.
Eloian
,
E.
, 2004,
Control of Lateral Dynamics using Four-Wheel Steering
, Master’s thesis, FHT Esslingen/DaimlerChrysler AG, Esslingen.
17.
Villegas-Ramos
,
C.
, 2004, “
Influence of an Active Suspension System on the Lateral Dynamics of a Passenger Vehicle
,” Master’s thesis, CINVESTAV-IPN/DaimlerChrysler, Mexico city/Esslingen.
18.
Keppler
,
D.
, 2005,
Lenkungsemulation in einem Steer-by-Wire-Versuchsfahrzeug
. Diplomarbeit,
Universität Karlsruhe
.
19.
Gillespie
,
T. D.
, 1992,
Fundamentals of Vehicle Dynamics
,
SAE International
,
Warrendale, PA
.
20.
Lindholm
,
M.
, 2003, “
Side Wind Compensation Using Active Suspension
,” Master’s thesis, Linköpings universitet, Linköping, Sweden.
21.
Rau
,
M.
, 2007, Koordination aktiver Fahrwerk-Regelsysteme zur Beeinflussung der Querdynamik mittels Verspannungslenkung, Ph.D. dissertation, Universität Stuttgart, Stuttgart, Germany.
22.
Barreras
,
M.
,
Villegas
,
C.
,
Garcia-Sanz
,
M.
, and
Kalkkuhl
,
J.
, 2006, “
Robust QFT Tracking Controller Design for a car Equipped With 4-Wheel Steer-by-Wire
,”
Proceedings of the IEEE International Conference on Control Applications
, Munich, Germany.
23.
Akar
,
M.
, and
Kalkkuhl
,
J. C.
, 2008, “
An Integrated Chassis Controller for Automotive Vehicle Emulation
,”
17th World Congress of The International Federation of Automatic Control
, Seoul, Korea.
24.
Carlson
,
C.
, and
Gerdes
,
J.
, 2003, “
Optimal Rollover Prevention With Steer by Wire and Differential Braking
,”
Proceedings of IMECE
, pp.
16
–
21
.
25.
Solmaz
,
S.
,
Akar
,
M.
,
Shorten
,
R.
, and
Kalkkuhl
,
J.
, 2008, “
Realtime Multiple-Model Estimation of Center of Gravity Position in Automotive Vehicles
,”
Veh. Syst. Dyn.
46
(
9
), pp.
763
–
788
.
Crossref
Search ADS
 
26.
Mitschke
,
M.
, and
Wallentowitz
,
H.
,
Dynamik der Kraftfahrzeuge
(
Springer
,
Germany
, 2004).
27.
Glover
,
K.
, and
McFarlane
,
D.
, 1989, “
Robust Stabilization of Normalized Coprime Factor Plant Descriptions With H∞ -Bounded Uncertainty
,”
IEEE Trans. Autom. Control
,
34
(
8
), pp.
821
–
830
.
Crossref
Search ADS
 
28.
Vinnicombe
,
G.
, 1993, “
Frequency Domain Uncertainty and the Graph Topology
,”
IEEE Trans. Autom. Control
,
38
(
9
), pp.
1371
–
1383
.
Crossref
Search ADS
 
29.
Vinnicombe
,
G.
, 2001,
Uncertainty and Feedback: H∞ Loop-shaping and the ν-gap Metric
(
Imperial College Press
,
London
, 2001).
30.
Qiu
,
L.
 and
Davison
,
E. J.
, 1992, “
Feedback Stability Under Simultaneous Gap Metric Uncertainties in Plant and Controller
,”
Syst. Control Lett.
18
(
1
), pp.
9
–
22
.
31.
Griggs
,
W. M.
,
Lanzon
,
A.
, and
Anderson
,
B. D. O.
, 2009, “
A Test for stability Robustness of Linear Time-Varying Systems Utilizing the Linear Time-Invariant ν-Gap Metric
,”
Int. J. Robust Nonlinear Control
,
19
(
9
), pp.
986
–
1015
.
Crossref
Search ADS
 
32.
Khalil
,
H. K.
, 2002,
Nonlinear Systems
, 3rd ed.,
Prentice Hall
,
Englewood Cliffs, NJ
.
33.
Corless
,
M.
, and
Shorten
,
R.
, 2010, “
On the Characterization of Strict Positive Realness for General Matrix Transfer Functions
,”
IEEE Trans. Autom. Control
,
55
(
8
), pp.
1899
–
1904
.
Crossref
Search ADS
 
34.
Rantzer
,
A.
, 1996, “
On the Kalman-Yakubovich-Popov Lemma
,”
Syst. Control Lett.
,
28
(
1
), pp.
7
–
10
.
Crossref
Search ADS
 
35.
Boyd
,
S.
, El
Ghaoui
,
L.
,
Feron
,
E.
, and
Balakrishnan
,
V.
,1994,
Linear Matrix Inequalities in System and Control Theory
,
Society for Industrial and Applied Mathematics
,
PA
.
36.
Doyle
,
J.
, 1985, “
Structured Uncertainty in Control System Design
,”
Proceedings of 24th IEEE Conference on Decision and Control
, Vol.
24
.
37.
Zhou
,
K.
, and
Doyle
,
J. C.
,
Essentials of Robust Control
(
Prentice Hall
,
Englewoods Cliffs, NJ
, 1998).
38.
Skogestad
,
S.
, and
Postlethwaite
,
I.
, 2005,
Multivariable Feedback Control - Analysis and Design
, 2nd ed.,
John Wiley
,
West Sussex, England
.
39.
Haddad
,
W. M.
,
Collins
,
E. G.
, and
Moser
,
R.
, 1994, “
Structured Singular Value Controller Synthesis Using Constant D-Scales Without D-K Iteration
,”
American Control Conference
.
40.
Shamma
,
J. S.
,1994, “
Robust Stability With Time-Varying Structured Uncertainty
,”
IEEE Trans. Autom. Control
,
39
(
4
), pp.
714
–
724
.
Crossref
Search ADS
 
Copyright © 2012
 by American Society of Mechanical Engineers
You do not currently have access to this content.