In this note, a comprehensive analysis of tire damping effect on H2-optimal, multi-objective, and robust control of quarter-car suspensions excited by random road disturbances is provided. First, H2-optimal and convex multi-objective control problems are formulated and the latter problem is solved using linear matrix inequalities. Next, the multi-objective control problem is reformulated as a nonconvex and nonsmooth optimization problem with controller order restricted to be less than or equal to the quarter-car model order. For a range of orders, controllers are synthesized by using the HIFOO toolbox. Parametric studies of this note show that the effect of tire damping on the closed-loop performance of actively controlled suspension systems can be significant. Lastly, a robust controller with guaranteed performance over all polytopic suspension models with tire damping coefficient confined to a prescribed interval is synthesized.

1.
Thompson
,
A. G.
, 1970, “
Design of Active Suspensions
,”
Proc. Inst. Mech. Eng.
0020-3483,
185
, pp.
553
564
.
2.
Hrovat
,
D.
,
Margolis
,
D. L.
, and
Hubbard
,
M.
, 1988, “
An Approach Toward the Optimal Semi-Active Suspension
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
110
, pp.
288
296
.
3.
Yamashita
,
M.
,
Fujimori
,
K.
,
Hayakawa
,
K.
, and
Kimura
,
H.
, 1994, “
Application of H∞ Control to Active Suspension Systems
,”
Automatica
0005-1098,
30
, pp.
1717
1729
.
4.
Karnopp
,
D.
, 1995, “
Active and Semi-Active Vibration Isolation
,”
ASME J. Mech. Des.
0161-8458,
117
, pp.
177
185
.
5.
Alleyne
,
A.
, and
Hedrick
,
J. K.
, 1995, “
Nonlinear Adaptive Control of Active Suspensions
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
3
, pp.
94
101
.
6.
Hrovat
,
D.
, 1997, “
Survey of Advanced Suspension Developments and Related Optimal Control Applications
,”
Automatica
0005-1098,
33
, pp.
1781
1817
.
7.
Gaspar
,
P.
,
Szaszi
,
I.
, and
Bokor
,
J.
, 2003, “
Design of Robust Controllers for Active Vehicle Suspension Using the Mixed mu Synthesis
,”
Veh. Syst. Dyn.
0042-3114,
40
, pp.
193
228
.
8.
Karnopp
,
D.
, 1986, “
Theoretical Limitations in Active Suspensions
,”
Veh. Syst. Dyn.
0042-3114,
15
, pp.
41
54
.
9.
Hedrick
,
J. K.
, and
Butsuen
,
T.
, 1990, “
Invariant Properties of Automotive Suspensions
,”
Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.)
0954-4070,
204
, pp.
21
27
.
10.
Levitt
,
J. A.
, and
Zorka
,
N. G.
, 1991, “
Influence of Tire Damping in Quarter Car Active Suspension Models
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
113
, pp.
134
137
.
11.
Smith
,
M. C.
, 1995, “
Achievable Dynamic Response for Automotive Active Suspensions
,”
Veh. Syst. Dyn.
0042-3114,
24
, pp.
1
33
.
12.
Smith
,
M. C.
, and
Walker
,
G. W.
, 2000, “
Performance Limitations and Constraints for Active and Passive Suspensions: A Mechanical Multi-Port Approach
,”
Veh. Syst. Dyn.
0042-3114,
33
, pp.
137
168
.
13.
Türkay
,
S.
, and
Akçay
,
H.
, 2008, “
Aspects of Achievable Performance for Quarter-Car Active Suspensions
,”
J. Sound Vib.
0022-460X,
311
, pp.
440
460
.
14.
Akçay
,
H.
, and
Türkay
,
S.
, 2008, “
RMS Performance Limitations and Constraints for Quarter-Car Active Suspensions
,”
Proceedings of the 16th Mediterranean Conference on Control and Automation
, Ajaccio, France, pp.
425
430
.
15.
Lieh
,
J.
, 2009, “
Tire Damping Effect on Ride Quality of Vehicles with Active Control Suspensions
,”
ASME J. Vibr. Acoust.
0739-3717,
131
, p.
031011
.
16.
Akçay
,
H.
, and
Türkay
,
S.
, 2009, “
Influence of Tire Damping on Mixed H2/H∞ Synthesis of Half-Car Active Suspensions
,”
J. Sound Vib.
0022-460X,
322
, pp.
15
28
.
17.
Türkay
,
S.
, and
Akçay
,
H.
, 2010, “
Tire Damping Effect on H2 Optimal Control of Half-Car Active Suspensions
,”
ASME J. Vibr. Acoust.
0739-3717,
132
, p.
024502
.
18.
Chen
,
H.
, and
Guo
,
K. H.
, 2005, “
Constrained H∞ Control of Active Suspensions: An LMI Approach
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
13
, pp.
412
421
.
19.
Papageorgiou
,
C.
, and
Smith
,
M. C.
, 2006, “
Positive Real Synthesis Using Matrix Inequalities for Mechanical Networks: Application to Vehicle Suspension
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
14
, pp.
423
435
.
20.
Chen
,
H.
,
Sun
,
P. Y.
, and
Guo
,
K. H.
, 2003, “
A Multi-Objective Control Design for Active Suspensions with Hard Constraints
,”
Proceedings of American Control Conference
, Denver, CO, pp.
4371
4376
.
21.
Gao
,
H.
,
Lam
,
J.
, and
Wang
,
C.
, 2006, “
Multi-Objective Control of Vehicle Active Suspension Systems via Load-Dependent Controllers
,”
J. Sound Vib.
0022-460X,
290
, pp.
654
675
.
22.
Overton
,
M. L.
, “
HIFOO: H-Infinity Fixed Order Optimization: A Matlab Package for Fixed-Order Controller Design
,” http://www.cs.nyu.edu/overton/software/hifoohttp://www.cs.nyu.edu/overton/software/hifoo
23.
Gümüşsoy
,
S.
, and
Overton
,
M. L.
, 2008, “
Fixed-Order H∞ Controller Design with HIFOO, a Specialized Nonsmooth Optimization Package
,”
Proceedings of American Control Conference
, Seattle, WA, pp.
2750
2754
.
24.
Du
,
H.
,
Lam
,
J.
, and
Sze
,
K. Y.
, 2003, “
Non-Fragile Output Feedback H∞ Vehicle Suspension Control Using Genetic Algorithm
,”
Eng. Appl. Artif. Intell.
,
16
, pp.
667
680
.
25.
Waters
,
T. P.
,
Hyun
,
Y.
, and
Brennan
,
M. J.
, 2009, “
The Effect of Dual-Rate Suspension Damping on Vehicle Response to Transient Road Inputs
,”
ASME J. Vibr. Acoust.
0739-3717,
131
, p.
011004
.
26.
Sun
,
Y. Q.
, and
Cole
,
C.
, 2009, “
Finite Element Modeling and Analysis of Friction Wedge Damping During Suspension Bounce Modes
,”
ASME J. Vibr. Acoust.
0739-3717,
131
, p.
054504
.
27.
Vidyasagar
,
M.
, 1985,
Control System Synthesis: A Factorization Approach
,
MIT
,
Cambridge, MA
.
28.
Zhou
,
K.
,
Doyle
,
J. C.
, and
Glover
,
K.
, 1996,
Robust and Optimal Control
,
Prentice-Hall
,
Upper Saddle River, NJ
.
29.
Tuan
,
H. D.
,
Ono
,
E.
, and
Apkarian
,
P.
, 2001, “
Nonlinear H∞ Control for an Integrated Suspension System via Parameterized Linear Matrix Inequality Characterizations
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
9
, pp.
175
185
.
30.
Gahinet
,
P.
,
Nemirowski
,
A.
,
Laub
,
A. J.
, and
Chilali
,
M.
, 1995,
LMI Control Toolbox
,
1st ed.
,
Mathworks
,
Natick, MA
.
31.
Scherer
,
C.
,
Gahinet
,
P.
, and
Chilali
,
M.
, 1997, “
Multiobjective Output-Feedback Control via LMI Optimization
,”
IEEE Trans. Autom. Control
0018-9286,
42
, pp.
896
911
.
32.
Gümüşsoy
,
S.
,
Henrion
,
D.
,
Millstone
,
M.
, and
Overton
,
M. L.
, 2009, “
Multiobjective Robust Control With HIFOO 2.0
,”
IFAC Symposium Robust Control Design
, Haifa, Israel.
You do not currently have access to this content.