The problem considered in this paper is the design and analysis of control strategies for semiactive suspensions in road vehicles. The most commonly used control algorithm is the well-known sky-hook (SH) damping. Recently, a new control approach named acceleration driven damping (ADD) has been developed, using optimal-control theory. It has been shown that SH and ADD have complementary characteristics: SH provides large benefits around the body resonance; otherwise performs similarly to a passive suspension; instead, ADD provides large benefits beyond the body resonance. The first goal of this paper is to show that—in their specific frequency domains—SH and ADD provide quasi-optimal performances, namely, that it is impossible to achieve (with the same semi-active shock-absorber) better performances. This result has been obtained using the framework of the optimal predictive control, assuming full knowledge of the disturbance. This result is very interesting since it provides a lower-bound to semi-active suspension performances. The second goal of the paper is to develop a control algorithm which is able to mix the SH and ADD performances. This algorithm is surprisingly simple and provides quasi-optimal performances.

1.
Campi
,
M. C.
,
Lecchini
,
A.
, and
Savaresi
,
S. M.
, 2003, “
An Application of the Virtual Reference Feedback Tuning (VRFT) Method to a Benchmark Active Suspension System
,”
Eur. J. Control
0947-3580,
9
, pp.
66
76
.
2.
Caponetto
,
R.
,
Diamante
,
O.
,
Fargione
,
G.
,
Risitano
,
A.
, and
Tringali
,
D.
, 2003, “
A Soft Computing Approach to Fuzzy Sky-Hook Control of Semi-Active Suspension
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
11
(
6
), pp.
786
798
.
3.
Choi
,
S. B.
,
Choi
,
J. H.
,
Lee
,
Y. S.
, and
Han
,
M. S.
, 2003, “
Vibration Control of an ER Seat Suspension for a Commercial Vehicle
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
125
(
1
), pp.
60
68
.
4.
Choi
,
S. B.
,
Park
,
D. W.
, and
Suh
,
M. S.
, 2002, “
Fuzzy Sky-Ground Hook Control of a Tracked Vehicle Featuring Semi-Active Electrorheological Suspension Units
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
124
(
1
), pp.
150
157
.
5.
Fialho
,
I.
, and
Balas
,
G. J.
, 2002, “
Road Adaptive Active Suspension Design Using Linear Parameter-Varying Gain-Scheduling
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
10
, pp.
43
54
.
6.
Foo
,
E.
, and
Goodall
,
R. M.
, 2000, “
Active Suspension Control of Flexible-Bodied Railway Vehicles Using Electro-Hydraulic and Electro-Magnetic Actuators
,”
Control Eng. Pract.
0967-0661,
8
, pp.
507
518
.
7.
Fujimori
,
K.
,
Hayakawa
,
K.
,
Kimura
,
H.
,
Matsumoto
,
K.
,
Suzuki
,
Y.
, and
Yamashita
,
M.
, 1999, “
Robust H∞ Output Feedback Control of Decoupled Automobile Active Suspension Systems
,”
IEEE Trans. Autom. Control
0018-9286,
44
(
2
), pp.
392
396
.
8.
Giuia
,
A.
,
Seatzu
,
C.
, and
Usai
,
G.
, 1999, “
Semiactive Suspension Design With an Optimal Gain Switching Target
,”
Veh. Syst. Dyn.
0042-3114,
31
(
4
), pp.
213
232
.
9.
Hong
,
K. S.
,
Sohn
,
H. C.
, and
Hedrick
,
J. K.
, 2003, “
Modified Skyhook Control of Semi-Active Suspensions: A New Model, Gain Scheduling, and Hardware-in-the-Loop Tuning
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
124
(
1
), pp.
158
167
.
10.
Hrovat
,
D.
, 1997, “
Survey of Advanced Suspension Developments and Related Optimal Control Applications
,
Automatica
0005-1098,
33
(
10
), pp.
1781
1817
.
11.
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
.
12.
Kawabe
,
T.
,
Isobe
,
O.
,
Watanabe
,
Y.
,
Hanba
,
S.
, and
Miyasato
,
Y.
, 1998, “
New Semi-Active Suspension Controller Design Using Quasi-Linearization and Frequency Shaping
,”
Control Eng. Pract.
0967-0661,
6
(
10
), pp.
1183
1191
.
13.
Kitching
,
K. J.
,
Cole
,
D. J.
, and
Cebon
,
D.
, 2000, “
Performance of a Semi-Active Damper for Heavy Vehicles
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
122
(
3
), pp.
498
506
.
14.
Nakai
,
H.
,
Oosaku
,
S.
, and
Motozono
,
Y.
, 2000, “
Application of Practical Observer to Semi-Active Suspensions
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
122
(
2
), pp.
284
289
.
15.
Sammier
,
D.
,
Sename
,
O.
, and
Dugard
,
L.
, 2001, “
Comparison of Skyhook and H∞ Control Applied on a Quarter-Car Suspension Model
,” 3rd IFAC Workshop on Advances in Automotive Control, pp.
107
112
.
16.
Sammier
,
D.
,
Sename
,
O.
, and
Dugard
,
L.
, 2003, “
Skyhook and H∞ Control of Semi-Active Suspensions: Some Practical Aspects
,”
Veh. Syst. Dyn.
0042-3114,
39
(
4
), pp.
279
308
.
17.
Savaresi
,
S. M.
,
Silani
,
E.
, and
Bittanti
,
S.
, 2005, “
Acceleration-Driven-Damper (ADD): An Optimal Control Algorithm for Comfort-Oriented Semi-Active Suspensions
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
127
(
2
), pp.
218
229
.
18.
Silani
,
E.
,
Fischer
,
D.
,
Savaresi
,
S. M.
,
Kaus
,
E.
, and
Isermann
,
R.
, 2004, “
Fault-Tolerant Filtering in Active Vehicle Suspensions
,” FISITA World Automotive Congress, Barcelona, Spain.
19.
Silani
,
E.
,
Savaresi
,
S. M.
,
Bittanti
,
S.
,
Fischer
,
D.
, and
Isermann
,
R.
, 2004, “
Managing Information Redundancy for the Design of Fault-Tolerant Slow-Active Controlled Suspension
,”
Tire Technology International
,
2004
, pp.
128
133
.
20.
Silani
,
E.
,
Savaresi
,
S. M.
,
Bittanti
,
S.
,
Visconti
,
A.
, and
Farachi
,
F.
, 2003, “
The Concept of Performance-Oriented Yaw-Control Systems: Vehicle Model and Analysis
,”
SAE Trans.
0096-736X,
2002
, pp.
1808
1818
.
21.
Valtolina
,
E.
,
Savaresi
,
S. M.
,
Bittanti
,
S.
,
Visconti
,
A.
, and
Longhi
,
A.
, 2001, “
A Co-ordinate Approach for the Control of Road Vehicles
,” 6th European Control Conference, Porto, Portugal, pp.
629
634
.
22.
Williams
,
R. A.
, 1997, “
Automotive Active Suspensions Part 1: Basic Principles
,”
IMechE Conf. Trans.
1356-1448,
211
, Part D, pp.
415
426
.
23.
Williams
,
R. A.
, 1997, “
Automotive Active Suspensions Part 2: Practical Considerations
,”
IMechE Conf. Trans.
1356-1448,
211
, Part D, pp.
427
444
.
24.
Yoshida
,
K.
, and
Okamoto
,
B.
, 1999, “
Bilinear Disturbance-Accommodating Optimal Control of Semi-Active Suspension for Automobiles
,” IEEE International Conference on Control Applications, pp.
1496
1501
.
25.
Active Shock Inc.
, 2005, Semi-Active Shock Absorber Control System, U.S. Patent No. 6,904,344.
26.
Ahmadian
,
M.
,
Reichert
,
B. A.
, and
Song
,
X.
, 2001, “
System Nonlinearities Induced by Skyhook Dampers
,”
Shock Vib.
1070-9622,
8
(
2
), pp.
95
104
.
27.
Atsugi Unisia Corporation
, 1992, “
Semi-Active Suspension Control System With Reduced Switching Frequency in Hard and Soft Suspension Characteristics
,” U.S. Patent No. 5,088,760.
28.
Bieber
,
M.
,
Mackool
,
S. M.
, and
Rhode
,
D. S.
, 1999, “
Vehicle Suspension Control Systems
, U.S. Patent No. 5,864,768.
29.
Fischer
,
D.
, and
Isermann
,
R.
, 2003, “
Mechatronic Semi-Active and Active Vehicle Suspensions
,”
Control Eng. Pract.
0967-0661,
12
(
11
), pp.
1353
1367
.
30.
General Motors Corporation
, 1991, “
On/Off Semi-Active Suspension Control
,” U.S. Patent No. 5,062,657.
31.
Lord Corporation
, 2001, “
Adaptive Off-State Control Method
, U.S. Patent No. 6,311,110.
32.
Lord Corporation
, 2000, “
No-Jerk Semi-Active Skyhook Control Method and Apparatus
,” U.S. Patent No. 6,115,658.
33.
Savaresi
,
S. M.
,
Silani
,
E.
,
Bittanti
,
S.
, and
Porciani
,
N.
, 2003, “
On Performance Evaluation Methods and Control Strategies for Semi-Active Suspension Systems
,” 42nd Control and Decision Conference, Maui, Hawaii, pp.
2264
2269
.
34.
Spencer
,
B. F.
Jr.
,
Dyke
,
S. J.
,
Sain
,
M. K.
, and
Carlson
,
J. D.
, 2003, “
Phenomenological Model of a Magnetorheological Damper
,” ASCE
J. Eng. Mech.
0733-9399,
123
(
3
), pp.
230
238
.
35.
Tseng
,
H. E.
, and
Hedrick
,
J. K.
, 1994, “
Semi-Active Control Laws—Optimal and Sub-Optimal
,”
Veh. Syst. Dyn.
0042-3114,
23
, pp.
545
569
.
36.
Valasek
,
M.
,
Kortum
,
W.
,
Sika
,
Z.
,
Magdolen
,
L.
, and
Vaculin
,
O.
, 1998, “
Development of Semi-Active Road-Friendly Truck Suspensions
,”
Control Eng. Pract.
0967-0661,
6
, pp.
735
744
.
37.
Ahmadian
,
M.
, and
Song
,
X.
, 1999, “
A Non-Parametric Model for Magneto-Rheological Dampers
,”
Proceedings of 1999 ASME Design Engineering Technical Conference
, Las Vegas, Nevada.
38.
Savaresi
,
S. M.
,
Bittanti
,
S.
, and
Montiglio
,
M.
, 2005, “
Identification of Semi-Physical and Black-Box Non-Linear Models: The Case of MR-Dampers for Vehicles Control
,”
Automatica
0005-1098,
41
, pp.
113
117
.
39.
Bertsekas
,
D. P.
, 2000,
Dynamic Programming and Optimal Control
,
2nd ed.
,
Athena Scientific
.
40.
Bosch
,
, 2000,
Automotive Handbook
,
5th ed.
,
BOSCH Gmbh
.
41.
Gillespie
,
T. D.
, 1992, “
Fundamentals of Vehicle Dynamics
, Society of Automotive Engineers Inc.
42.
Isermann
,
R.
, 2003,
Mechatronic Systems: Fundamentals
,
Springer Verlag
, UK.
43.
Kiencke
,
U.
, and
Nielsen
,
L.
, 2000,
Automotive Control Systems for Engine, Driveline, and Vehicle
,
Springer Verlag
.
44.
Guardabassi
,
G. O.
, and
Savaresi
,
S. M.
, 1997, “
Approximate Feedback Linearization of Discrete-Time Non-Linear Systems Using Virtual Input Direct Design
,”
Syst. Control Lett.
0167-6911,
32
, pp.
63
74
.
45.
Guzzella
,
L.
, and
Isidori
,
A.
, 1993, “
On Approximate Linearization of Nonlinear Control Systems
,
Int. J. Robust Nonlinear Control
1049-8923,
3
, pp.
261
276
.
46.
Nijmeijer
,
H.
, and
Savaresi
,
S. M.
, 1998, “
On Approximate Model-Reference Control of SISO Discrete-Time Nonlinear Systems
,”
Automatica
0005-1098,
34
(
10
), pp.
1261
1266
.
47.
Savaresi
,
S. M.
, and
Guardabassi
,
G. O.
, 1998, “
Approximate I/O Feedback Linearization of Discrete-Time Non-Linear Systems via Virtual Input Direct Design
,”
Automatica
0005-1098,
34
(
6
), pp.
715
722
.
48.
Savkin
,
A. V.
, and
Evans
,
R. J.
, 2002,
Hybrid Dynamical Systems
,
Birkhauser
.
49.
Guardabassi
,
G. O.
, and
Savaresi
,
S. M.
, 2001, “
Approximate Linearization via Feedback—an Overview
,”
Automatica
0005-1098,
27
, pp.
1
15
.
50.
Bittanti
,
S.
, and
Savaresi
,
S. M.
, 2000, “
On the Parametrization and Design of an Extended Kalman Filter Frequency Tracker
,”
IEEE Trans. Autom. Control
0018-9286,
45
(
9
), pp.
1718
1724
.
51.
Pintelon
,
R.
, and
Schoukens
,
J.
, 2001,
System Identification: A Frequency Domain Approach
,
IEEE
, New York.
52.
Savaresi
,
S. M.
,
Bitmead
,
R.
, and
Dunstan
,
W.
, 2001, “
Nonlinear System Identification Using Closed-Loop Data With no External Excitation: The Case of a Lean Combustion Process
,”
Int. J. Control
0020-7179,
74
, pp.
1796
1806
.
53.
Savaresi
,
S. M.
,
Taroni
,
F.
,
Previdi
,
F.
, and
Bittanti
,
S.
, 2004, “
Control System Design on a Power-Split CVT for High-Power Agricultural Tractors
,”
IEEE/ASME Trans. Mechatron.
1083-4435,
9
(
3
), pp.
569
579
.
54.
Schoukens
,
J.
,
Pintelon
,
R.
,
Rolain
,
Y.
, and
Dobrowiecki
,
T.
, 2001, “
Frequency Response Function Measurements in the Presence of Nonlinear Distortions
,”
Automatica
0005-1098,
37
, pp.
939
946
.
55.
Stack
,
A. J.
, and
Doyle
,
F. J.
III
, 1995, “
A Measure for Control Relevant Nonlinearity
,” American Control Conference, Seattle, pp.
2200
2204
.
56.
Gelb
,
A.
, and
Van der Velde
,
W. E.
, 1968,
Multiple-Input Describing Functions and Nonlinear System Design
,
McGraw-Hill
, New York.
57.
Reed
,
D. H.
, and
Radcliffe
,
S. T.
, 1991, “
Output Filter and Method for On/Off Semi-Active Suspension System
,” U.S. Patent No. 5,024,460.
58.
Levine
,
W. S.
, 1996,
The Control Handbook
,
IEEE
.
59.
Robson
,
J. D.
, and
Dodds
,
C. J.
, 1970, “
The Response of Vehicle Component to Random Road-Surface Undulations
,” 13th FISITA Congress, Brussels, Belgium.
60.
Fu-Cheng
,
W.
, and
Smith
,
M. C.
, 2002, “
Controller Parameterization for Disturbance Response Decoupling: Application to Vehicle Active Suspension Control
,”
IEEE Trans. Control Syst. Technol.
1063-6536,
10
(
3
), pp.
393
407
.
You do not currently have access to this content.