A polynomial function supervising fuzzy sliding mode control (PSFαSMC), which embedded with skyhook surface method, is proposed for the ride comfort of a vehicle semi-active suspension. The multi-objective microgenetic algorithm (MOμGA) has been utilized to determine the PSFαSMC controller’s parameter alignment in a training process with three ride comfort objectives for the vehicle semi-active suspension, which is called the “offline” step. Then, the optimized parameters are applied to the real-time control process by the polynomial function supervising controller, which is named “online” step. A two-degree-of-freedom dynamic model of the vehicle semi-active suspension systems with the stability analysis is given for passenger’s ride comfort enhancement studies, and a simulation with the given initial conditions has been devised in MATLAB. The numerical results have shown that this hybrid control method is able to provide real-time enhanced level of reliable ride comfort performance for the semi-active suspension system.

References

References
1.
Yi
,
K.
,
Wargelin
,
M.
, and
Hedrick
,
K.
, 1993, “
Dynamic Tire Force Control by Semi-Active Suspensions
,”
ASME J. Dyn. Syst., Meas., Control
,
115
(
3
), pp.
465
474
.
2.
Karnopp
,
D. C.
,
Crosby
,
M. J.
, and
Harwood
,
R. A.
, 1974, “
Vibration Control Using Semi-Active Force Generators
,”
ASME J. Eng. Ind.
,
94
, pp.
619
626
.
3.
Jalili
,
N.
, 2002, “
A Comparative Study and Analysis of Semi-Active Vibration-Control Systems
,”
ASME J. Vibr. Acoust.
,
124
(
4
), pp.
593
605
.
4.
Stanway
,
R.
, 1996, “
The Development of Force Actuators using ER and MR Fluid Technology
,”
IEE Colloquium on Actuator Technology: Current Practice and New Developments
(Digest No: 1996/110), pp. 6/1–6/5.
5.
Spencer
,
B. F.
, Jr.
,
Dyke
,
S. J.
,
Sain
,
M. K.
, and
Carlson
,
J. D.
, 1997, “
Phenomenological Model of Magnetorheological Damper
,”
J. Eng. Mech.
,
123
(
3
), pp.
230
238
.
6.
Caracoglia
,
L.
, and
Jones
,
N.
, 2007, “
Passive Hybrid Technique for the Vibration Mitigation of Systems of Interconnected Stays
,”
J. Sound Vib.
,
307
(
3–5
), pp.
849
864
.
7.
Zhou
,
Q.
,
Nielsen
,
S.
, and
Qu
,
W.
, 2008, “
Semi-Active Control of Shallow Cables With Magnetorheological Dampers Under Harmonic Axial Support Motion
,”
J. Sound Vib.
,
311
(
3–5
), pp.
683
706
.
8.
Emelyanov
,
S. V.
, 1967,
Variable Structure Control Systems
,
Nauka
,
Moscow
(in Russian).
9.
Itkis
,
Y.
, 1976,
Control Systems of Variable Structure
,
Wiley
,
New York
.
10.
Utkin
,
V. A.
, 1978,
Sliding Modes and Their Application in Variable Structure Systems
,
Nauka
,
Moscow
(in Russian) (also Mir, Moscow, 1978, in English).
11.
Slotine
,
J. -J. E. E.
, and
Li
,
W.-P.
, 1991,
Applied Nonliear Control
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
12.
Hung
,
J. Y.
,
Gao
,
W.
, and
Hung
,
J. C.
, 1993, “
Variable Structure Control: A Survey
,”
IEEE Trans. Ind. Electron.
,
40
(
1
), pp.
2
22
.
13.
Zadeh
,
L. A.
, 1965, “
Fuzzy Sets
,”
Inf. Control
,
8
(
3
), pp.
338
353
.
14.
Ishigame
,
A.
,
Furukawa
,
T.
,
Kawamoto
,
S.
, and
Taniguchi
,
T.
, 1991, “
Sliding Mode Controller Design Based on Fuzzy Inference for Non-Linear System
,”
International Conference on Industrial Electronics, Control and Instrumentation
, Kobe, Japan, Oct. 28–Nov. 1, Vol.
3
, pp.
2096
2101
.
15.
Ishigame
,
A.
,
Furukawa
,
T.
,
Kawamoto
,
S.
, and
Taniguchi
,
T.
, 1993, “
Sliding Mode Controller Design Based on Fuzzy Inference for Nonlinear Systems
,”
IEEE Trans. Ind. Electron.
,
40
(
1
), pp.
64
70
.
16.
O’Dell
,
B.
, 1997, “
Fuzzy Sliding Mode Control: A Critical Review
,” Advanced Control Laboratory, Oklahoma State University, Technical Report ACL-97-001.
17.
Ng
,
K. C.
,
Li
,
Y.
,
Murray-Smith
,
D. J.
, and
Sharman
,
K. C.
, 1995, “
Genetic Algorithm Applied to Fuzzy Sliding Mode Controller Design
,”
First International Conference on Genetic Algorithms in Engineering Systems: Innovations and Applications, GALESIA
, Sep. 12–14, pp.
220
225
.
18.
Kung
,
C.
, and
Kao
,
W.
, 1998, “
GA-Based Grey Fuzzy Dynamic Sliding Mode Controller Design
,”
The 1998 IEEE International Conference on Fuzzy Systems Proceedings, IEEE World Congress on Computational Intelligence
,
Anchorage, AK
, Vol.
1
, pp.
583
588
.
19.
Chen
,
P. C.
,
Chen
,
C. W.
, and
Chiang
,
W. L.
, 2009, “
GA-Based Fuzzy Sliding Mode Controller for Nonlinear Systems
,”
Expert Sys. Applic.
,
36
(
3
), pp.
5872
5879
.
20.
Lo
,
J. C.
, and
Kuo
,
Y. H.
, 1998, “
Decoupled Fuzzy Sliding-Mode Control
,”
IEEE Trans. Fuzzy Syst.
,
6
, pp.
426
435
.
21.
Choi
,
B. J.
,
Kwak
,
S. W.
, and
Kim
,
B. K.
, 1999, “
Design of a Single-Input Fuzzy Logic Controller and Its Properties
,”
Fuzzy Sets Syst.
,
106
, pp.
299
308
.
22.
Kung
,
C.
,
Chen
,
T.
, and
Kung
,
L.
, 2005, “
Modified Adaptive Fuzzy Sliding Mode Controller for Uncertain Nonlinear Systems
,”
IEICE Trans. Fundamentals
,
E88-A
(
5
), pp.
1328
1334
.
23.
Wang
,
J.
,
Rad
,
A. B.
, and
Chan
,
P. T.
, 2001, “
Indirect Adaptive Fuzzy Sliding Mode Control: Part I: Fuzzy Switching
,”
Fuzzy Sets Syst.
,
122
(
1
), pp.
21
30
.
24.
Wang
,
C. H.
,
Liu
,
H. L.
, and
Lin
,
T. C.
, 2002, “
Direct Adaptive Fuzzy-Neural Control With State Observer and Supervisory Controller for Unknown Nonlinear Dynamical Systems
,”
IEEE Trans. Fuzzy Syst.
,
10
, pp.
39
49
.
25.
Yau
,
H. T.
, and
Chen
,
C. L.
, 2006, “
Chattering-Free Fuzzy Sliding-Mode Control Strategy for Uncertain Chaotic Systems
,”
Chaos, Solitons Fractals
,
30
, pp.
709
718
.
26.
Eksin
,
I.
,
Güzelkaya
,
M.
, and
Tokat
,
S.
, 2002, “
Self-Tuning Mechanism for Sliding Surface Slope Adjustment in Fuzzy Sliding Mode Controllers
,”
Proc. Inst. Mech. Eng., Part I: J. Syst. Control Eng.
,
216
(
5
), pp.
393
406
.
27.
Iglesias
,
E.
,
García
,
Y.
,
Sanjuan
,
M.
,
Camacho
,
O.
, and
Smith
,
C.
, 2007, “
Fuzzy Surface-Based Sliding Mode Control
,”
ISA Trans.
,
46
(
1
), pp.
73
83
.
28.
Roopaeia
,
M.
,
Zolghadrib
,
M.
, and
Meshksarc
,
S.
, 2009, “
Enhanced Adaptive Fuzzy Sliding Mode Control for Uncertain Nonlinear Systems
,”
Commun. Nonlinear Sci. Numer. Simul.
,
14
(
9–10
), pp.
3670
3681
.
29.
Holland
,
J.
, 1975,
Adaptation in Natural and Artificial Systems
,
University of Michigan Press
,
Ann Arbor, MI
.
30.
Chen
,
Y.
, and
Zhang
,
G.-F.
, 2012, “
Exchange Rates Determination Based on Genetic Algorithms Using Mendel’s Principles: Investigation and Estimation Under Uncertainty
,”
Inf. Fusion
, http://dx.doi.org/10.1016/j.inffus.2011.12.003
31.
Chen
,
Y.
, and
Song
,
Z.-J.
, 2012, “
Spatial Analysis for Functional Region of Suburban-Rural Area Using Micro Genetic Algorithm With Variable Population Size
,”
Expert Sys. Applic.
,
39
(
7
), pp.
6469
6475
.
32.
Chen
,
Y.
,
Ma
,
Y.
,
Lu
,
Z.
,
Peng
,
B.
, and
Chen
,
Q.
, 2011, “
Quantitative Analysis of Terahertz Spectra for Illicit Drugs Using Adaptive-Range Micro-Genetic Algorithm
,”
J. Appl. Phys.
,
110
(
4
), p.
044902
.
33.
Chen
,
Y.
,
Ma
,
Y.
,
Lu
,
Z.
,
Qiu
,
L.-X.
, and
He
,
J.
, 2011, “
Terahertz Spectroscopic Uncertainty Analysis for Explosive Mixture Components Determination Using Multi-Objective Micro Genetic Algorithm
,”
Adv. Eng. Software
,
42
(
9
), pp.
649
659
.
34.
Chen
,
Y.
,
Ma
,
Y.
,
Lu
,
Z.
,
Xia
,
Z.-N.
, and
Cheng
,
H.
, 2011, “
Chemical Components Determination via Terahertz Spectroscopic Statistical Analysis Using Micro Genetic Algorithm
,”
Opt. Eng.
,
50
(
3
), p.
034401
.
35.
Chen
,
Y.
, and
Cartmell
,
M. P.
, 2007, “
Multi-Objective Optimisation on Motorized Momentum Exchange Tether for Payload Orbital Transfer
,”
2007 IEEE Congress on Evolutionary Computation (CEC)
, Singapore, Sept. 25–28.
36.
Krishnakumar
,
K.
, 1989, “
Micro-Genetic Algorithms for Stationary and Non-Stationary Function Optimization
,”
Proc. SPIE
,
1196
, pp.
289
296
.
37.
Goldberg
,
D.
, 1989, “
Sizing Populations for Serial and Parallel Genetic Algorithms
,”
Proceedings of the Third International Conference on Genetic Algorithms
, San Mateo, CA, Vol.
1196
, pp.
70
79
.
38.
Ogata
,
K.
, 1996,
Modern Control Engineering
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
39.
Chen
,
Y.
, 2009, “
Skyhook Surface Sliding Mode Control on Semi-Active Vehicle Suspension Systems for Ride Comfort Enhancement
,”
Engineering
,
1
(
1
), pp.
23
32
.
40.
Chen
,
Y.
, and
Cartmell
,
M. P.
, 2009, “
Hybrid Fuzzy and Sliding-Mode Control for Motorised Tether Spin-Up When Coupled With Axial Vibration
,”
7th International Conference on Modern Practice in Stress and Vibration Analysis
, Sept. 8–10,
New Hall
,
Cambridge, UK
.
41.
Chen
,
Y.
, and
Cartmell
,
M. P.
, 2009, “
Hybrid Fuzzy Skyhook Surface Sliding Mode Control for Motorised Space Tether Spin-Up Coupled With Axial Oscillation
,”
Advanced Problems in Mechanics
, June 30–July 5,
Russian Academy of Sciences
,
St. Petersburg, Russia
.
42.
Chen
,
Y.
, and
Cartmell
,
M. P.
, 2010, “
Hybrid Sliding Mode Control for Motorised Space Tether Spin-Up When Coupled With Axial and Torsional Oscillation
,”
Astrophys. Space Sci.
,
326
(
1
), pp.
105
118
.
43.
Chen
,
Y.
, 2010,
Dynamical Modelling of Space Tether: Flexible Motorised Momentum Exchange Tether and Hybrid Fuzzy Sliding Mode Control for Spin-Up
,
LAP Lambert Academic Publishing AG & Co.
,
Saarbrucken, Germany
.
44.
Slotine
,
J. J. E.
, 1982, “
Tracking Control of Non-Linear Systems Using Sliding Surfaces With Application to Robot Manipulations
,” Ph.D. dissertation, Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA.
45.
Burns
,
R.
, 2001,
Advanced Control Engineering
,
Butterworth-Heinemann
,
Oxford
.
46.
Passino
,
K. M.
, and
Yurkovich
,
S.
, 1998,
Fuzzy Control
,
Addison Wesley Longman
,
Menlo Park, CA
.
47.
Mamdani
,
E. H.
, and
Assilian
,
S.
, 1975, “
An Experiment in Linguistic Synthesis With a Fuzzy Logic Controller
,”
Int. J. Man-Mach. Stud.
,
7
(
1
), pp.
1
13
.
48.
Mamdani
,
E. H.
, 1976, “
Advances in the Linguistic Synthesis of Fuzzy Controllers
,”
Int. J. Man-Mach. Stud.
,
8
(
1
), pp.
669
678
.
49.
Mamdani
,
E. H.
, 1977, “
Applications of Fuzzy Logic to Approximate Reasoning Using Linguistic Synthesis
,”
IEEE Trans. Comput.
,
26
(
12
), pp.
1182
1191
.
50.
Zadeh
,
L. A.
, 1973, “
Outline of a New Approach to the Analysis of Complex Systems and Decision Processes
,”
IEEE Trans. Syst. Man Cybern.
,
3
(
1
), pp.
28
44
.
51.
Chen
,
Y.
,
Fang
,
Z.
,
Luo
,
H.
, and
Deng
,
Z.
, 2004, “
Simulation Research on Real-Time Polynomial Function Supervising PID Control Based on Genetic Algorithms
,”
J. Syst. Simul.
,
16
(
6
), pp.
1171
1174
. Available at: http://www.cnki.com.cn/Article/CJFDTotal-XTFZ200406016.htmhttp://www.cnki.com.cn/Article/CJFDTotal-XTFZ200406016.htm
52.
Coello Coello
,
C. A.
, and
Pulido
,
G.
, 2001, “
A Micro-Genetic Algorithm for Multiobjective Optimization
,”
Proceedings of the Genetic and Evolutionary Computation Conference
, Springer-Verlag, pp.
126
140
.
53.
Lo
,
K. L.
, and
Khan
,
L.
, 2004, “
Hierarchical Micro-Genetic Algorithm Paradigm for Automatic Optimal Weight Selection in H Loop-Shaping Robust Flexible AC Transmission System Damping Control Design
,”
IEE Proc.: Gener. Transm. Distrib.
,
151
(
1
), pp.
109
118
.
54.
Tam
,
V.
,
Cheng
,
K. Y.
, and
Lui
,
K. S.
, 2006, “
Using Micro-Genetic Algorithms to Improve Localization in Wireless Sensor Networks
,”
J. Commun.
,
1
(
4
), pp.
1
10
.
55.
Davidyuk
,
O.
,
Selek
,
I.
,
Ceberio
,
J.
, and
Riekki
,
J.
, 2007, “
Application of Micro-Genetic Algorithm for Task Based Computing
,”
Proceeding of International Conference on Intelligent Pervasive Computing (IPC-07)
, Jeju Island, Korea, October, pp.
140
145
.
56.
Szőllős
,
A.
,
Šmíd
,
M.
, and
Hájek
,
J.
, 2009, “
Aerodynamic Optimization via Multi-Objective Micro-Genetic Algorithm With Range Adaptation, Knowledge-Based Reinitialization, Crowding and ɛ-Dominance
,”
Adv. Eng. Software
,
40
(
6
), pp.
419
430
.
57.
Deb
,
K.
, and
Goldberg
,
D. E.
, 1989, “
An Investigation of Niche and Species Formation in Genetic Function Optimization
,”
Proceedings of the Third International Conference on Genetic Algorithms
,
J. D.
Schaffer
, ed.,
Morgan Kauffman
,
San Mateo, CA
, pp.
42
50
.
58.
Goldberg
,
D.
, 1989,
Genetic Algorithms in Search, Optimization and Machine Learning
,
Kluwer Academic Publishers
,
Boston, MA
.
59.
Fonseca
,
C. M.
, and
Fleming
,
P. J.
, 1993, “
Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generalization
,”
Proceedings of the Fifth International Conference on Genetic Algorithms
,
S.
Forrest
, ed.,
Morgan Kauffman
,
San Mateo, CA
, pp.
416
423
.
60.
International Organization for Standardization, 1997, “
Mechanical Vibration and Shock—Evaluation of Human Exposure to Whole-Body Vibration—Part 1: General Requirements
,” ISO 2631-1:1997.
61.
Sayers
,
M. W.
, 1996, “
Interpretation of Road Roughness Profile Data
,” Final Report, Report No. UMTRI-96-19.
62.
Wei
,
L.
,
Fwa
,
T. F.
,
Asce
,
M.
, and
Zhe
,
Z.
, 2005, “
Wavelet Analysis and Interpretation of Road Roughness
,”
J. Transp. Eng.
,
131
(
2
), pp.
120
130
.
63.
International Organization for Standardization, 1995, “
Mechanical Vibration—Road Surface Profiles—Reporting of Measured Data
,” ISO 8608:1995.
64.
Wong
,
J. Y.
, 2001,
Theory of Ground Vehicles
,
3rd ed.
,
Wiley
,
New York
.
65.
International Organization for Standardization, 1982, “
Reporting Vehicle Road Surface Irregularities
,” ISO/TC108/SC2/WG4 N57.
66.
Elbeheiry
,
E. M.
, and
Karnopp
,
D. C.
, 1996, “
Optimal Control of Vehicle Random Vibration With Constrained Suspension Deflection
,”
J. Sound Vib.
,
189
(
5
), pp.
547
564
.
67.
Ramji
,
K.
,
Gupta
,
A.
,
Saran
,
V. H.
,
Goel
,
V. K.
, and
Kumar
,
V.
, 2004, “
Road Roughness Measurements Using PSD Approach
,”
J. Inst. Eng.
,
85
, pp.
193
201
.
68.
Liu
,
Y.
,
Matsuhisa
,
H.
, and
Utsuno
,
H.
, 2008, “
Semi-Active Vibration Isolation System With Variable Stiffness and Damping Control
,”
J. Sound Vib.
,
313
(
1–2
), pp.
16
28
.
69.
Rocquigny
,
E.
,
Devictor
,
N.
, and
Tarantola
,
S.
, 2008,
Uncertainty in Industrial Practice
,
Wiley
,
New York
.
70.
International Organisation for Standardisation, 2008, “
The Guide to the Expression of Uncertainty in Measurement (GUM)
,” ISO/IEC Guide 98-3:2008.
71.
Chen
,
Y.
, 2009, “
Simple Genetic Algorithm Laboratory Toolbox for MATLAB
,” http://www.mathworks.co.uk/matlabcentral/fileexchange/5882
72.
Choi
,
S.-K.
,
Grandhi
,
R. V.
, and
Canfield
,
R. A.
, 2007,
Reliability-Based Structural Design
,
Springer-Verlag
,
London
.
You do not currently have access to this content.