Optimal operation of continuously variable transmissions (CVTs) is essential to meet tightening emission and fuel consumption requirements. This is achieved by accurately tracking a prescribed transmission ratio reference and simultaneously optimizing the internal efficiency of the CVT. To reduce the power losses in a CVT, the absolute pressure levels are lowered, which increases the sensitivity to torque disturbances and increases the importance of disturbance feedforwards. This requires a high performance feedback controller for the hydraulic actuation system in a CVT. The aim of this paper is to develop a multivariable feedback controller for the hydraulic actuation system that is robust with respect to the varying system dynamics that are induced by the varying operating conditions, including transmission ratio changes. Hereto, new connections between system identification and robust control are exploited to achieve high performance. As a result, the varying system dynamics are directly evaluated in terms of closed-loop performance objectives. Subsequent robust control design reveals an increase of the control performance of almost a factor two in terms of the criterion value. This leads to improved simulated and measured closed-loop step responses, including a decrease in settling time from 0.4 s to 0.2 s. Finally, the designed robust controller is successfully validated in a standardized driving cycle experiment.

References

1.
Pfiffner
,
R.
, and
Guzzella
,
L.
,
2001
, “
Optimal Operation of CVT-Based Powertrains
,”
Int. J. Rob. Nonlinear Control
,
11
(
11
), pp.
1003
1021
.10.1002/rnc.642
2.
Liu
,
S.
, and
Paden
,
B.
,
1997
, “
A Survey of Today's CVT Controls
,”
Proceedings of 36th Conference Decision and Control
, pp.
4738
4743
.
3.
Lechner
,
G.
, and
Naunheimer
,
H.
,
1999
,
Automotive Transmissions: Fundamentals, Selection, Design and Application
,
Springer
,
Berlin, Germany
.
4.
Van der Sluis
,
F.
,
Van Dongen
,
T.
,
Van Spijk
,
G.-J.
,
Van der Velde
,
A.
, and
Van Heeswijk
,
A.
,
2006
, “
Fuel Consumption Potential of the Pushbelt CVT
,”
Proceedings of FISITA 2006 World Automotive Congress
, Paper No. F2006P218.
5.
Akehurst
,
S.
,
Vaughan
,
N. D.
,
Parker
,
D. A.
, and
Simner
,
D.
,
2004
, “
Modelling of Loss Mechanisms in a Pushing Metal V-Belt Continuously Variable Transmission. Part 1 - 3
,”
Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.)
,
218
(
11
), pp.
1269
1306
.10.1243/0954407042580020
6.
Bonsen
,
B.
,
Klaassen
,
T. W. G. L.
,
Pulles
,
R. J.
,
Simons
,
S. W. H.
,
Steinbuch
,
M.
, and
Veenhuizen
,
P. A.
,
2005
, “
Performance Optimisation of the Push-Belt CVT by Variator Slip Control
,”
Int. J. Veh. Des.
,
39
(
3
), pp.
232
256
.10.1504/IJVD.2005.008473
7.
Van der Noll
,
E.
,
Van der Sluis
,
F.
,
Van Dongen
,
T.
, and
Van der Velde
,
A.
,
2009
, “
Innovative Self-Optimising Clamping Force Strategy for the Pushbelt CVT
,”
SAE Int. J. Eng.
,
2
(
1
), pp.
1489
1498
.
8.
Van der Meulen
,
S.
,
de Jager
,
B.
,
Van der Noll
,
E.
,
Veldpaus
,
F.
,
Van der Sluis
,
F.
, and
Steinbuch
,
M.
,
2009
, “
Improving Pushbelt Continuously Variable Transmission Efficiency via Extremum Seeking Control
,”
Proceedings of 2009 Multi-Conference on Systems and Control
, pp.
357
362
.
9.
Van der Meulen
,
S.
,
de Jager
,
B.
,
Veldpaus
,
F.
,
Van der Noll
,
E.
,
Van der Sluis
,
F.
, and
Steinbuch
,
M.
,
2012
, “
Improving Continuously Variable Transmission Efficiency With Extremum Seeking Control
,”
IEEE Trans. Control Syst. Technol.
,
20
(
5
), pp.
1376
1383
.10.1109/TCST.2011.2160980
10.
Cheng
,
Y.
, and
De Moor
,
B. L. R.
,
1994
, “
Robustness Analysis and Control System Design for a Hydraulic Servo System
,”
IEEE Trans. Control Syst. Technol.
,
2
(
3
), pp.
183
197
.10.1109/87.317976
11.
Jelali
,
M.
, and
Kroll
,
A.
,
2003
, “
Hydraulic Servo-Systems: Modelling, Identification and Control
,”
Advances in Industrial Control
,
Springer-Verlag
,
London
.
12.
Van der Meulen
,
S.
,
Van Iperen
,
R.
,
de Jager
,
B.
,
Veldpaus
,
F.
,
Van der Sluis
,
F.
, and
Steinbuch
,
M.
,
2011
, “
A Validated Modular Model for Hydraulic Actuation in a Pushbelt Continuously Variable Transmission
,”
J. Dyn. Syst., Meas., Control
,
133
(
041004
), pp.
1
15
.10.1115/1.4003207
13.
Shafai
,
E.
,
Simons
,
M.
,
Neff
,
U.
, and
Geering
,
H. P.
,
1995
, “
Model of a Continuously Variable Transmission
,” Proceedings of IFAC 1st Workshop on Advances in Automotive Control,
U.
Kiencke
and
L.
Guzzella
, eds., pp.
105
113
.
14.
Zavarehi
,
M. K.
,
Lawrence
,
P. D.
, and
Sassani
,
F.
,
1999
, “
Nonlinear Modeling and Validation of Solenoid-Controlled Pilot-Operated Servovalves
,”
IEEE Trans. Mech.
,
4
(
3
), pp.
324
334
.10.1109/3516.789690
15.
Lin
,
S. J.
, and
Akers
,
A.
,
1989
, “
A Dynamic Model of the Flapper-Nozzle Component of an Electrohydraulic Servovalve
,”
J. Dyn. Syst., Meas., Control
,
111
(
1
), pp.
105
109
.10.1115/1.3153006
16.
Handroos
,
H. M.
, and
Vilenius
,
M. J.
,
1990
, “
The Utilization of Experimental Data in Modelling Hydraulic Single Stage Pressure Control Valves
,”
J. Dyn. Syst., Meas., Control
,
112
(
3
), pp.
482
488
.10.1115/1.2896168
17.
Lin
,
S. J.
, and
Akers
,
A.
,
1991
, “
Dynamic Analysis of a Flapper-Nozzle Valve
,”
J. Dyn. Syst., Meas., Control
,
113
(
1
), pp.
163
167
.10.1115/1.2896343
18.
Tsai
,
S. T.
,
Akers
,
A.
, and
Lin
,
S. J.
,
1991
, “
Modeling and Dynamic Evaluation of a Two-Stage Two-Spool Servovalve Used for Pressure Control
,”
J. Dyn. Syst., Meas., Control
,
113
(
4
), pp.
709
713
.10.1115/1.2896479
19.
Vaughan
,
N. D.
, and
Gamble
,
J. B.
,
1996
, “
The Modeling and Simulation of a Proportional Solenoid Valve
,”
J. Dyn. Syst., Meas., Control
,
118
(
1
), pp.
120
125
.10.1115/1.2801131
20.
Srivastava
,
N.
, and
Haque
,
I.
,
2009
, “
A Review on Belt and Chain Continuously Variable Transmissions (CVT): Dynamics and Control
,”
Mech. Mach. Theory
,
44
(
1
), pp.
19
41
.10.1016/j.mechmachtheory.2008.06.007
21.
Oomen
,
T.
, and
Bosgra
,
O.
,
2012
, “
System Identification for Achieving Robust Performance
,”
Automatica
,
48
(
9
), pp.
1975
1987
.10.1016/j.automatica.2012.06.011
22.
Skogestad
,
S.
, and
Postlethwaite
,
I.
,
2005
,
Multivariable Feedback Control: Analysis and Design
, 2nd ed.,
John Wiley & Sons
,
West Sussex, UK
.
23.
Van der Meulen
,
S.
,
de Jager
,
B.
,
Veldpaus
,
F.
, and
Steinbuch
,
M.
,
2010
, “
Combining Extremum Seeking Control and Tracking Control for High-Performance CVT Operation
,”
Proceedings of 49th Conference Decision and Control
, pp.
3668
3673
.
24.
McFarlane
,
D. C.
, and
Glover
,
K.
,
1990
,
Robust Controller Design Using Normalized Coprime Factor Plant Descriptions
, Vol.
138
of
LNCIS
.
Springer-Verlag, Berlin, Germany
.
25.
de Callafon
,
R. A.
, and
Van den Hof
,
P. M. J.
,
1997
, “
Suboptimal Feedback Control by a Scheme of Iterative Identification and Control Design
,”
Math. Mod. Syst.
,
3
(
1
), pp.
77
101
.
26.
Pintelon
,
R.
, and
Schoukens
,
J.
,
2012
,
System Identification: A Frequency Domain Approach
, 2nd ed.,
IEEE Press
,
New York, NY
.
27.
Schrama
,
R. J. P.
,
1992
, “
Accurate Identification for Control: The Necessity of an Iterative Scheme
,”
IEEE Trans. Autom. Control
,
37
(
7
), pp.
991
994
.10.1109/9.148355
28.
Douma
,
S. G.
, and
Van den Hof
,
P. M. J.
,
2005
, “
Relations Between Uncertainty Structures in Identification for Robust Control
,”
Automatica
,
41
(
3
), pp.
439
457
.10.1016/j.automatica.2004.11.005
29.
Oomen
,
T.
, and
Bosgra
,
O.
,
2008
, “
Estimating Disturbances and Model Uncertainty in Model Validation for Robust Control
,”
Proceedings of 47th Conference Decision Control
, pp.
5513
5518
.
30.
Oomen
,
T.
, and
Bosgra
,
O.
,
2009
, “
Well-Posed Model Uncertainty Estimation by Design of Validation Experiments
,”
15th IFAC Symposium System Identification
, pp.
1199
1204
.
31.
Smith
,
R. S.
, and
Doyle
,
J. C.
,
1992
, “
Model Validation: A Connection Between Robust Control and Identification
,”
IEEE Trans. Autom. Control
,
37
(
7
), pp.
942
952
.10.1109/9.148346
32.
Poolla
,
K.
,
Khargonekar
,
P.
,
Tikku
,
A.
,
Krause
,
J.
, and
Nagpal
,
K.
,
1994
, “
A Time-Domain Approach to Model Validation
,”
IEEE Trans. Autom. Control
,
39
(
5
), pp.
951
959
.10.1109/9.284871
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