Abstract

This paper analyzes the dynamic effects of an electrohydraulic drive that uses a counterbalance valve for rod volume compensation. It shows that local stability analysis is not sufficient in this particular case to get general statements of the system's chattering properties. A reduced-order switched system is proposed to gain deeper insights in system dynamics with saturation effects such as the end-stop of a valve poppet and solutions are compared numerically to the full-system dynamics which incorporates pressure built-up, piston, and valve dynamics as well as motor dynamics. It is shown that in cases of, e.g., fast valves with small cracking pressures undesirable chattering of the full system exists which can be easily understood in terms of the reduced-order system in form of sliding mode solutions. The paper also describes under which conditions such sliding modes exist, how they behave, and how they can be interpreted in terms of the full system.

References

1.
Padovani
,
D.
,
Rundo
,
M.
, and
Altare
,
G.
,
2020
, “
The Working Hydraulics of Valve-Controlled Mobile Machines: Classification and Review
,”
ASME. J. Dyn. Sys., Meas., Control
,
142
(
7
), p.
070801
.10.1115/1.4046334
2.
Agostini
,
T.
,
De Negri
,
V.
,
Minav
,
T.
, and
Pietola
,
M.
,
2020
, “
Effect of Energy Recovery on Efficiency in Electro-Hydrostatic Closed System for Differential Actuator
,”
Actuators
,
9
(
1
), p.
12
.10.3390/act9010012
3.
Zhang
,
S.
,
Li
,
S.
, and
Minav
,
T.
,
2020
, “
Control and Performance Analysis of Variable Speed Pump-Controlled Asymmetric Cylinder Systems Under Four-Quadrant Operation
,”
Actuators
,
9
(
4
), p.
123
.10.3390/act9040123
4.
Michel
,
S.
, and
Weber
,
J.
,
2012
, “
Energy-Efficient Electrohydraulic Compact Drives for Low Power Applications
,”
ASME Paper No.
93.
5.
Ivantysynova
,
M.
,
2000
, “
Displacement Controlled Linear and Rotary Drives for Mobile Machines With Automatic Motion Control
,”
SAE
Paper No. 2000-01-2562.10.4271/2000-01-2562
6.
Huang
,
J.
,
Yan
,
Z.
,
Quan
,
L.
,
Lan
,
Y.
, and
Gao
,
Y.
,
2015
, “
Characteristics of Delivery Pressure in the Axial Piston Pump With Combination of Variable Displacement and Variable Speed
,”
Proc. Inst. Mech. Eng., Part I: J. Syst. Control Eng.
,
229
(
7
), pp.
599
613
.10.1177/0959651815578967
7.
Rahmfeld
,
R.
,
2002
,
Development and Control of Energy Saving Hydraulic Servo Drives for Mobile Systems, Fortschrittberichte VDI/12: Verkehrstechnik, Fahrzeugtechnik
,
VDI–Verlag
, Düsseldorf, Germany.
8.
Schmidt
,
L.
,
Roemer
,
D. B.
,
Pedersen
,
H. C.
, and
Andersen
,
T. O.
,
2015
, “
Speed–Variable Switched Differential Pump System for Direct Operation of Hydraulic Cylinders
,”
ASME
Paper No. FPMC2015-9575.10.1115/FPMC2015-9575
9.
Ritelli
,
G. F.
, and
Vacca
,
A.
,
2013
, “
Energetic and Dynamic Impact of Counterbalance Valves in Fluid Power Machines
,”
Energy Convers. Manage.
,
76
, pp.
701
711
.10.1016/j.enconman.2013.08.021
10.
Eaton Counterbalance Valves
,
2018
, “
How to Select a Counterbalance Valve
,” Eaton, accessed June 5, 2021, www.eaton.com
11.
Bosch Rexroth Oil Control S.p.A.
,
2018
, “
Counterbalance Valves
,” Bosch, accessed June 5, 2021, www.boschrexroth.com
12.
Hansen
,
M.
,
Andersen
,
T.
,
Pedersen
,
P.
, and
Conrad
,
F.
,
2004
, “
Design of Over Center Valves Based on Predictable Performance
,”
ASME
Paper No. IMECE2004-61654.10.1115/IMECE2004-61654
13.
Miyakawa
,
S.
,
1978
, “
Stability of a Hydraulic Circuit With a Counter-Balance Valve
,”
Bull. JSME
,
21
(
162
), pp.
1750
1756
.
14.
Yeming
,
Y.
,
Zhou
,
H.
,
Chen
,
Y.
, and
Yang
,
H.
,
2014
, “
Stability Analysis of a Pilot Operated Counterbalance Valve for a Big Flow Rate
,”
ASME Paper No. FPMC2014-7806.
10.1115/FPMC2014-7806
15.
Zagar
,
P.
, and
Scheidl
,
R.
,
2020
, “
On the Use of Singular Perturbation Based Model Hierarchies of an Electrohydraulic Drive for Virtualization Purposes
,”
Proceedings of the 12 International Fluid Power Conference
, Vol.
2
, Oct. 12–14, Dresden, pp.
45
53
.
16.
Osterland
,
S.
, and
Weber
,
J.
,
2019
, “
Analytical Analysis of Single-Stage Pressure Relief Valves
,”
Int. J. Hydromechatronics
,
2
(
1
), pp.
32
53
.10.1504/IJHM.2019.098951
17.
Mayo-Maldonado
,
J. C.
, and
Rapisarda
,
P.
,
2014
, “
Modeling of Switching Dynamics in Electrical Systems
,”
Proceedings of 21st International Symposium on Mathematical Theory of Networks and Systems
, The Netherlands, Groningen, Nov. 7, pp.
985
992
.
18.
Utkin
,
V. I.
,
1993
, “
Sliding Mode Control Design Principles and Applications to Electric Drives
,”
IEEE Trans. Ind. Electron.
,
40
(
1
), pp.
23
36
.10.1109/41.184818
19.
Cristiano
,
R.
,
Ponce
,
E.
,
Pagano
,
D.
, and
Granzotto
,
M.
,
2019
, “
On the Teixeira Singularity Bifurcation in a DC–DC Power Electronic Converter
,”
Nonlinear Dyn.
,
96
(
2
), pp.
1243
1266
.10.1007/s11071-019-04851-8
20.
Liberzon
,
D.
,
2003
,
Switching in Systems and Control
,
Springer Science & Business Media
, Birkhäuser, Boston.
21.
Liscko
,
G.
,
Champneys
,
A.
, and
Hos
,
C.
,
2009
, “
Nonlinear Analysis of a Single Stage Pressure Relief Valve
,”
IAENG Int. J. Appl. Math.
,
39
(
4
), p. 12.
22.
Akhmet
,
M.
, and
Çağ
,
S.
,
2017
, “
Chattering as a Singular Problem
,”
Nonlinear Dyn.
,
90
(
4
), pp.
2797
2812
.10.1007/s11071-017-3840-3
23.
Schmidt
,
L.
,
Andersen
,
T. O.
, and
Pedersen
,
H. C.
,
2013
, “
Robust Non-Chattering Observer Based Sliding Control Concept for Electro-Hydraulic Drives
,”
IFAC Proc. Vols.
,
46
(
5
), pp.
99
108
.10.3182/20130410-3-CN-2034.00041
24.
Schmidt
,
L.
, and
Andersen
,
T. O.
,
2016
, “
Application of Second Order Sliding Mode Algorithms for Output Feedback Control in Hydraulic Cylinder Drives With Profound Valve Dynamics
,”
Elektrotech. Inftech
,
133
(
6
), pp.
238
247
.10.1007/s00502-016-0425-7
25.
Horn
,
M.
, and
Steinberger
,
M.
,
2016
, “
Sliding Mode Applications on Hydraulics and Pneumatics
,”
Elektrotech. Inftech
,
133
(
6
), pp.
99
108
.
26.
Strogatz
,
S. H.
,
2015
,
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering
,
Westview Press, a Member of the Perseus Books Group
,
Boulder, CO
.
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