Abstract

This paper develops a discrete constrained controller for electrohydraulic system (EHS) controlled by proportional directional control (PDC) valve while taking parametric uncertainties into account. The proposed controller solves the discrete barrier Lyapunov function via convex optimization while taking into consideration the system constraints such as state and actuator constraints. The proposed control law successfully tracks the reference trajectory while satisfying the state and actuator constraints. It is proven that the tracking error always converges to an arbitrary small neighborhood which is validated using Lyapunov stability analysis. The effectiveness of the proposed discrete barrier Lyapunov function based constrained controller was verified in a simulation environment and also through experimentation. From the simulation and experimental results, it is clear that the proposed controller drives the load to accurately track the reference trajectory in the presence of uncertainty and unknown disturbances.

References

1.
Chaudhuri
,
S.
,
Saha
,
R.
,
Chatterjee
,
A.
,
Mookherjee
,
S.
, and
Sanyal
,
D.
,
2020
, “
Development of a Motion Sensing System Based on Visual Servoing of an Eye-In-Hand Electrohydraulic Parallel Manipulator
,”
IEEE Sens. J.
,
20
(
14
), pp.
8108
8116
.10.1109/JSEN.2020.2979490
2.
Zhao
,
J.
,
Wang
,
J.
, and
Wang
,
S.
,
2013
, “
Fractional Order Control to the Electro-Hydraulic System in Insulator Fatigue Test Device
,”
Mechatronics
,
23
(
7
), pp.
828
839
.10.1016/j.mechatronics.2013.02.002
3.
Han
,
S.
,
Jiao
,
Z.
,
Yao
,
J.
, and
Shang
,
Y.
,
2014
, “
Compound Velocity Synchronizing Control Strategy for Electro-Hydraulic Load Simulator and Its Engineering Application
,”
ASME J. Dyn. Syst., Meas., Control
,
136
(
5
), p.
051002
.10.1115/1.4026921
4.
Baghestan
,
K.
,
Rezaei
,
S. M.
,
Talebi
,
H. A.
, and
Zareinejad
,
M.
,
2015
, “
An Energy-Saving Nonlinear Position Control Strategy for Electro-Hydraulic Servo Systems
,”
ISA Trans.
,
59
, pp.
268
279
.10.1016/j.isatra.2015.10.012
5.
Kaddissi
,
C.
,
Kenne
,
J.-P.
, and
Saad
,
M.
,
2007
, “
Identification and Real-Time Control of an Electrohydraulic Servo System Based on Nonlinear Backstepping
,”
IEEE/ASME Trans. Mechatron.
,
12
(
1
), pp.
12
22
.10.1109/TMECH.2006.886190
6.
Ba
,
D. X.
,
Ahn
,
K. K.
,
Truong
,
D. Q.
, and
Park
,
H. G.
,
2016
, “
Integrated Model-Based Backstepping Control for an Electro-Hydraulic System
,”
Int. J. Precis. Eng. Manuf.
,
17
(
5
), pp.
565
577
.10.1007/s12541-016-0069-x
7.
Zhao
,
X.
,
Li
,
L.
,
Song
,
J.
,
Li
,
C.
, and
Gao
,
X.
,
2016
, “
Linear Control of Switching Valve in Vehicle Hydraulic Control Unit Based on Sensorless Solenoid Position Estimation
,”
IEEE Trans. Ind. Electron.
,
63
(
7
), pp.
4073
4085
.10.1109/TIE.2016.2541080
8.
Tavernini
,
D.
,
Vacca
,
F.
,
Metzler
,
M.
,
Savitski
,
D.
,
Ivanov
,
V.
,
Gruber
,
P.
,
Hartavi
,
A. E.
,
Dhaens
,
M.
, and
Sorniotti
,
A.
,
2020
, “
An Explicit Nonlinear Model Predictive ABS Controller for Electro-Hydraulic Braking Systems
,”
IEEE Trans. Ind. Electron.
,
67
(
5
), pp.
3990
4001
.10.1109/TIE.2019.2916387
9.
Toufighi
,
M.
,
Sadati
,
S.
,
Najafi
,
F.
, and
Jafari
,
A.
,
2013
, “
Simulation and Experimentation of a Precise Nonlinear Tracking Control Algorithm for a Rotary Servo-Hydraulic System With Minimum Sensors
,”
ASME J. Dyn. Syst., Meas., Control
,
135
(
6
), p.
061004
.10.1115/1.4024799
10.
Yang
,
M.
,
Ma
,
K.
,
Shi
,
Y.
, and
Wang
,
X.
,
2019
, “
Modeling and Position Tracking Control of a Novel Circular Hydraulic Actuator With Uncertain Parameters
,”
IEEE Access
,
7
, pp.
181022
181031
.10.1109/ACCESS.2019.2959296
11.
Ding
,
H.
,
Zhao
,
J.
, and
Zhu
,
Q.
,
2018
, “
A New Hydraulic Speed Regulation Scheme: Valve-Pump Parallel Variable Mode Control
,”
IEEE Access
,
6
, pp.
55257
55263
.10.1109/ACCESS.2018.2872605
12.
Vaezi
,
M.
,
Asgharifard
,
A.
, and
Izadian
,
A.
,
2018
, “
Control of Hydraulic Wind Power Transfer System Under Wind and Load Disturbances
,”
IEEE Trans. Ind. Appl.
,
54
(
4
), pp.
3596
3603
.10.1109/TIA.2018.2813970
13.
Fu
,
W.
,
Yuan
,
X.
,
Li
,
Y.
, and
Zhang
,
L.
,
2022
, “
Research on Optimal Control of Excavator Negative Control System Based on Secondary Controllable Main Valve
,”
IEEE Access
,
10
, pp.
7566
7573
.10.1109/ACCESS.2022.3141446
14.
Li
,
Y.
, and
Wang
,
Q.
,
2018
, “
Adaptive Neural Finite-Time Trajectory Tracking Control of Hydraulic Excavators
,”
Proc. Inst. Mech. Eng., Part I
,
232
(
7
), pp.
909
925
.10.1177/0959651818767770
15.
Eryilmaz
,
B.
, and
Wilson
,
B. H.
,
2006
, “
Unified Modeling and Analysis of a Proportional Valve
,”
J. Franklin Inst.
,
343
(
1
), pp.
48
68
.10.1016/j.jfranklin.2005.07.001
16.
Wang
,
H.
,
Wang
,
X.
,
Huang
,
J.
, and
Quan
,
L.
,
2021
, “
Performance Improvement of a Two-Stage Proportional Valve With Internal Hydraulic Position Feedback
,”
ASME J. Dyn. Syst., Meas., Control
,
143
(
7
), p.
071005
.10.1115/1.4049793
17.
Rezayi
,
S.
, and
Arbabtafti
,
M.
,
2017
, “
A New Model-Based Control Structure for Position Tracking in an Electro-Hydraulic Servo System With Acceleration Constraint
,”
ASME J. Dyn. Syst., Meas., Control
,
139
(
12
), p.
121006
.10.1115/1.4036878
18.
Xu
,
B.
,
Su
,
Q.
,
Zhang
,
J.
, and
Lu
,
Z.
,
2017
, “
Analysis and Compensation for the Cascade Dead-Zones in the Proportional Control Valve
,”
ISA Trans.
,
66
, pp.
393
403
.10.1016/j.isatra.2016.10.012
19.
Liu
,
S.
,
Wang
,
L.
,
Li
,
C.
,
Sun
,
Q.
,
Chen
,
Z.
,
Sun
,
M.
, and
Zeng
,
X.
,
2020
, “
Disturbance Rejection Control With Voltage Constraint for Electro-Hydraulic System Involving Unknown Dead-Zones and Drastic Supply Pressure Variation
,”
IEEE Access
,
8
, pp.
84551
84568
.10.1109/ACCESS.2020.2991162
20.
Dong
,
Z.
,
Yao
,
J.
, and
Ma
,
D.
,
2016
, “
Robust Asymptotic Tracking Control of a Chain of Integrator Nonlinear Systems With Input Constraint and Hysteresis Nonlinearity
,”
Trans. Inst. Meas. Control
,
38
(
12
), pp.
1500
1508
.10.1177/0142331215596565
21.
Kumawat
,
A. K.
,
Kumawat
,
R.
,
Rawat
,
M.
, and
Rout
,
R.
,
2021
, “
Real Time Position Control of Electrohydraulic System Using PID Controller
,”
Mater. Today: Proc.
,
47
, pp.
2966
2969
.10.1016/j.matpr.2021.05.203
22.
Kumawat
,
A. K.
,
Rawat
,
M.
,
Kumawat
,
R.
, and
Rout
,
R.
,
2021
, “
A Review of Nonlinear Control for Electrohydraulic Actuator System in Automation
,”
Manufacturing and Industrial Engineering: Theoretical and Advanced Technologies
,
CRC Press
,
Boca Raton, FL
, p.
229
.
23.
Ahn
,
K. K.
,
Nam
,
D. N. C.
, and
Jin
,
M.
,
2014
, “
Adaptive Backstepping Control of an Electrohydraulic Actuator
,”
IEEE/ASME Trans. Mechatron.
,
19
(
3
), pp.
987
995
.10.1109/TMECH.2013.2265312
24.
Yao
,
B.
,
Bu
,
F.
,
Reedy
,
J.
, and
Chiu
,
G.-C.
,
2000
, “
Adaptive Robust Motion Control of Single-Rod Hydraulic Actuators: Theory and Experiments
,”
IEEE/ASME Trans. Mechatron.
,
5
(
1
), pp.
79
91
.10.1109/3516.828592
25.
Mohanty
,
A.
, and
Yao
,
B.
,
2011
, “
Integrated Direct/Indirect Adaptive Robust Control of Hydraulic Manipulators With Valve Deadband
,”
IEEE/ASME Trans. Mechatron.
,
16
(
4
), pp.
707
715
.10.1109/TMECH.2010.2051037
26.
Dong
,
Z.
, and
Ma
,
J.
,
2020
, “
Quasi-Adaptive Sliding Mode Motion Control of Hydraulic Servo-Mechanism With Modeling Uncertainty: A Barrier Function-Based Method
,”
IEEE Access
,
8
, pp.
143359
143365
.10.1109/ACCESS.2020.3014146
27.
Rout
,
R.
,
Cui
,
R.
, and
Yan
,
W.
,
2022
, “
Sideslip-Compensated Guidance-Based Adaptive Neural Control of Marine Surface Vessels
,”
IEEE Trans. Cybern.
,
52
(
5
), pp.
2860
2871
.10.1109/TCYB.2020.3023162
28.
Rout
,
R.
,
Cui
,
R.
, and
Han
,
Z.
,
2020
, “
Modified Line-Of-Sight Guidance Law With Adaptive Neural Network Control of Underactuated Marine Vehicles With State and Input Constraints
,”
IEEE Trans. Control Syst. Technol.
,
28
(
5
), pp.
1902
1914
.10.1109/TCST.2020.2998798
29.
Agrawal
,
A.
, and
Sreenath
,
K.
,
2017
, “
Discrete Control Barrier Functions for Safety-Critical Control of Discrete Systems With Application to Bipedal Robot Navigation
,”
Robotics: Science and Systems
, Boston, MA, July, Vol.
13
, pp.
1
10
.https://roboticsproceedings.org/rss13/p73.pdf
30.
Ames
,
A. D.
,
Coogan
,
S.
,
Egerstedt
,
M.
,
Notomista
,
G.
,
Sreenath
,
K.
, and
Tabuada
,
P.
,
2019
, “
Control Barrier Functions: Theory and Applications
,” Proceedings of the 2019 18th European Control Conference (
ECC
),
Naples, Italy
,
June 25–28
, pp.
3420
3431
.10.23919/ECC.2019.8796030
31.
Guo
,
Q.
,
Li
,
X.
, and
Jiang
,
D.
,
2018
, “
Full-State Error Constraints Based Dynamic Surface Control of Electro-Hydraulic System
,”
IEEE Access
,
6
, pp.
53092
53101
.10.1109/ACCESS.2018.2870956
32.
Merritt
,
H. E.
,
1967
,
Hydraulic Control Systems
,
Wiley
, Hoboken, NJ.
33.
Grizzle
,
J.
, and
Kang
,
J.-M.
,
2001
, “
Discrete-Time Control Design With Positive Semi-Definite Lyapunov Functions
,”
Syst. Control Lett.
,
43
(
4
), pp.
287
292
.10.1016/S0167-6911(01)00110-4
34.
Xiong
,
Y.
,
Zhai
,
D.-H.
,
Tavakoli
,
M.
, and
Xia
,
Y.
,
2023
, “
Discrete-Time Control Barrier Function: High-Order Case and Adaptive Case
,”
IEEE Trans. Cybern.
,
53
(
5
), pp.
3231
3239
.10.1109/TCYB.2022.3170607
35.
Ferraguti
,
F.
,
Bertuletti
,
M.
,
Landi
,
C. T.
,
Bonfè
,
M.
,
Fantuzzi
,
C.
, and
Secchi
,
C.
,
2020
, “
A Control Barrier Function Approach for Maximizing Performance While Fulfilling to ISO/TS 15066 Regulations
,”
IEEE Rob. Autom. Lett.
,
5
(
4
), pp.
5921
5928
.10.1109/LRA.2020.3010494
36.
Khalil
,
H. K.
,
2002
,
Nonlinear Systems
, 3rd ed.,
Inderscience Publishers
.
37.
Welch
,
G.
, and
Bishop
,
G.
,
1995
, “
An Introduction to the Kalman Filter
,”
University of North Carolina
,
Chapel Hill, NC
, Report No. TR 95–041.
38.
Kumawat
,
A. K.
,
Rout
,
R.
,
Kumawat
,
R.
, and
Rawat
,
M.
,
2023
, “
Design of an Optimal Tracking Controller With Unmeasured States for Electro-Hydraulic Actuation System Using 4/3 Proportional DC Valve
,”
Int. J. Autom. Control
(in press).10.1504/IJAAC.2023.10052883
You do not currently have access to this content.