In this paper, a robust fixed-gain linear output pressure controller is designed for a double-rod electrohydrostatic actuator using quantitative feedback theory (QFT). First, the family of frequency responses of the system is identified by applying an advanced form of fast Fourier transform on the open-loop input–output experimental data. This approach results in realistic frequency responses of the system, which prevents the generation of unnecessary large QFT templates, and consequently contributes to the design of a low-order QFT controller. The designed controller provides desired transient responses, desired tracking bandwidth, robust stability, and disturbance rejection for the closed-loop system. Experimental results confirm the desired performance met by the QFT controller. Then, the nonlinear stability of the closed-loop system is analyzed considering the friction and leakage, and in the presence of parametric uncertainties. For this analysis, Takagi–Sugeno (T–S) fuzzy modeling and its stability theory are employed. The T–S fuzzy model is derived for the closed-loop system and the stability conditions are presented as linear matrix inequalities (LMIs). LMIs are found feasible and thus the stability of the closed-loop system is proven for a wide range of parametric uncertainties and in the presence of friction and leakages.

References

References
1.
Habibi
,
S.
, and
Goldenburg
,
A.
,
1999
, “
Design of a New High Performance Electrohydraulic Actuator
,”
IEEE/ASME Trans. Mechatronics
,
5
(
2
), pp.
227
232
.
2.
Manring
,
N.
, and
Luecke
,
G.
,
1998
, “
Modeling and Designing a Hydrostatic Transmission With a Fixed-Displacement Motor
,”
ASME J. Dyn. Syst., Meas. Control
,
120
(
1
), pp.
45
50
.
3.
Lovrec
,
D.
, and
Kastrevc
,
M.
,
2011
, “
Modelling and Simulating a Controlled Press-Brake Supply System
,”
Int. J. Simul. Modell.
,
10
(
3
), pp.
133
144
.
4.
Racklebe
,
S.
, and
Helduser
,
S.
,
2007
, “
Electric Hydrostatic Drive—A Concept for the Clamping Unit of a High-Speed Injection Moulding Machine
,”
Bath Workshop of Power Transmission and Motion Control
,
Bath, UK
, pp.
246
253
.
5.
Lovrec
,
D.
, and
Ulaga
,
S.
,
2007
, “
Pressure Control in Hydraulic Systems With Variable or Constant Pumps?
,”
J. Exp. Tech.
,
31
(
2
), pp.
33
41
.
6.
Helbig
,
A.
,
2002
, “
Injection Moulding Machine With Electric-Hydrostatic Drives
,”
Third International Fluid Power Conference
,
Aachen, Germany
, pp.
67
82
.
7.
Lovrec
,
D.
,
Kastrevc
,
M.
, and
Ulaga
,
S.
,
2009
, “
Electro-Hydraulic Load Sensing With a Speed-Controlled Hydraulic Supply System on Forming-Machines
,”
Int. J. Adv. Manuf. Technol.
,
41
(
11–12
), pp.
1066
1075
.
8.
Yao
,
B.
,
Bu
,
F.
,
Reedy
,
J.
, and
Chiu
,
G.
,
2000
, “
Adaptive Robust Motion Control of Single-Rod Hydraulic Actuators: Theory and Experiments
,”
Mechatronics
,
5
(
1
), pp.
79
91
.
9.
Chinniah
,
Y.
,
2004
, “
Fault Detection in the Electro Hydraulic Actuator Using Extended Kalman Filter
,” Ph.D. thesis, University of Saskatchewan, Saskatoon, SK, Canada.
10.
Turolla
,
2013
, “
Hydraulic Fluids & Lubricant
,” Turolla, Frankfurt am Main, Germany, Technical Information. L1021414 (Rev C).
11.
Horowitz
,
I.
,
1993
,
Quantitative Feedback Design Theory
,
QFT Publications
,
Boulder, CO
.
12.
Niksefat
,
N.
, and
Sepehri
,
N.
,
2001
, “
Designing Robust Force Control of Hydraulic Actuators Despite System and Environmental Uncertainties
,”
IEEE Control Syst. Mag.
,
21
(
2
), pp.
66
77
.
13.
Karpenko
,
M.
, and
Sepehri
,
N.
,
2008
, “
Equivalem Time-Invariant Modeling of Electro Hydraulic Actuators With Application to Robust Control Synthesis
,”
Int. J. Fluid Power
,
9
(
3
), pp.
7
18
.
14.
Golubev
,
B.
, and
Horowitz
,
I.
,
1982
, “
Plant Rational Transfer Approximation From Input-Output Data
,”
Int. J. Control
,
36
(
4
), pp.
711
723
.
15.
Tischler
,
B.
, and
Remple
,
K.
,
2012
,
Aircraft and Rotorcraft System Identification
,
American Institute of Aeronautics and Astronautics
,
Reston, VA
.
16.
Tanaka
,
K.
, and
Wang
,
H.
,
2001
,
Fuzzy Control Systems Design and Analysis
,
Wiley
,
Hoboken, NJ
.
17.
Banos
,
A.
,
Barreiro
,
A.
,
Gordillo
,
F.
, and
Aracil
,
J.
,
2002
, “
A QFT Framework for Nonlinear Robust Stability
,”
Int. J. Robust Nonlinear Control, (Isaac Horowitz Spec. Issue)
,
12
(
12
), pp.
357
372
.
18.
Boyd
,
S.
,
El Ghaoui
,
L.
,
Feron
,
E.
, and
Balakrishnan
,
V.
,
1994
,
Linear Matrix Inequalities in System and Control Theory
, Society for Industrial and Applied Mathematics, Philadelphia, PA.
19.
Gahinet
,
P.
,
Nemirovski
,
A.
,
Laub
,
A.
, and
Chilali
,
M.
,
1995
, “
LMI Control Toolbox
,”
The Math Works
,
Natick, MA
.
20.
Karpenko
,
M.
, and
Sepehri
,
N.
,
2009
, “
Hardware-in-the-Loop Simulator for Research on Fault Tolerant Control of Electrohydraulic Actuators in a Flight Control Application
,”
Mechatronics
,
19
(
7
), pp.
1067
1077
.
21.
Karpenko
,
M.
, and
Sepehri
,
N.
,
2012
, “
Electrohydraulic Force Control Design of a Hardware-in-the-Loop Load Emulator Using a Nonlinear QFT Technique
,”
Control Eng. Pract.
,
20
(
6
), pp.
598
609
.
22.
Ren
,
G.
,
Song
,
J.
, and
Sepehri
,
N.
,
2017
, “
Fault-Tolerant Actuating Pressure Controller Design for an Electrohydrostatic Actuator Experiencing a Leaky Piston Seal
,”
ASME J. Dyn. Syst., Meas., Control
,
139
(
6
), p.
061004
.
23.
Ren
,
G.
,
Esfandiari
,
M.
,
Song
,
J.
, and
Sepehri
,
N.
,
2016
, “
Position Control of an Electrohydrostatic Actuator With Tolerance to Internal Leakage
,”
IEEE Trans. Control Syst. Technol.
,
24
(
6
), pp.
2224
2232
.
24.
Tran
,
X.
,
Hafizah
,
N.
, and
Yanada
,
H.
,
2012
, “
Modeling of Dynamic Friction Behaviors of Hydraulic Cylinders
,”
Mechatronics
,
22
(
1
), pp.
65
75
.
25.
Annus
,
P.
,
Land
,
R.
,
Min
,
M.
, and
Ojarand
,
J.
,
2012
, Simple Signals for System Identification (
Fourier Transform—Signal Processing)
,
Intech
,
London
.
26.
Rupnik
,
B.
,
2005
, “
CIFER-MATLAB Interfaces, Development and Application
,” Master thesis, California Polytechnic State University, San Luis Obispo, CA.
27.
D'Azzo
,
J.
, and
Houpis
,
C.
,
1988
,
Linear Control System Analysis and Design
,
McGraw-Hill
,
New York
.
28.
Yaniv
,
O.
,
1999
,
Quantitative Feedback Design of Linear and Nonlinear Control Systems
,
Kluwer
,
South Holland, The Netherlands
.
29.
Robinson
,
D.
,
2000
, “
Design and Analysis of Series Elasticity in Closed-loop Actuator Force Control
,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
30.
Esfandiari
,
M.
, and
Sepehri
,
N.
,
2016
, “
A Solution for Nonlinear Stability Analysis of QFT Controllers Designed for Hydraulically Actuated Systems
,”
Trans. Can. Soc. Mech. Eng.
,
40
(
3
), pp.
265
287
.
31.
Takagi
,
T.
, and
Sugeno
,
M.
,
1985
, “
Fuzzy Identication of Systems and Its Applications to Modeling and Control
,”
IEEE Trans. Syst., Man, Cybern.
,
15
(
1
), pp.
116
132
.
32.
Wang
,
H.
,
Tanaka
,
K.
, and
Griffin
,
M.
,
1998
, “
Parallel Distributed Compensation of Nonlinear Systems by Takagi-Sugeno Fuzzy Model
,”
IEEE
International Conference on Fuzzy System, Yokohama, Japan, Mar. 20–24, pp.
531
538
.
33.
Ohtake
,
H.
,
Tanaka
,
K.
, and
Wang
,
H.
,
2003
, “
Fuzzy Modeling Via Sector Nonlinearity Concept
,”
Integr. Comput. Aided Eng.
,
10
(
4
), pp.
333
341
.
34.
Rowell
,
D.
,
2002
,
Analysis and Design of Feedback Control Systems
,
Massachusetts Institute of Technology
,
Cambridge, MA
.
35.
Sala
,
A.
, and
Arino
,
C.
,
2007
, “
Relaxed Stability and Performance Conditions for Takagi–Sugeno Fuzzy Systems With Knowledge on Membership Function Overlap
,”
IEEE Trans. Syst., Man, Cybern., Part B (Cybern.)
,
37
(
3
), pp.
727
732
.
36.
Du
,
H.
, and
Zhang
,
N.
,
2009
, “
Static Output Feedback Control for Electrohydraulic Active Suspensions Via T-S Fuzzy Model Approach
,”
ASME J. Dyn. Syst., Meas. Control
,
131
(
5
), pp.
1004
1015
.
37.
Du
,
H.
, and
Zhang
,
N.
,
2010
, “
Takagi-Sugeno Fuzzy Control Scheme for Electrohydraulic Active Suspensions
,”
Control Cybern.
,
39
(
4
), pp.
1096
1115
.https://pdfs.semanticscholar.org/535f/e3c2df4dd4dc5c586ce037a7f362b45ac08a.pdf
You do not currently have access to this content.