Proceedings of the Fortieth National Conference on Fluid Mechanics and Fluid Power
December 12-14, 2013, NIT Hamirpur, Himachal Pradesh, India
FMFP 2013 Paper ID 277
COMPARISON OF FUZZY CONTROL AND SLIDING MODE CONTROL IN REAL-TIME
TRACKING OF RUGGED ELECTROHYDRAULIC SYSTEM
Sibsankar Dasmahapatra
SRF
Jadavpur University
Kolkata, West Bengal, India
sdmpmekgec@gmail.com
Rana Saha
Assistant Professor
Jadavpur University
Kolkata, West Bengal, India
rsaha24@rediffmail.com
Pranibesh Mandal
SRF
Jadavpur University
Kolkata, West Bengal, India
m.pran11@gmail.com
Saikat Mookherjee
Associate Professor
Jadavpur University
Kolkata, West Bengal, India
smookherjee13@gmail.com
ABSTRACT
Rugged electrohydraulic actuation systems have
wide range of heavy-duty applications. But, the
challenges in the controller development for such
systems are nonlinearities, inexact mathematical
models, unmodeled dynamics, parameter
variations and uncertainties. Nonlinearities of
high static friction in industrial cylinders and
large deadband of proportional valves in rugged
systems are more severe than in precision
systems with servovalves and servocylinders. A
model-free fuzzy controller and a model-based
sliding mode controller (SMC) with biasing for
the deadband have been developed and
compared here against tracking of piston
displacement in the cylinder with sinusoidal
demands of different frequencies. Errors in
piston displacement and velocity have been used
in both the control techniques as input
parameters to the controllers. Satisfactory realtime performances have been achieved in both
the cases for sinusoidal frequency as high as 1
Hz that is quite commendable in view of attaining
it without using components that are not of
servoclass. The model-free controller has been
showing better response except in some few
cases.
Keywords: Motion control, Proportional valve.
Dipankar Sanyal
Professor
Jadavpur University
Kolkata, West Bengal, India
dipans26@gmail.com
INTRODUCTION
Electro-hydraulic actuation systems are widely
used for their high power to volume ratio, fast
speed of response and fault tolerance.
Applications range from forest and agricultural
harvesting [1-3], vehicle steering [4, 5], mining
[6], construction [7, 8], aircraft navigation [9] to
manufacturing [10, 11]. Inherent non-linearities
and parameter variations are the major obstacles
against designing precision controllers. The early
research remained limited to developing modelbased controllers. Sliding-mode controller [8,
12], or SMC, is gaining popularity for its
robustness. There is a renewed interest in recent
time for developing model-free controllers that
have been found to work well for nonlinear
systems as well. Among them, fuzzy controller is
quite popular that attempts implementing
linguistic rules in terms of fuzzy membership
functions and expert rule base. The objective of
the present work is a comparison of the real-time
performances of an SMC and a fuzzy controller.
SYSTEM DESCRIPTION
Fig. 1 shows an electro-hydraulic actuation
system [13] set up comprising a power pack, a
proportional valve and a hydraulic cylinder.
1
Q1 Q2 Aa v ,
(1a)
where Aa is the annular flow area of chambers
C h1 and C h 2 of the cylinder. Depending on
whether the control voltage e is greater or less
than the threshold voltage e0 , the cylinder
chamber pressures P1 and P2 can be derived by
considering the pressure drops at the metered
orifices, one receiving the pump flow at pressure
PP and the other returning the flow to the tank at
pressure PT . For the piston extension
e0 , the relations are
corresponding to e
Fig 1: Experimental Setup of Hydraulic
Actuation System.
An axial-piston pump from Rexroth [14] driven
by a 1450rpm motor M raises oil from the
reservoir and feeds the hydraulic circuit. A
single-stage relief valve RV limits the maximum
pressure in the hydraulic circuit. There are a
4WRE 10E1-50-2X/G24K4/V proportional valve
PV from Rexroth along with the usual check
valve CV and the oil filters. For executing the
real-time control, a feedback of the piston
position acquired by a linear variable differential
transducer (LVDT) has been used by the
controllers loaded on a National Instrument
Reconfigurable Input/Output system (NI-cRIO).
A fuzzy control and an SMC have been
implemented and their performances compared.
P1 PP {( Aa v)/(Cv1e)}2
(2a)
P2 PT {( Aa v)/(Cv 2e)}2 ,
and for piston retraction achieved by e
pressure equations are
P1 PT {( Aa v)/(Cv1e)}2 .
(2b)
e0 , the
(2c)
(2d)
P2 PP {( Aa v)/(Cv2e)}2 .
where C v1 and C v 2 are the constant orifice
coefficients at Ports A and B respectively .
The simplified friction model
F f F0
(3a)
vv ,
used in the control formulation comprises of
discontinuous static frictions
F0 max sgn(v),0 F0 p max sgn( v),0 F0n ,
(3b)
and viscosity-dominated kinematic friction
coefficient
v max sgn( v),0
vp max sgn( v),0
vn , (3c)
where subscripts p and n correspond respectively
to positive and negative piston velocity v .
If y d is demand and y LVDT is the LVDT reading,
the position error can be obtained as
y e y d y LVDT .
(4a)
Hence, the state-space model of the system in
feedback-linearized form can be written as
SLIDING-MODE CONTROLLER DESIGN
A simplified incompressible flow modelling
through the proportional valve depicted in terms
of Fig. 2 has been employed for the SMC design.
The continuity equation models the discharges
between the valve and the double-rod symmetric
cylinder as
y e ve ,
ye ve (k / ma ) ye (
(4b)
v / m a )ve
u,
(4c)
where m a is moving mass, k is spring stiffness
and u is the linearized input given by
Fig 2: Schematic of flow through proportional
valve at neutral and for positive excitation.
2
u yd (k / ma ) y d (
v
S 2 ye ,
S2 ae (k / ma ) ye (
/ m a )v d
( P1 Aa P2 Aa F0 ) / ma .
(4d)
The sliding-mode contribution of the voltage for
piston extension is determined from (2a), (2b)
and (4c) as
eSMC [ Aa3{(1/ Cv21 ) (1/ Cv22 )}/{ma (u yd )
u,
(7b)
c
in
m s and a rotational variable
ve
ye ,
(7c)
the 2-SMC variable is expressed as
u uv 2 c [
c {sgn( y e )}] /(
c ) for y e
v vd
and u v 2
c
sgn( ve ) for y e
0.
0 , (7d)
(7e)
FUZZY CONTROLLER DESIGN
The fuzzy controller depicted in Fig. 4 attempts a
reduction of a composite error
( PP PT ) Aa F0 }]1/ 2 | v | for y e 0 .
(5b)
The overall controller structure is now expressed
with reference to Fig. 3 as
kyd
v / ma )ve
where in terms of a user-defined parameter
( PP PT ) Aa F0 }]1/ 2 | v | for ye 0 ,
(5a)
and that for piston retraction from (2c),(2d) and
(4c) as
eSMC [ Aa3{(1/ Cv21 ) (1/ Cv22 )}/{ma ( yd u)
kyd
(7a)
v vd
ce
(dye / dt) s y ye
(8)
where s y is a coefficient in s-1 . The controller
computes the requisite control signal voltage e fu
by carrying out a fuzzy operation
IF ce is Fi THEN e fu
( i ei ) , for i=1 to q,
i
e euo eSMC if v vc ,
(6a)
e euo eb if v vc ,
(6b)
where eu 0 is the voltage for leakage
compensation in the proportionl valve and eb is a
bias voltage that is used to overcome the stiction
in the cylinder until the piston achieves a velocity
vc employed to cut off the bias.
Assuming linear pressure-gain characteristic of
the valve, a voltage contribution corresponding to
u 0 is written as
eu 0 e0 k ( y d y0 ) ( PP Aa PT Aa ) .
(6c)
where e0 is the threshold voltage, y 0 is the initial
spring position and
is its pre-compression.
The 2-SMC switching function is expressed as
and calculating membership function values
linearly increasing from 0 at ci 1 to 1 at c i and
decreasing to 0 at and beyond ci 1 , as given by
1 min[max[( ci ce ) /(ci ci 1 ),0],1]
i
min[max[( ce ci ) /(ci 1 ci ),0],1]
(9)
where Fi are fuzzy input subsets and e i denotes
the singleton output voltage corresponding to
each input subset. The membership function
parameter values are obtained from trial and error
method in order to find a suitable control
phenomenon. The control voltage in turn excites
the solenoid of the proportional valve through the
NI-cRIO. This causes the spool valve ports to
open that in turn causes flow to the actuator that
controls its movement. Fig. 4 shows the input
and output spaces with q equal 5 designating
negative large, negative, zero, positive and
positive large subsets respectively.
Fig 3: Sliding-mode controller structure.
Fig. 4: Fuzzy Controller Architecture
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RESULTS AND DISCUSSION
The results of SMC and fuzzy control against
sinusoidal control demands of 0.67Hz and 1Hz
are compared in Figs. 5 and 6. At 0.67 Hz, both
the control techniques have shown good overall
tracking capabilities, though the error plot in Fig.
5 indicate the performance of the fuzzy controller
to be marginally better. For the 1 Hz demand,
Fig. 6 reveals the fuzzy controller performance to
be much better. This can be attributed to the
suddenness of the application or withdrawal of
the bias voltage in the SMC framework.
Fig. 6: Comparison of SMC and FLC
responses for sinusoidal demand of 1.0 Hz
CONCLUSION:
A real-time electrohydraulic control system has
been used to track sinusoidal position demands of
different frequencies with the help of SMC and
fuzzy control. Satisfactory performances have
been achieved for both the controllers for
frequency of 0.67 Hz. With the increase in
frequency of demand to 1 Hz, a deterioration of
the SMC has been noticed.
Fig. 5: Comparison of SMC and Fuzzy
responses for sinusoidal demand of 0.67 Hz
4
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ACKNOWLEDGEMENTS:
We sincerely acknowledge the supports of
University Grants Commission, Aeronautical
Research & Development Board and Extramural
Research & Intellectual Property Rights of India
for developing the experimental set up and
Council of Scientific for the scholars support.
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