high precision position control of electro-hydraulic servo system

Research Journal of Applied Sciences, Engineering and Technology 4(4): 289-298, 2012ISSN: 2040-7467© Maxwell Scientific Organization, 2012Submitted: August 03, 2011 Accepted: September 25, 2011 Published: February 15, 2012

Corresponding Author: Yao Jian-jun, College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin150001, Heilongjiang China

289

High Precision Position Control of Electro-Hydraulic Servo System Basedon Feed-Forward Compensation

1Yao Jian-jun, 1Di Duo-tao, 1Jiang Gui-lin and 2Liu Sheng1College of Mechanical and Electrical Engineering,

2College of Automation, Harbin Engineering University, Harbin 150001, China

Abstract: The study is focused on an electro-hydraulic servo system which is a position control system. It isa non-minimum phase system when it was discretized with a certain sample time. To improve its trackingperformance and extend its bandwidth, based on invariance principle, feed-forward compensation is developedby pole-zero placement theory for the system. The task is accomplished by transforming instable zero of thesystem into pole of the fitted closed-loop transfer function, forming the zero of feed-forward compensator andcompleting the compensation of the instable zero for the closed-loop system. The simulation and experimentalresults show the validity of the analytical results and the ability of the proposed algorithm to efficiently improvethe system tracking performance and greatly extend system bandwidth.

Key words: Feed-forward compensation, invariance principle, non-minimum phase system, pole-zeroplacement, system bandwidth, tracking performance

INTRODUCTION

Hydraulic control systems are widely used in manymain industrial fields, including aerospace, metallurgy,transportation, machine, marine technology, modernscientific experimental device and weapon control (Li,1990; Yao et al., 2007). Compared with others types ofdrives, they have many distinct advantages, such asdeveloping a comparatively small device with muchlarger torque, high precision, higher respond speed, higherstiffness and higher force-to-weight ratio (Yao et al.,2008).

As for the control algorithm aspects for electro-hydraulic servo system, classical PID controller has beenemployed in real applications. The regulation law of theconventional PID controller is effective for quite anumber of plants, especially for linear time-invariantsystem. The control performance is dependent on theparameters of PID controller. However, its parameters areset under certain operation condition. Becausenonlinearities and uncertainty usually occur in the electro-hydraulic servo system, when the classical PID controlleris used for the system, it only gives mediocre controlperformance.

Adaptive position control based on Radial BasisFunction (RBF) neural network and LQ controller wasdeveloped by Knohl and Unbehauen (2000) for ahydraulic system controlled by a 4/3 way proportionalvalve. Its structure is complex and it has a problem ofcomputation burden, thus its real-time performance can

not be guaranteed. Adaptive sliding control by Guan andPan (2008a) and nonlinear adaptive robust control byGuan and Pan (2008b) were presented for electro-hydraulic system with nonlinear unknown parameters toimprove the tracking performance. Self-tuning fuzzy PIDcontroller in which the fuzzy controller was used toupdate the three parameters of the PID controller wasdeveloped by Wu et al. (2004). Its key issue is how todesign the membership function and it needs to know thesystem model. Adaptive control scheme based on Popovcriterion was proposed by Yao et al. (2006). But it haslarge computation. Adaline neural network using LMSadaptive filtering algorithm was proposed by Yao et al.(2007), whose task was accomplished by adjusting theweights of the network using LMS algorithm when phasedelay existed between the input and its correspondingoutput, and the reference input was weighted in such away that it makes the system output track the inputefficiently, thus the weighted input signal was added tothe control system such that the output phase delay wascancelled leaving the desired signal alone. To cancelamplitude attenuation and phase delay, Yao et al. (2011b)developed a network using normalized LMS adaptivefiltering algorithm, whose weights were on-line updatedaccording to the estimation error between the desiredinput and the weighted feedback, the updated weights thuswere copied to the input correction. The two methods cangreatly improve sinusoidal tracking performance.However, this method is only applicable to fixed-pointsine wave. An adaptive tracking control with reference

Res. J. Appl. Sci. Eng. Technol., 4(4): 289-298, 2012

290

sp bp

iVq oVq

ip opA

iV oV

LF

B

y

vx

m

Fig. 1: Block diagram of electro-hydraulic servo system

model being 1 was presented by Wang et al. (2005) toachieve zero phase tracking. The initial value of integraladaptive law has great influence on the system output.

With the increase of test system requirements, itrequires high performance both in amplitude frequencybandwidth and in phase frequency bandwidth, especiallyfor large frequency bandwidth system, for example,electro-hydraulic servo shaking table, in which itsfrequency bandwidth may be required to be bigger than100 Hz. Though three-variable control can extend systemfrequency bandwidth for an electro-hydraulic servoshaking table (Yao et al., 2010, 2011a), this improvementis limited by the servo valve frequency bandwidth and thehydraulic natural frequency. The methods can improve thesystem performance, especially the tracking performance,but it can not widen frequency bandwidth (Yao et al.,2006, 2007; Knohl and Unbehauen, 2000; Guan and Pan,2008 a; Guan and Pan, 2008 b; Wu et al., 2004).

In the study, to improve the tracking performance ofelectro-hydraulic servo system and extend its bandwidth,based on invariance principle, feed-forward compensationis developed by pole-zero placement theory for thesystem. High precision position control is accomplishedby transforming instable zero of the system into pole ofthe fitted closed-loop transfer function, forming the zeroof feed-forward compensator and completing thecompensation of the instable zero for the closed-loopsystem. The proposed control scheme is validated by thesimulation and experimental results.

SYSTEM DESCRIPTION

The valve-controlled hydraulic actuator is used as aforce amplifier. Very little force is forced to position thevalve, but a large fo xv rce is obtained. The hydraulic unitis relatively small, which makes its application veryattractive. Figure 1 is the hydraulic system, which iscomprised of a symmetric cylinder, a symmetric servovalve and a load force. The motion xv of the valveregulates the flow of oil to either side of the maincylinder. An input motion of a few thousands of an inch

results in a large change of oil flow (John andConstantime, 1993). The resulting difference in pressureon the main piston causes motion of the output shaft. Theoil flowing in is supplied by a hydraulic source thatmaintains a constant high supply pressure ps, and the oilon the opposite side of the piston flows into the drain atlow return pressure pb.

The load-induced pressure pL is the differencebetween the pressures on each side of the main piston:

(1)pFA

p pLL

i= = − o

where A is the effective area of the cylinder piston, FL theexternal force, and pi, p° are the input and output pressureof the cylinder, respectively.

The pressure drop ªp across the orifice is a functionof the supply pressure ps and the load-induced pressure pL.Since ps is assumed to be constant, the flow equation forq is a function of valve displacement xv and pL:

q = f(xv1, pL)

where, q is the rate of flow of hydraulic fluid through thevalve. The differential rate of flow dq, expressed in termsof partial derivates, is!

(2)dqqx

dxqp

dpv

vL

L= +∂∂

∂∂

If q, xv and pL are measured from zero values as referencepoints, and if the partial derivatives are constant at thevalues they have at zero, the integration of Eq. (2) givesthe flow equation of fluid entering the main cylinder:

(3)q q

xx q

pPL

K x K pv

ov

Lo

q v c L

=⎛

⎝⎜

⎞

⎠⎟ +

⎛

⎝⎜

⎞

⎠⎟

= −

∂∂

∂∂0 0

where,

is the flow-gain coefficientK qxq

v o=⎛

⎝⎜

⎞

⎠⎟

∂∂

is flow-pressure coefficientKc qpL o

=⎛

⎝⎜

⎞

⎠⎟

∂∂

The oil flow can also be written as:

(4)qq qv v=

+1

2o


291

Controller Plant

( )pG s

yFeed-forward compensation

( )FG s

+−

( )cG s

r e u

where qv1, qvB is the input/output oil flow of the cylinder,respectively. The continuity equations of the cylinder aregiven as:

(5)( )& &pV

q Ayii

vi= −β

(6)( )& &pV

Ay qvoo

o= −β

where $ is the bulk modulus of the hydraulic oil and & isthe velocity of the piston, $ is defined as the ratio ofincremental stress to incremental strain. Thus:

β =Δ

Δ

p

V VL

/

where V is the effective volume of fluid undercompression.

From Eq. (1), (4), (5) and (6), the flow continuityequation of the cylinder is:

(7)q AyV

ptL= +& &

4β

where Vt is the total oil volume of the cylinder, Vt = Vi+Vo.The balance of the force at the sliding carriage is:

(8)Ap my By FL L= + +&& &

where m is the total mass of the piston and the load, B theequalized viscous damping coefficient, the acceleration&&yof the piston.

Using Eq. (3), (7), (8) and applying the Laplacetransformation to the resulting third-order differentialequation results (Yao et al., 2007):

(9)Y

KA

X KA

s F

ss

s

qv

cL

h

h

h

=− +

⎛

⎝⎜

⎞

⎠⎟

+ +⎛

⎝⎜

⎞

⎠⎟

21

2

2

1

21

ω

ωζω

where

ωβ

ζβ

β

ωβ

ht

hc

t

t

c

t

AmV

KA

mV

BA

Vm

KV

=

= +

=

4

2 44

2

1

Feed-forward compensation: In order to improve thecontrol precision of random vibration PSD (PowerSpectral Density) replication, Guan (2007) improved the

Fig. 2: Feed-forward compensation

correction algorithm of drive signals PSD and thegeneration of time domain drive signals in the classicalalgorithm. The drive signals PSD iteration algorithm withdifferent step length in different frequency band waspresented to raise the rate of convergence. The method ofgenerating the drive signal in time domain by filtering aseries of independent white noise with designed FIR(Finite Impulse Response) filter was presented. The FIRfilter was designed by the Parks-McClellan algorithmwith the information contained in the in the drive signalPSD. To avoid the time domain randomization procedure,the execution time of the algorithm was reduced. Theimproved PSD iteration algorithm can improve the controlprecision, but it has great computation burden, because itneeds to off-line calculate FFT (Fast Fourier Transform)and IFFT (Inverse Fast Fourier Transform) in timedomain and in frequency domain to generate the drivesignal. What more, for a elastic load, ite convergencemay not be ensured.

For a servo control system, the feed-forwardcompensation scheme can extend the system frequencybandwidth and improve the system tracking performance.Generally, the feed-forward compensation scheme isbased on the invariance principle (Lin and Tian, 2005). Inother words, the feed-forward compensation loop isdesigned to be the inverse of the system closed-looptransfer function such that the transfer function of thecompensated system is unity. However, when the closed-loop system is a non-minimum phase system, this methodwill face difficulty. In the invariance principle (Lee et al.,2001), the unstable zeros of a non-minimum phase systembecome the poles of the feed-forward compensation loop,leading to instability of the feed-forward compensationpart. In real applications, with the increase of the samplefrequency, discrete-time systems discretized fromcontinuous systems will be non-minimum phase systems.

In this study, for such non-minimum phase systems,zeros are introduced into the feed-forward compensator tocompensate the unstable zeros of the closed-loop system(Wang et al., 2005). Its basic theory is the pole-zerodisplacement theory.

The feed-forward compensation scheme can bedescribed by Fig. 2. Gc(s) is the closed loop systemtransfer function including the controller, the inputrcommand. Let Gc(zG1) be a stable discrete-time systemwhich is discretized from a continuous closed loop


292

0

-10

-20

-30

-40-50

-600

-90

-180

-27010-1

100 101 102

Frequency (Hz)

Phas

e (d

eg)

Am

plitu

de (d

B)

Pole

Zero

1.5

1.0

0.5

0

-0.5

-1.0

-1.5-4 -3.5 -3.0 -2.5 -2.0 -1.5 -1 -0.5 0 0.5 1 1.5

Imag

inar

y pa

rt

Real part

Fig. 3: System closed-loop Bode plot before feed-forwardcompensation

system,Gc(s) and Gc(zG1) has s non-minimum phase zeroswith unity static gain. Thus Gc(zG1) can be written as:

(10)G zz N z N z

D zc

du a( )( ) ( )

( )−

− − −

−=11 1

1

where, Nu(zG1) = n0+n1zG1+...+n5zG5, n0 … 0. Nu(zG1)contains zeros of Gc(zG1) on the unit circle and instablezeros of Gc(zG1) beyond the unit circle, while Na(zG1)includes all stable zeros of Gc(zG1) within the unit circle.

Theorem (Liu, 2003; Xia and Meng, 1995): Let H(zG1) =Nu(z)Nu(zG1) which meets:

( )∠ =−H e j rω 0

and

( ) ( )[ ]

( )[ ]∠ =

+ ∀ ∈

− −

−

H e N e

N e R

j Tu

j T

uj T

ω ω

ω ω

2 2

2

Re

Im

where, T is the sample time. Thus the feed-forwardcompensator can represented by Liu (2003):

(11)( ) ( ) ( )( ) ( )[ ]

G zz Nu z D z

N z NF

s

a u

−− −

−=1

1

1 21

Currently, the Proportional-Integral-Derivative (PID)algorithm is the most common control algorithm used inindustry applications. In PID control, a feedback variable

Fig. 4: Zero- pole plot

and a set-point should be specified. The feedback variableis the system parameter, which the designer wants tocontrol, and the set-point is the desired value for theparameter. The PID controller generates a controlleroutput, for example, valve position. The controller appliesthis output value to the system, which in turn drives thefeedback variable toward the set-point value. The PIDcontroller calculates the controller action as:

( ) ( ) ( )( )

u t K e tT

e t dt Tde t

dtpI

D

t= + +

⎡

⎣⎢

⎤

⎦⎥∫

10

where e is the error signal obtained by comparing the set-point to the feedback variable. Kp is the controller gain.TI is the integral time, which is also called the reset time.TD is the derivative time or the rate time.

Simulation results: To validate the proposed feed-forward compensation scheme, the system was used foran electro-hydraulic servo shaking table is adopted as theplant (Yao et al., 2006). Its transfer function is:

( ) ( )G ss s sp =

+ +

180315818747 855 24586 242

.. .

For real electro-hydraulic servo system, P controller ismostly applied. Before feed-forward compensation isapplied, the system closed-loop bode plot is shown inFig. 3 with proportional coefficient Kp = 0.3. From thefigure, it can be seen that there are small -3 dB amplitudeand -90º phase frequency bandwidth, especially for theamplitude frequency bandwidth. To improve the systemfrequency bandwidth and its tracking performance, thefeed-forward compensation in Fig. 2 is applied.

During the simulation, system sample time is 1 ms.After it is discretized with the sample time, the closed-loop transfer function is:


293

10-1100 101 10

2

Frequency (Hz)

Phas

e (d

eg)

Am

plitu

de (d

B)

0

-0.5

-1

-1.5

-2

-2.5

0

-45

-90

-135

0.10

0.05

0.00

-0.05

-0.100.0 0.1 0.2 0.3 0.4 0.5

Desired signal Actual output

Time (t/s)

Dis

plac

emen

t (y/

m)

0.0

Desired signal Actual output

Time (t/s)

Dis

plac

emen

t (y/

m)

0.20

0.15

0.10

0.05

0.00

-0.05-0.10

-0.15

-0.200.3 0.6 0.9 1.2 1.5

Fig. 5: System closed-loop bode plot after feed-forwardcompensation

Fig. 6: System sinusoidal response

( )G zz z

z z zc =× + × + ×

− + −

− − −8898 10 3513 10 8 688 102 929 2 883 0 9533

5 2 4 5

3 2. . .

. . .

Its zero-pole plot is shown in Fig. 4, from which it can beseen that there is an instable zero, so it is a non-minimumphase system.

According to Eq. (10), the feed-forward compensatorGF (zG1) is:

( )G zz z z z

zF− =

− + − −+

14 3 21887 5016 3940 3217 488 6

0 265. .

.

For real control application, desired output ahead oftime can not be known. Since the system sample time isvery small, the value ahead of three sampling period canbe ignored, thus the feed-forward compensator becomes:

( )G zz z z z

zF−

− − − −

−=− + − −

+1

1 2 3 4

11887 5016 3940 3217 488 6

1 0 265. .

.

Fig. 7: System sinusoidal response with hybrid frequencies

Table 1: Experimental parametersItem Value UnitCylinder stroke 1350 mmCylinder piston K125 mmCylinder rod K90 mmOil supply pressure 5 MPaEquivalent external load 5500 kgSample time 2 ms

Table 2: Sinusoidal response analysisAmplitude

Frequency (Hz) attenuation (dB) Phase delay (deg)0.1 0 -5.6160.5 -0.5691 -17.281.0 -0.6144 -21.61.7 -0.6600 -30.65.0 -3.7352 -64.8

The system closed-loop bode plot after feed-forwardcompensation is shown in Fig. 5. It can be seen that thesystem amplitude and phase bandwidth are all greatlyenhanced. This is very useful for the applications wherewide frequency bandwidth is required for electro-hydraulic servo system.

When the input is 0.1sin(20Bt) m, the systemresponse is shown in Fig. 6. Figure 7 is the responsecorresponding to the command: 0.1sin(16Bt) +0.05sin(30Bt) + 0.02sin(40Bt) m. From the two figures,the compensated system has good tracking performance.

Experimental results: The experimental setup of anelectro-hydraulic servo system which is an asymmetriccylinder controlled by a MOOG D792 servo valve is usedto validate the proposed control scheme. The systemconfiguration is shown in Fig. 8. The hydraulic powersupply provides a high supply pressure ps of 5 MPa asshown in Table 1, which gives the system parameters. r isthe command input, and y is the feedback displacement.The servo controller compares the feedback signal fromsensor with the input to produce a command signal todrive the servo valve, which adjusts the flow ofpressurized oil to move the hydraulic cylinder until thedesired position is attained (Yao et al., 2011a).


294

Hydraulicpower supply

Servo valveServo controller

H ydraulic cylinder

Load

Sensor

r y

D/AD/A

conditioner Servo valveK0.18 10.06 1

ss++

A/D A/Dconditioner

Displacementsensor

Signalgenerator

+−

170 175 180 185 190 195 200 205 210-2.1

-1.4

-0.7

0.0

0.7

1.4

2.1

Dis

plac

emen

t y/

mm

Time t/s

Command Feedback

245 247 249 251 253 255 257 259 261

-1.4

-0.7

0.0

0.7

1.4

2.1

Dis

plac

emen

t y/m

m

Time t/s

Command Feedback

Fig. 8: System configuration of the electro-hydraulic servo system

Fig. 9: Block diagram of the control system

(a) Input frequency is 0.1 Hz

(b) Input frequency is 0.5 Hz


295

290 291 292 293 294 295 296 297 298 299 300-2.1

-1.4

-0.7

0.0

0.7

1.4

2.1

Dis

plac

emen

t y/m

m

Time t/s

Command Feedback

329 330 331 332 333 334 335-2.1

-1.4

-0.7

0.0

0.7

1.4

2.1

Dis

plac

emen

t y/m

m

Time t/s

Command Feedback

375 376 377 378-2.1

-1.4

-0.7

0.0

0.7

1.4

2.1

Dis

plac

emen

t y/m

m

Time t/s

Command Feedback

(c) Input frequency is 1 Hz

(d) Input frequency is 1.7 Hz

(e) Input frequency is 5 HzFig. 10: Sinusoidal response at different frequencies


296

175 180 185 190 195 200 205-2.1

-1.4

-0.7

0.0

0.7

1.4

2.1

Disp

lacem

ent y

/mm

Time t/s

Command Feedback

290 292 294 296 298 300-2.1

-1.4

-0.7

0.0

0.7

1.4

2.1

Dis

plac

emen

t y/m

m

Time t/s

Command Feedback

392 394 396 398 400-2.1

-1.4

-0.7

0.0

0.7

1.4

2.1

Dis

plac

emen

t y/m

m

Time t/s

Command Feedback

(a) Input frequency is 0.1 Hz

(b) Input frequency is 0.5 Hz

(c) Input frequency is 1 Hz


297

388 3 89 39 0 391 3 92 39 3 394-2.1

-1.4

-0.7

0.0

0.7

1.4

2.1

Dis

plac

emen

t y/m

m

Tim e t/s

C om mand Feed back

4 4 2 .0 4 4 2 .5 4 43 .0 44 3 .5 4 4 4 .0-2 .1

-1 .4

-0 .7

0 .0

0 .7

1 .4

2 .1

Disp

lace

men

t y/m

m

T i m e t/ s

C o m m a nd F e edb ac k

(d) Input frequency is 1.7 Hz

(e) Input frequency is 5 HzFig. 11: Sinusoidal response at different frequencies after using the proposed control method

The control system is shown in Fig. 9. The signalgenerator is used to generate the command input. Thesaturation unit is to make the control signal in the range of[-10, 10] V, which is also the volt range of D/A (digital toanalog, D/A). The D/A and A/D (analog to digital, A/D)conditioner are used to condition signals for servo valvedriving signal and for A/D board, respectively.

The sinusoidal responses are shown in Fig. 10, and itsanalysis is shown in Table 2, from which it can be seenclearly that with the increase of input frequency, theamplitude attenuation and the phase delay become moreserious.

With the frequency response data in Table 2, thesystem closed-loop transfer function can be identified bythe MATLAB command, invfreqs, which is useful inconverting magnitude and phase data into transferfunctions. The identified system closed-loop transferfunction is:

( )( )

y sR s

ss s s s

=

− ++ + − + ×

1482 76740 0703 1023 2364 4 78 104 3 2 4. . .

The proposed control scheme is then applied to theelectro-hydraulic servo system, and its experimentalresults are shown in Fig. 11 plotted with the commandand the feedback signals. From the results, it can beclearly seen that the feedback signal nearly coincides wellwith the command input at all five frequencies, thus thecompensated system has good tracking performance,improving its frequency characteristics.

CONCLUSION

Though PID controller is widely used in electro-hydraulic servo system, because of its limitations, goodtracking can not be achieved in every operation condition.To enhance system bandwidth and improve the trackingperformance, feed-forward compensator, which is basedon pole-zero placement theory, is developed. When theelectro-hydraulic servo system is discretized, it becomesa non-minimum phase system. The zeros of the feed-forward compensator are obtained by transforming thesystem instable zeros to the poles of the fitted transferfunction of the closed-loop system, compensating the


298

instable zeros of the closed-loop system, and highprecision tracking performance is achieved.

For a real system, its amplitude and phase frequencycharacteristics can be established by sine sweep tests, thusthe feed-forward compensator can be obtained based onthe fit of the closed-loop system, so the proposed controlscheme can be applied to real application.

ACKNOWLEDGMENT

The author is grateful for the support of the NationalNatural Science Foundation of China (No. 50905037),Specialized Research Fund for the Doctoral Program ofHigher Education of China (No. 20092304120014),Special Financial Grant from the China PostdoctoralScience Foundation (No. 201104414), China PostdoctoralScience Foundation (No.20100471021), PostdoctoralScience–Research Developmental Foundation ofHeilongjiang Province (No. LBH-Q09134) and theFoundation of Harbin Engineering University (No.HEUFT09013).

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high precision position control of electro-hydraulic servo system

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