10.1007_s12239-009-0004-6

International Journal of Automotive Technology, Vol. 10, No. 1, pp. 27−36 (2009)DOI 10.1007/s12239−009−0004−6

Copyright © 2009 KSAE1229−9138/2009/044−04

27

RESEARCH ON THE ELECTRO-HYDRAULIC VARIABLE VALVE ACTUATION SYSTEM BASED ON A THREE-WAY PROPORTIONAL

REDUCING VALVE

J.-R. LIU1), B. JIN1)*, Y.-J. XIE1), Y. CHEN1) and Z.-T. WENG2)

1)The State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China2)Ningbo HOYEA Machinery Manufacture Co., Ltd, Ningbo 315131, China

(Received 4 September 2007; Revised 26 July 2008)

ABSTRACT−As the internal combustion engine moves into the 21st century, fully flexible valve actuation systems are beingproposed as an enabling technology for advanced internal combustion engine concepts. Electro-hydraulic valve actuatorsystems are being considered as a potential variable valve technology. Compared to the servo control system, the system usinga proportional valve has the advantages of low price, high anti-pollution ability and high reliability. Our research focuses onexploring the dynamic characteristic of the electro-hydraulic variable valve system, which is based on three-way proportionalreducing valve. In this paper, the structure and working principles of the system are described. The dynamic mathematicalmodel of the system is derived. From the analysis of a linearized model and dynamic simulation, it is demonstrated that thesystem will be stable only if the proportional reducing valve has a positive opening. Some structural factors that affect thesystem’s dynamic characteristics, such as input signal, the stiffness of the return spring and the pre-tightening force of thereturn spring, are studied using AMESim. The experimental results coincide with the theoretical and simulated analyses.Further study shows that the dynamic response can be improved effectively by adopting closed-loop control of valve lift.

KEY WORDS: Electro-hydraulic, Variable valve, Dynamic characteristics, Three-way, Proportional reducing valve

NOMENCLATURE

Pc : input pressure of the single-rod hydraulic cylinderKI : constantU : input voltage signalAp : area of the hydraulic cylinderK : stiffness of the return springXp : displacement of the pistonX0 : initial reduction length of the return springFL : load forceKu : pulse duty factorL : coil inductanceR : resistance of the coil and amplifierKe : velocity back electromotive force coefficientI : input currentXv : displacement of the valve spoolFm : magnetic force of the proportional electromagnetmv : mass of the armature and valve spoolD : viscous damping coefficient of the valve spoolFv : load force of the valve spoolKi : current-force gain of the proportional electromagnetKv : displacement-force gain of the proportional electro-

magnetQL : flow rate of the load

Kq : flow rate gain coefficientKc : flow rate-pressure coefficientCip : inner leakage coefficient of the hydraulic cylinderVc : volume of the controlled chamber of the hydraulic

chamberβe : bulk modulus of elasticityMp : total mass of the piston and loadBp : viscous damping coefficient of the pistonKce : total flow rate-pressure coefficientCd : flow rate coefficientw : area gradientZ : positive opening sizeρ : oil densityPs : system pressureKp : proportional coefficientKD : differential coefficientKi : integral coefficiente : errory0 : expected valve liftyf : feedback of valve lift

1. INTRODUCTION

Valve timing, lift and duration of conventional internalcombustion engine driving systems, which use a cammechanism to control the intake and/or exhaust valve,*Corresponding author. e-mail: [email protected]

28 J.-R. LIU et al.

cannot be adjusted because the border line of the cam isfixed. Flexible intake and/or exhaust valve motions cangreatly improve the fuel economy, emissions and torqueoutput performance of internal combustion engines (Chenand Cui, 2002). Flexible valve actuation can be achievedusing mechanical, electromagnetic and electro-hydraulicvalve mechanisms (Dresner, 1989). The cam-based mech-anisms can offer limited flexibility of the valve event. TheFiat 3D cam variable valve mechanism (Titolo, 1991) canimplement variable valve lift and timing, but only within ina certain range. The Honda VTEC mechanism (Takefuml,1991) is a multiple-step device that can switch between twodiscrete cams and offer discontinuous change of valvetiming. To achieve continuous valve timing, lift and duration,camless engines, which include electromagnetic and electro-hydraulic mechanisms, are proposed. The electromagneticmechanisms, such as the GM R&D Magnavalue (Theobaldet al., 1994), FEV (Boie et al., 2000), Siemens (Hartke andKoch, 2002), Aura (Schneider, 2001) and Magneti Maralli(Cristiani et al., 2002), can generate continuous variablevalve timing and duration, but these devices cause highvalve-seating velocities. The electro-hydraulic systems, suchas the Ford camless (Wright et al., 1994) and the Sturmansystems (Sturman, 1997), can provide fully flexible controlof valve events. The advantages of the electro-hydraulicmechanisms are low energy consumption and high reliabi-lity.

This paper is organized as follows: Section 2 presentsthe structure and working principle of the electro-hydraulicvariable valve system, which is based on a three-way pro-portional reducing valve. Section 3 presents the structuralfactors which influence the dynamic performance of thesystem which is analyzed using a linearized mathematicalmodel, and the stability of the system is also analyzed inthis section. Section 4 addresses the simulation model ofthe system, which is built by AMESim. Through simu-lation, the dynamic performance of the electro-hydraulicsystem, which is affected by the structural factors, is analy-zed. Section 5 presents the experimental results of electro-hydraulic variable valve system. Section 6 presents futurework on improving the dynamic performance. Section 7contains a summary of the work.

2. STRUCTURE AND WORKING PRINCIPLE OF ELECTRO-HYDRAULIC VARIABLE VALVE SYSTEM

The schematic diagram of the electro-hydraulic variablevalve system, which is based on the three-way proportionalreducing valve, is shown in Figure 1. As shown in Figure 1,the system consists of a proportional relief valve, oil reser-voir, hydraulic pump, high-speed proportional reducingvalve, motor, single-rod hydraulic cylinder, return springand valve.

In the steady state, the input pressure of the single-rodhydraulic cylinder is proportional to the input voltage signal

of the high-speed proportional reducing valve. Theexpression can be defined as follows

(1)

Where, Pc is the input pressure of the single-rod hydrauliccylinder, Pa; K1 is the constant; U is input voltage signal, V.

The relationship between the output hydraulic force ofthe hydraulic cylinder and the load force in the steady statecan be described by

(2)

Where, Ap is the area of the hydraulic cylinder, m2; K is thestiffness of the return spring, N/m; Xp is the displacement ofthe piston, m; Xo is initial reduction length of the returnspring, m; and FL is the load force, N.

According to Equations (1)~(2), one can write

(3)

It is clear from Equation (3) that the valve lift, timingand duration can be changed by varying the input voltagemagnitude, triggered time and pulse width, respectively.

3. ANALYSIS OF THE STABILITY OF THE ELECTRO-HYDRAULIC VARIABLE VALVE SYSTEM

3.1. Dynamic Mathematical Model of the Electro-hydraulicVariable Valve SystemIn order to determine how structural factors influence thedynamic performance of electro-hydraulic variable valvesystems, the dynamic mathematical model of the system isrequired (Merritt, 1967; Wong et al., 2008).

The dynamic differential equation of the coil current in aproportional electromagnet can be defined as follows (Sabri,2006).

(4)

Pc=K1U

PcAp=K Xp X0+( )+FL

Xp=K1

K-----UAp−Xo−

FL

K-----

KuU=LdIdt-----+IR+Ke

dXv

dt--------

Figure 1. Schematic diagram of the electro-hydraulic vari-able valve system.

RESEARCH ON THE ELECTRO-HYDRAULIC VARIABLE VALVE ACTUATION SYSTEM BASED 29

Where, Ku is the pulse duty factor; L is the coil inductance,H; R is the resistance of the coil and the amplifier, Ω; Ke isthe velocity back electromotive force coefficient; I is theinput current, A; and Xv is the displacement of the valvespool, m.

The dynamic force equilibrium equation of the valvespool can be defined as follows

(5)

Where, Fm is the magnetic force of proportional electro-magnet, N; mv is the mass of the armature and valve spool,Kg; D is the viscous damping coefficient of the valvespool, N/(m/s); and Fv is the load force of the valve spool,N.

The dynamic output force of the proportional electro-magnet can be described by (Guan, 2003)

(6)

Where, Ki is the current-force gain of the proportionalelectromagnet; and Ky is the displacement-force gain of theproportional electromagnet.

The Laplace transform expressions of Equations (4)~(6)can be described by

(7)

(8)

(9)

According to Equations (7)~(9), one can write

(10)

The linearized discharge expression of the valve can bedefined as follows

(11)

Where, QL is the flow rate of the load, L/min; Kq is the flowrate gain coefficient; and Kc is the flow rate-pressure coeffi-cient.

The continuity expression of the working chamber of thehydraulic cylinder can be defined as follows

(12)

Where, Cip is the inner leakage coefficient of the hydrauliccylinder; Vc is the volume of the controlled chamber of thehydraulic chamber, m3; and βe is the bulk modulus ofelasticity, Pa.

The dynamic relationship between the output force ofthe piston and the load force can be described by

(13)

Where, Mp is the total mass of the piston and load, Kg; andBp is viscous damping coefficient of the piston, N/(m/s);

The Laplace transform expressions of Equations (11)~(13) can be described by

(14)

(15)

(16)

According to Equations (14)~(16), one can write:

(17)

(18)

Where Kce is the total flow rate-pressure coefficient.According to Equations (10)~(17), one can write

(19)

It is clear from Equation (19) that Ku, K, FL and U are themain structural factors that influence the dynamic perfor-mance of the electro-hydraulic variable valve system.

3.2. Analysis on Stability of the System in Diffierent Open-ing ModesIn this system, the three-way proportional reducing valve isthe key component whose opening mode determines thestability of the electro-hydraulic variable valve system.

In positive opening mode, the flow rate gain coefficientKq and flow rate-pressure coefficient Kc can be defined asfollows

(20)

(21)

Where, Cd is the flow rate coefficient; w is the areagradient; Z is the positive opening size; ρ is the oil density;and Ps is the system pressure.

In zero-opening mode, the flow rate gain coefficient Kq

and flow rate-pressure coefficient Kc can be defined asfollows

(22)

(23)

The system parameters are listed in Table 1 and the poles ofthe system are listed in Table 2.

The system is unstable because there are two poles in theright half S-plane in the zero-opening mode. However, in

Fm=mvd2Xv

dt2----------+DdXv

dt--------+Fv

Fm=KiI−KyXv

KuU s( )=LIs+IR+KeXvs

Fm=mvXvs2+DXvs+Fv

Fm=KiI s( )−KyXv s( )

Xv s( )= KuKiU s( )− Ls R+( )Fv

MvLs3+ LD MvR+( )s2+ LKy RD KeKi+ +( )s+RKy

---------------------------------------------------------------------------------------------------------------

QL=KqXv−KcPc

QL−CipPc=ApdXp

dt--------+Vc

βe

-----dPc

dt--------

PcAp=Mpd2Xp

dt2----------+Bp

dXp

dt--------+KXp+FL

QL=KqXv s( )−KcPc s( )

QL−CipPc s( )=ApXp s( )s+Vc

βe

-----Pc s( )s

Pc s( )Ap=MpXp s( )s2+BpXp s( )s+KXp s( )+FL

Xp s( )=βeKqApXv−Kceβe 1 Vc

βeKce------------s+⎝ ⎠

⎛ ⎞FL

VcMps3+ BpVc+MpβeKce( )s2+ KceBpβe+KVc+βeAp

2( )s+KceKβe

-----------------------------------------------------------------------------------------------------------------------------------------

Kce=Kc+Cip

Xp s( )U s( )------------= KuKi

MvLs3+ LD+MvR( )s2+ LKy RD KeKi+ +( )s+RKy

--------------------------------------------------------------------------------------------------------------

βeKqAp

VcMps3+ BpVc+MpβeKce( )s2+ KceBpβe+KVc+βeAp

2( )s+KceKβe

-----------------------------------------------------------------------------------------------------------------------------------------

Kq=Cdw2 Ps Pc–( )

ρ------------------------ 2Pc

ρ--------+⎝ ⎠

⎛ ⎞

Kc=2

2-------CdwZ 1

ρ Ps Pc–( )------------------------- 1

ρPc

-------------+⎝ ⎠⎛ ⎞

Kq=Cdw2 Ps Pc–( )

ρ------------------------

Kc=CdwXv1

2ρ Ps Pc–( )----------------------------

30 J.-R. LIU et al.

the positive opening mode, the system is stable because allpoles are located in the left half S-plane.

As shown in Figure 2, the simulation model is builtby AMESim and the simulation parameters are listed inTable 3.

The simulation results are shown in Figure 3 and Figure 4.

The output pressure of the proportional reducing valvePc is unstable in the zero-opening mode, whereas the outputpressure of the proportional reducing valve Pc is stable inthe positive opening mode.

In order to validate the simulation results, the experi-mental system is built (as shown in Figure 19) and theexperimental results are shown in Figure 5 and Figure 6. Itis clear in Figure 5 and Figure 6 that the experimentalresults agree well with the simulation results.

Table 1. System parameters of the electro-hydraulic vari-able valve system.

Parameter Value UnitKi 6 nullCd 0.68 nullVc 2.601e-6 m3

w 1.884e-2 mMp 0.1 KgZ 2e-4 mPs 6 MPaAp 1.13e-4 m2

ρ 870 Kg/m3

mv 0.02 Kgβe 700 MPaBp 50 N/(m/s)Cip 4e-12 m3/S/PaK 8000 N/mKu 1 null

Table 2. System poles in the positive and zero openingmodes.

Positive opening Value Zero

opening Value

1 −18433 1 2169+9397i2 −859+7999i 2 2169-9397i3 −859-7999i 3 −85634 −225+141i 4 −213+147i5 −225-141i 5 −213-147i

Figure 2. Model of the electro-hydraulic variable valvesystem.

Table 3. Simulation parameters of the electro-hydraulicvariable valve system.

Parameter Value UnitValve diameter 6 mmrod diameter of the valve 3 mmLower displacement limit −0.002 mHigher displacement limit 0.002 mPiston diameter 12 mmRod diameter of the piston 7 mmLeakage coefficient 0.001 L/min/bar

Figure 3. Output pressure of the proportional reducingvalve Pc in zero opening mode.

Figure 4. Output pressure of the proportional reducingvalve Pc in positive opening mode.


4. SIMULATION ANALYSIS OF THE DYNAMIC PERFORMANCE OF THE ELECTRO-HYDRAULIC VARIABLE VALVE SYSTEM

It would appear that structural factors that affect the dynamicperformance of the electro-hydraulic variable valve systemwere found. They are Ku, K, FL, and U. In order to analyzethe dynamic performance of the system, a simulationmodel was built using AMESim.

In the following simulation results, the opening time isdefined as the necessary time when the lift rises from 10%of the stable value to 90% of the stable value, and theclosing time is defined as the necessary time when the liftfalls from 90% of the stable value to 10% of the stablevalue.

4.1. Simulation Result of Input Voltage MagnitudeIn order to analyze the influence of the input voltagemagnitude on the dynamic performance of the system, asimulation is adopted. The simulation results are shown inFigure 9.

It is obvious in Figure 7 that the valve lift increaseswith increasing input voltage. This result agrees well with

Equation (3).Figure 8 shows that the output pressure of the propor-

tional reducing valve Pc increases and the hydraulic force,which acts on the piston of the hydraulic cylinder, isproportional to Pc. Hence, Pc increases with increasinginput voltage. This result agrees well with Equation (1).

In Figure 9, the input signal pulse width is 47 ms, thesystem pressure is 6 MPa and the stiffness of the returnspring is 8000 N/m with a 52 N pre-tightening force. It isobvious that valve lift increases from 4 mm to 9 mm whenthe input voltage magnitude increases from 1 V to 1.5 V.

Figure 5. Experimental output pressure of the proportionalreducing valve in zero-opening mode.

Figure 6. Experimental output pressure of the proportionalreducing valve in positive opening mode.

Figure 7. Valve lift for different input magnitudes.

Figure 8. Output pressure of the proportional reducingvalve for different input magnitudes.

Figure 9. Influence of variable input voltage magnitude.

32 J.-R. LIU et al.

In order to analyze the average velocity when the valveis opening and closing, the average velocities of 0.5 mm~3.5 mm lift for different input magnitudes are analyzedand the simulation result is shown in Figure 10. It is clearin Figure 10 that the opening average velocity increases,because the driving force (hydraulic force minus the sumof the spring and pre-tightening forces) increases withincreasing input voltage. And closing average velocityincreases slightly because the return spring force increaseswith increasing input voltage magnitude.

4.2. Simulation Result of Input Pulse WidthIn order to analyze the influence of input pulse width on thedynamic performance of the system, the simulation isadopted. The simulation results are shown in Figure 11.

The system pressure is 6 MPa, the input voltage is 1.5 Vand the stiffness of return spring is 8000 N/m with a 52 Npre-tightening force. It is clear in Figure 11 that the valvelift increases from 3 mm to 8 mm when the pulse widthincreases from 9 ms to 39 ms with the input voltage magni-tude at 1.5 V.

In order to analyze the average velocity when the valveis open and closed, the average velocities of 0~3 mm liftwith different input pulse widths are shown in Figure 12.

Figure 12 shows that the average opening velocity increasesslightly because the Ku and input voltage are increasing.However, the average closing velocity is increasing whenthe input pulse width is increased. This phenomenon iscaused by the increased spring force.

4.3. Simulation Result of the Pre-tightening Force the ofReturn SpringThe results of the pre-tightening force on the dynamic

Figure 10. Average velocity curves of different inputmagnitudes.

Figure 11. Influence of variable input pulse width.

Figure 12. Average velocity curves of different pulsewidths.

Figure 13. Valve lift curves of different pre-tighteningforces.

Figure 14. Influence of the pre-tightening force of thereturn spring.


performance of the system are shown in Figure 14 andFigure 15.

The input signal pulse width is 47 ms with the inputvoltage magnitude at 1.25 V, the system pressure at 6 MPaand the stiffness of return spring at 8000 N/m.

Figure 13 shows that the valve lift decreases when thepre-tightening force of the return spring increases. Thisresult agrees well with Equation (3).

It is clear in Figure 14 that the valve lift decreases from9 mm to 5.5 mm when the pre-tightening force of the returnspring increases from 36 N to 68 N.

In order to analyze the average velocity when the valveis open and closed, the average velocities of 0.6 mm~5.4mm lift with different pre-tightening forces for the returnspring are shown in Figure 15. Figure 15 shows that theaverage opening velocity decreases because the drivingforce (hydraulic force minus the sum of the spring and pre-tightening forces) decreases with the increase of the pre-tightening force. However, the average closing velocity isincreasing due to the increasing sum of the pre-tighteningand spring force.

4.4. Simulation result of the stiffness of the return spring

The results of the stiffness of the return spring on thedynamic performance of the system are shown in Figure 17and Figure 18. The input signal pulse width is 47ms withthe input voltage magnitude at 1.25V, the system pressureat 6 MPa and the pre-tightening force at 52 N.

Figure 16 shows that the valve lift decreases when thestiffness of the return spring increases. This result agreeswell with Equation (3).

In order to analyze the influence of the stiffness of thereturn spring on the dynamic performance of the systemwhile maintaining the pre-tightening constant, the simu-lation is performed. The simulation result is shown inFigure 17. It is clear in Figure 17 that the valve lift de-creases from 7 mm to 4 mm when the stiffness of the returnspring increases from 8000 N/m to 14000 N/m.

In order to analyze the average velocity when the valveis opening and closing, the average velocities of 0.4 mm~4mm lift with different stiffnesses of the return spring areshown in Figure 18. It is clear in Figure 18 that the averageopening velocity is decreasing because the driving force(hydraulic force minus the sum of the spring and pre-tightening forces) decreases with the increase of the stiff-ness. The average closing velocity has an optimal valuewhen the stiffness of the return spring is increasing becausethe valve lift decreases when the stiffness of the return

Figure 15. Average velocity curves of different pre-tighten-ing forces.

Figure 16. Valve lift of different stiffnesses of the returnspring.

Figure 17. Influence of the stiffness of the return spring.

Figure 18. Average velocity curves of different stiffnessesof the return spring.

34 J.-R. LIU et al.

spring increases. Hence, the spring force is at its maximumvalue when the stiffness of the return spring is increasing.

5. EXPERIMENT OF THE ELECTRO-HYDRAULIC VARIABLE VALVE SYSTEM

In order to validate the simulation results and analyze thedynamic performance, the following experiments werecarried out.

The experimental system of the electro-hydraulic vari-able valve system, which is based on the three-way reduc-ing valve, is shown in Figure 19.

The pressure transducer is used for measuring the inputpressure of the single-rod cylinder. The displacement trans-ducer, which can linearly convert a 0~25 mm displacementsignal to a 0~5 V voltage signal, is used for measuring thedisplacement of the valve. The oscilloscope is used for displaying and storing the input, pressure and displacement

signals.

5.1. Experimental Results of the Variable Input VoltagemagnitudeThe experimental results of different input voltage magni-tudes are shown in Figure 21. In the experiment, the inputsignal pulse width is 47 ms, the system pressure is 6 MPaand the stiffness of the return spring is 8000 N/m with a 52N pre-tightening force. Figure 21 shows that the valve liftincreases from 3.8 mm to 8.8 mm when the input voltagemagnitude increases from 1 V to 1.5 V. Figure 21 showsthat the opening time is shortened and closing time isslightly shortened at the same lift interval when the inputvoltage magnitude increases.

5.2. Experimental Results of the Variable Input VoltagePulse WidthThe experimental results of the different input pulse widthare shown in Figure 22. In the experiment, the input signalmagnitude is 1.5 V, the system pressure is 6 MPa and thestiffness of the return spring is 8000 N/m with a 52 N pre-tightening force. Figure 22 shows that the valve liftincreases from 2.5 mm to 7.5 mm when the pulse width isFigure 19. Block diagram of the experimental system.

Figure 20. Picture of the experimental system.

Figure 21. the experiment results of variable input voltagemagnitude.

Figure 22. the experiment results of variable input pulsewidth.


increasing from 9 ms to 39 ms. It is clear in Figure 22 thatthe opening time is basically unchanged and closing time isshortened over the same lift interval when the input pulsewidth increases. 5.3. Experimental Results of Different Pre-tightening ForceThe experiment results of the different pre-tightening forcesof the return spring are shown in Figure 23. In the experi-ments, the input signal magnitude is 1.25 V with a 47 mspulse width, a system pressure of 6 MPa and a stiffness ofthe return spring of 8000 N/m. Figure 23 shows that thevalve lift decreases from 8.5 mm to 4.5mm when the pre-tightening force of the piston increases from 36 N to 68 N.It is clear in Figure 23 that the opening time is increasingand the closing time is shortened over the same lift intervalwhen the pre-tightening force of the return spring isincreased.

5.4. Experimental Results of Different Stiffness of theReturn SpringThe experimental results of different stiffness of the returnspring are shown in Figure 24. In those experiments, theinput signal magnitude was 1.25 V with a 47 ms pulsewidth, a system pressure of 6 MPa and a pre-tightening

force of 52 N. Figure 24 shows that valve lift is decreasedfrom 7 mm to 3.5 mm when the stiffness of the returnspring is increased from 8000 N/m to 14000 N/m. It is clearin Figure 24 that the opening time is increasing at the samelift interval when the stiffness of the return spring isincreasing. However, the closing is not shortened with aincrease in the stiffness. It has an optimal value. 6. FUTURE DEVELOPMENTS

It is obvious from the experimental results that the risingand falling time of the valve is too long in the open loopsystem. It is not suitable for a high-speed engine. As shownin Figure 10, increasing the input signal can accelerate thevalve speed. Hence, in order to improve the dynamicperformance of the system, study of the closed-loop of thevalve lift needs to be conducted.

A PID controller is added and the transfer function isshown as follows.

(24)

Where, Kp is the proportional coefficient; KD is the differ-ential coefficient; Ki is the integral coefficient; e is the errorwhose expression is defined in Equation (25).

(25)

Where, yo is the expected valve lift; yf is the feedback of thevalve lift.

The simulation of the closed-loop system is done byAMESim. The simulation results are shown in Figure 25.

It is obvious that the rising and falling times are shorten-ed by adopting closed-loop control of the valve lift. It cangreatly improve the dynamic performance of the system.

7. CONCLUSIONS

This paper presents an electro-hydraulic variable valvesystem which is based on the three-way reducing valve.

U s( )e s( )-----------=Kp+KDs+Ki

s-----

e=yo−yf

Figure 23. the experiment results of the pre-tighteningforce of return spring.

Figure 24. the experiment results of the stiffness of returnspring.

Figure 25. Dynamic performance of the open and closedloop system.

36 J.-R. LIU et al.

The key factors affecting the dynamic performance of thesystem are discussed in detail. The conclusions are asfollows.(1) The system is more inexpensive than using the servo

valves because it uses high-speed proportional valves.(2) The system is stable only if the proportional reducing

valve has a positive opening mode.(3) The valve lift, timing and duration can be controlled by

changing the input signal of the proportional reducingvalve.

(4) The experimental results agree with the simulationresults. This model can be used for optimizing systemparameters such as the pre-tightening force and stiff-ness of the return spring.

(5) By using the closed-loop PID controller, the systemdynamic performance can be greatly improved.

The work in this paper is just a beginning. In order tomeet the demand of high-speed motors (6000 rpm ormore), much more work must be done in the future.

ACKNOWLEDGEMENT−This paper is supported by thenature science foundation of Zhejiang province, China. ProjectNumber: Z106543.

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