Paper Number: 20.2

Direct Displacement Control of Hydraulic Actuators Based on a Self-spinning Rotary On/off Valve

Meng Wang, Perry Y. Li, Haink Tu, Mike Rannow, Thomas R. Chase

Center for Compact and Efficient Fluid Power University of Minnesota

ABSTRACT

Throttling loss of hydraulic systems is a major loss that degrades the system efficiency. One approach to eliminate the throttling loss is displacement control. The flow rate going to the actuator is directly controlled from the power source (pump). In this way, the throttling valve is eliminated. This paper presents an open circuit to realize direct displacement control of a single actuator. The circuit includes one variable flow source, one directional valve, and one proportional valve. A hybrid nonlinear control strategy based on back-stepping technique and consideration of the pressure states was developed for actuator trajectory tracking while maintaining a low system operating pressure. The controller guarantees that neither of the two actuator chambers can cavitate nor go unbounded. The novel 3-way valve based virtually variable displacement pump (VVDP) was selected as the power source to implement the circuit.

1. INTRODUCTION

Hydraulic systems are typically controlled using two approaches: throttling valve control and displacement control. The first approach has the advantages of compactness, low cost, and high control bandwidth, and can be used to control multiple actuators from one single power supply. However, it is inefficient since significant energy is wasted through throttling. To address the high power consumption of valve control, load-sensing (LS) systems have been popular in the past decade. Since the system pressure is regulated to be only incrementally higher than the maximum required load pressure, LS system is more efficient than a typical constant pressure system. However, when one power source is used to power multiple actuators, and the pressure requirements have a large variation, only the actuator requiring the highest pressure can be controlled in an energy efficient manner. Another drawback with LS system is its challenge to maintain system stability [1]. In displacement control, a variable displacement pump (VDP) is used to generate

only the amount of flow required for each circuit. However, multiple VDPs are required in a multi-circuit system.

This paper focuses on displacement control of a hydraulic actuator. From hydraulic configuration point of view, displacement control systems can be categorized into open circuits or closed circuits. In an open circuit, the pump inlet and the actuator return (via a directional valve) are connected to the hydraulic tank. In a closed circuit, the actuator return is directly connected to the pump inlet. Closed circuits eliminate the directional valves; however, when driving asymmetrical cylinders, the unequal volume of the cylinder should be compensated. In 1994, Hewett [1] developed a closed circuit with a charge pump, an accumulator, and a 3way 2position valve. The valve is actively controlled to connect a charge line to the low pressure side when volume compensation is required. In 2000, Rahmfeld and Ivantysynova [2] proposed a different closed circuit where the charging line and the low pressure side are connected via pilot-operated check valves. Heybroek [3] proposed an open circuit, in which four 2way valves are used to realize four-quadrant operation. If the pump can operate as a motor, energy regeneration can be achieved as well.

Given the displacement control configurations, a lot of efforts have been spent on developing control strategy to manipulate the actuator in an energy efficient way. Instability can happen when the actuator switches operation mode, as reported by Williamson and Ivantysynova [4][5]. Cavitation is another issue which may be caused by over-running load. Control strategy has been developed to compensate this cavitation to the maximum flow capacity using the open circuit in reference [3]. In their works, the analysis was based on linearized dynamics.

If the metering in and metering out pressures of the actuator cannot be controlled independently, one order of zero dynamics will be introduced. The stability of the zero dynamics has been investigated when the trajectory to be tracked has a constant velocity [6]. With an adaptive robust controller, the zero dynamics for tracking any nonzero constant velocity trajectory is shown to be

globally uniformly stable. However, the results cannot be easily adapted to an arbitrary trajectory.

In this paper an open-loop circuit is developed to achieve direct displacement control using one pump, one directional valve, and one proportional valve. The proportional valve, placed on the return line, is to ensure that cavitation does not occur. A nonlinear control strategy based on back-stepping techniques was developed for a single actuator trajectory tracking. The hybrid control algorithm operates in various discrete modes based upon pressure states. A rigorous stability analysis of the actuator in all operating range was conducted. The controller guarantees accurate trajectory tracking in the presence of unknown load. It can lock the pressure on the charging line when it goes low to prevent cavitation. The control efforts are designed to maintain the throttling valve fully open whenever it is feasible, and use the variable flow source to achieve trajectory tracking.

One variable displacement pump is required as the power source. Although VDPs have the advantage of high control precision, they are typically more expensive, bulkier and heavier than fixed displacement units with similar displacements. In addition, to achieve a high bandwidth, powerful actuators are needed to change the pump geometry (e.g. the swash plate angle). To take advantage of fixed displacement pumps, a virtually variable displacement pump (VVDP) was developed and implemented as the power source for displacement control.

The VVDP consists of an on/off valve, a fixed displacement pump and an accumulator [7][8][9], as shown in Figure 1. By pulse-width-modulating (PWM) the on/off valve, mean partial flow is achieved with the virtual displacement set by the PWM duty ratio. Since the on/off valve has low loss in either on or off states, this approach reduces throttling loss. In addition, many types of fixed displacement pumps, including those that are low cost and compact but whose displacements cannot normally be varied, can be made variable.

Figure 1: Software enabled VVDP Circuit

The key component to an efficient VVDP is the on/off valve. Ideally, the on/off valve should meet four requirements simultaneously, including: a large orifice, a fast transition, the ability to operate at high PWM frequencies, and a low actuation power. A novel type of high speed rotary self-spinning on/off valve has been developed, which can meet the four requirements at the same time [7].

The rest of the paper is organized as follows. In the next section, the working principle of the novel 3way valve based VVDP will be introduced. In section 3, the open circuit of displacement control using the VVDP will be described. The dynamic modeling of the system will be presented. An advanced nonlinear control strategy developed for actuator trajectory tracking in an energy efficient manner will be presented in section 4. Simulation results will be presented in section 5. Finally, some concluding remarks and the future research plan will be presented in section 6.

2. A NOVEL 3WAY VALVE BASED VVDP

Figure 2 shows a novel 3-way on/off valve based VVDP. The valve is composed of a stationary sleeve and a moving spool. To reduce the fluid volume between the pump outlet and the valve inlet, so as to minimize the compressible loss, the valve sleeve is directly mounted onto a fixed displacement pump by modifying the pump housing. Inlet nozzles tangential to the bore are casted inside the sleeve. A pressure rail inside the sleeve connects the nozzles and the pump outlet on the pump housing. The rhombus shape of the valve nozzle provides a fast transition

Figure 2: A novel 3-way rotary self-spinning on/off valve based VVDP

Figure 3 shows the structure of the valve spool. The valve spool consists of three sections: one center PWM section and two outlet turbines. Helical barriers are wrapped

around the center PWM section. These barriers partition the center PWM section into two parts. The internal axial path directs the flow from the center PWM section to the adjacent outlet turbine. Both the center PWM section and the outlet turbines are designed to capture fluid moment to achieve spool self-spinning. The center PWM section functions as an impulse turbine. Fluid is accelerated through the nozzles inside the sleeve. The outlet section is designed as a reaction turbine. The turbine blade guides the fluid from flowing axially to exit the spool tangentially, and therefore a reaction torque is generated. In this way, the spool rotary motion is realized via self-spinning. The unidirectional rotary motion of the valve spool minimizes the on/off motion power consumption (proportional to PWM frequency squared) compared with linear poppet or spool type of on/off valves (proportional to PWM frequency cubed)

As the spool rotates, the inlet nozzles land on the red triangles and blue triangles alternately. The red branch directs the fluid to load, and the blue branch directs the fluid back to tank. In this way, the valve pulse width modulates the inlet flow. If there are N triangle sets around the spool, then the PWM frequency is N times the spool rotary frequency. The PWM duty ratio is determined by the fraction of the time when the nozzles lands on the red triangle over one revolution. The helical shape offers a linear relationship between the duty ratio and the spool axial position.

Figure 3: Valve spool structure

The spool axial motion is controlled externally, as shown in Figure 4. The spool axial position is controlled using an electro-hydraulic gerotor pump powered by a DC motor in a hydrostatic configuration. The gerotor pump ports fluid into the axial position ports as shown in Figure 1. By pumping fluid from one axial chamber to the other, the spool axial position is varied. One feature to notice is that

fluid enters the spool tangentially, and leaves the spool tangentially as well. There is no net moment in the axial position, which minimizes the power required to regulate the spool axial position. Sensing of the axial and rotary positions of the spool is realized using non-contact optical sensors to maintain a simple sealing structure.

Figure 4: Valve spool sensing and actuation

3. DIRECT DISPLACEMENT OPEN CIRCUIT CONTROL USING A VVDP

HYDRAULIC CIRCUIT - Figure 5 shows the hydraulic circuit for direct displacement control. The VVDP replaces a VDP as the flow source. The average flow is controlled by the PWM duty ratio. Compared with the VVDP presented in Figure 1, the accumulator is eliminated. Based on the preliminary experimental test, it is revealed that given the ability to operate at a high PWM frequency (~90Hz), the compliance of hoses is sufficient for smoothing out the pressure and flow ripples. A 2-position directional valve is used to change the flow direction. The directional valve is always fully open to reduce throttling loss. A proportional throttling valve is added on the return line, which will be used to avoid actuator chamber cavitation. In most operations, the throttling valve is fully open to reduce throttling.

Figure 5: Hydraulic configuration using VVDP to control one single actuator in displacement control open circuit

SYSTEM DYNAMICS – The hydraulic cylinder is modeled as a mass acted upon by the pressure in the two cylinder chambers, the linear viscous friction force, and the load force.

LFxbAPAPxm +−−= 2211 (1)

m is the mass of the cylinder rod. 1A and 2A are the areas of the cylinder cap end and the rod end. b is the viscous friction coefficient, and LF summarizes the carrying load, leakage, and un-modeled dynamics.

Depending on the position of the directional valve, the circuit has two configurations, as shown in Figure 6. x is the position of the cylinder rod. Q is the flowrate into the upstream chamber. 1V and 2V are the volumes in the respective chamber and hose when 0=x . The throttling valve on the return line is modeled as an orifice.

Figure 6: Hydraulic circuit for different directional valve position

The 2 positions of the directional control valve are denoted by { }1,1 −=du and the respective circuits are shown in

Fig. 6 (a) and (b). Let the tank pressure be tP ,

ρ/2maxACK dv = , with maxA being the maximum valve opening area, and ]10[ , u∈ be the normalized throttling valve command.

Depending on the operation of the directional valve, the pressure dynamics are:

• When 1=du (Fig. 6 (a)):

))(||(

)(

22222

2

111

1

ttv PPsignPPuKxAxAV

P

xAQxAV

P

−−−−

=

−+

=

β

β

(2)

• When 1−=du (Fig. 6 (b)):

)(

))(||(

222

2

11111

1

QxAxAV

P

PPsignPPuKxAxAV

P ttv

+−

=

−−−+

=

β

β

(3)

4. CONTROL STRATEGY

The control objective is for the actuator position )(tx to track a trajectory )(tr in the presence of unknown load )(tFL . The system pressure should remain low to improve efficiency. Cavitation should be avoided in both cylinder chambers during the operation and the chamber pressures should be bounded.

SYSTEM DYNAMICS IN STATE SPACE FORM – Four states are defined to represent the system dynamics: actuator position xx =1 , actuator velocity xx =2 , and the cylinder chamber pressures 21,PP . Define a new state

22113 APAPx −= , and mFd L /= . Eqs. (1)-(3) become:

( )

totalU

ddd uuPPuxGQuxHxxKx

dxm

xmbx

xx

⋅Ψ+⋅+

−=

++−=

=

,,),(),( )(

1

2111

213

322

21

(4)

where

122

22

111

21

1)(xAV

AxAV

AxK−

++

=ββ

⎪⎪⎩

⎪⎪⎨

⎧

−=−

−

=+

=1

1),(

122

2

111

1

1

d

d

d

uxAV

A

uxAV

A

uxH ,

,

β

β

⎪⎪⎩

⎪⎪⎨

⎧

−=+

−

=−

=1

1),(

111

1

122

2

1

d

d

d

uxAVA

uxAV

A

uxG ,

,

β

β

⎪⎩

⎪⎨⎧

−=−−

=−−=Ψ

1),(||1),(||

),,(11

2221

dttv

dttvd uPPsignPPK

uPPsignPPKuPP

The pressure dynamics are the same as described in Eqns (2) and (3).

Since one control objective is cylinder position trajectory tracking, define three system tracking error states as: 11 xre −= , 22 xre −= , 33 xrbrme −+= . Define

also the augment integral error state: ∫= dteei 1 we have:

total

i

UexKrxKrbrme

dem

embe

eeee

−−++=

++−=

=

=

2113

322

21

1

)()(

1

(5)

where totalUxK and ),( 1 are defined in Eqn (4). There are three control inputs to manipulate: flowrate of the variable flow source 0≥Q , the orifice area of the throttling valve

0≥u , and the directional valve { }1 ,0∈du .

BACK-STEPPING CONTROLLER -The error dynamics represented in Eqn (5) is in a strict-feedback form, which allows a Lyapunov function based back-stepping control technique to be applied.

Step 1 – Since the first two states are linear, using 2e as the virtual control input, the first two states can be stabilized simultaneously. Assuming all the states are measurable, the control input is determined by doing a pole placement with full states feedback. The poles are placed at 1λ and 2λ , 0,0 21 << λλ . The pole-placement control law with 2e as the input is:

121211 )(: eei λλλλα ++−= (6)

The closed loop dynamics becomes:

Let ⎥⎦

⎤⎢⎣

⎡=

2221

1211

PPPP

P be the symmetric positive definite

matrix that satisfies the Lyapunov equation:

IPAPA clTcl −=+ . Define the Lyapunov function for the

first step as: PeeV T=1

(8) ( ) )(2 122211221

21 ePePeeeV ii +−+−−= α

Step 2 – The Lyapunov function defined in Eqn (8) is augmented with the error between 2e and 1α :

2122 )(

21

α−+= ePeeV T

[ ])()(2)( 12122211221

22 αα −++−+−−= eePePeeeV ii

(9)

From this, the control law with 3e in Eq. (5) being the virtual control input is defined as:

])(2)(

)(

12221221

12121232

ePePe

eembem

i +−++

⎢⎣

⎡ −+−−=

λλ

λλαλα

(10)

where 03 >λ . The derivative of the Lyapunov function becomes:

))((1)()(

2312

122

12321

22

αα

ααλ

−−+

−+−−−−=

eem

deeeeV i

(11)

Step 3 – the Lyapunov function defined in Eqn (9) is augmented with the error between the virtual control input 2α and 3e :

223

2123 )(

21)(

21

αα −+−+= eePeeV T

)(

10

)(10

12121211

αλλλλ

−⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

+−=⎟⎟

⎠

⎞⎜⎜⎝

⎛e

ee

ee

dtd

e

i

Acl

i

(7)

))(())((1)()(

23232312

122

12321

23

αααα

ααλ

−−+−−+

−+−−−−=

eeeem

deeeeV i

(12)

The desired value for 3e is: for 04 >λ :

)()(1 2341223 αλαα −−−−= eem

e d (13)

According to Eqns. (4)-(5), the control inputs Q , u , and du appear in the dynamics of 3e via the total control

effort )(tUtotal .The desired total control efforts should therefore satisfy:

2113*

*

)()(:)(

)()(

exKrxKrbrmetUtUtU

dtotal

totaltotal

−+++−=

=

(14)

With this control effort, Eqn (12) becomes:

223412

2123

21

23 )()()( αλααλ −−−+−−−−= edeeeeV i (15)

If the disturbance 0=d , 2V will be negative definite, and the tracking errors will go to zero exponentially. In the presence of the disturbance d , the errors do not vanish but by choosing 3λ large enough, the quadratic

term 2123 )( αλ −− e can dominate the disturbance

term )( 12 α−ed so that the tracking error can be arbitrarily bounded.

CONTROL EFFORT DISTRIBUTION – The control objectives are to ensure:

1. The trajectory tracking performance 01→e . From the backstepping control design, this is ensured by:

( )

)(

,,),(),(:)(*

2111

tUuuPPuxGQuxHtU

total

dddtotal

=

⋅+⋅= ψ (16)

2. The pressure in both chambers should be higher than a threshold values tPP >1 and tPP >2 for each chamber to prevent cavitation:

tPPP >≥ 11 , tPPP >≥ 22 (17)

The pressure dynamics Eqns. (2)-(3) can be written as:

When 1=du

)( 2111

1 xAQxAV

P −+

=β

(18a)

)),(( ,212222

2 uuPPxAxAV

P dΨ−−

=β

(18b)

When 1−=du

)),,(( 212111

1 uuPPxAxAV

P dΨ−+

=β

(18c)

)( 2222

2 QxAxAV

P +−

=β

(18d)

From (4), the signs of ( )duxH ,1 and ( )duxG ,1 are the

same as the sign of by du . If the pressure in the both cylinder chambers satisfies: For }2,1{=i

,)( tii PPtP >≥ ,

Then ),,( 21 duPPΨ is also positive. Hence, to satisfy (16),

since 0≥u and 0≥Q , du can be determined by the sign

of *totalU :

⎩⎨⎧

<−

≥=

0)(10)(1

)( *

*

tUtU

tutotal

totald

(19)

The usage of Q andu is based on the rule that: u is fully open whenever it is feasible to reduce throttling loss, and to maintain the return line pressure low. There are three operating modes depending on whether any of the pressure constraints is active or not.

Mode 1: 11 )( PtP > and 22 )( PtP > : This mode applies to

the cases when no pressure constraint is active. *totalU is

solved in an energy efficient way, which minimizes the usage of the throttling valve. Since the flow source is of positive displacement, if a negative flow is required, the flow is set to zero, and the trajectory tracking is achieved by using the throttling valve.

Mode 2: ( 0* >totalU and 11 )( PtP ≤ ), or ( 0* <totalU and

22 )( PtP ≤ ): In this mode, the pressure in the upstream cylinder chamber connected with the flow source is low, and has the potential to cavitate. From Eqns (18a) and (18c), the variable flow source Q will be used to increase the pressure. The throttling valve u will be used for trajectory tracking according to the variable flow sourceQ to satisfy Eqn (16). The controller will stay in this mode to increase the chamber pressure until the pressure is higher than the threshold, and the operation goes back to Mode 1. The control law is:

(22)

Notice that this imposes lower bound on Q (or an upper bound on u ). If the upper bound on u is greater than 1, then we can set 1=u , and (22) reduces to Eq. (20) in mode 1.

Mode 3 – This mode applies to the cases when the pressure in the return chamber is low. To prevent the pressure from going below the threshold, considering pressure dynamics in Eqns (18b) and (18d), the throttling valve u will be used to increase the chamber pressure when it reaches the threshold. The controller will stay in this mode to increase the chamber pressure until the

pressure is higher than the threshold, and the operation goes back to Mode 1. The control law is:

In both cases, once u is chosen,

(23)

Similar to mode 2, this imposes an upper bound on u . If this bound is greater than 1, then we can set 1=u , and (23) reduces to Eq. (20) in mode 1.

In the above controller modes, the calculation of du , Q and u are based on the Lyapunov function as presented in Eqn. (11). The control inputs can guarantee that the Lyapunov function remains decreasing during modes switching. This guarantees the trajectory tracking performance. Since whenever the pressure reaches the pressure lower bound iP , the controller will force the chamber pressure to increase (Mode 2 and Mode 3); this will guarantee that if the initial chamber pressures are above the threshold, they will continue to be above threshold iP . Thus, cavitation cannot happen in the cylinder chamber.

5. SIMULATION RESULTS

The control strategy is simulated using Simulink Matlab. Some of the system parameters of are based on an experimental set up that is being constructed currently; the other parameters are estimated from typical values, as shown in Table 1.

Parameter Description Symbol Value

Cylinder mass m kg3

Cylinder cap area 1A 226.20 cm

),(),,(),(

1

211*

d

ddtotal

uxHuuPPuxGU

Qψ−

=

Case 1:

22* ,0 PPUtotal ≤> :

),,( 21

22

duPPxAu

ψ<

Case 2:

11

* ,0 PPUtotal ≤< :

),,( 21

21

duPPxAu

ψ−

<

Case 1: 11* ,0 PPUtotal ≤> :

21xAQ >

Case 2: 22* ,0 PPUtotal ≤< :

22xAQ −>

In both cases,

),,(),(),(

211

1*

dd

dtotal

uPPuxGQuxHU

uψ

−=

Case 1: ),(

),,(),(

1

211*

d

ddtotal uxH

uPPuxGU Ψ> ,

),(),,(),(

,1

1

211*

d

ddtotal

uxHuPPuxGU

Q

uΨ−

=

=

(20)

Case 2: ),(

),,(),(

1

211*

d

ddtotal uxH

uPPuxGU Ψ≤ ,

),,(),(

,0

211

*

dd

total

uPPuxGUu

Q

Ψ=

=

(21)

Cylinder rod area 2A 277.10 cm

Viscous friction coefficient b sec)//(65.1 mN

Oil Bulk Modulus β Pa7101×

Throttling Valve Full Open Area valveA 22.0 cm

Table 1 Simulated system parameter The constant bulk modulus of the oil is estimated by assuming the air volume content in the hydraulic oil at atmosphere pressure is %7 , and the load pressure is under bar70 [14].

The actuator was simulated to track a sinusoid trajectory with amplitude of cm3 , and a frequency of Hz1 . A constant load of N50 was added as the disturbance load. The initial volume on the cap side of the cylinder is L2.1 , and the initial volume on the rod side is L0.1 . The control gains were selected as: 301 −=λ , 302 −=λ , 303 =λ ,

and 304 =λ .The pressure lower bound for both cylinder chambers are set to be barPP 221 == .

The trajectory tracking of the cylinder is shown in Figure 7. With the introduction of the integral control, the cylinder can track the trajectory accurately even with a load disturbance. The pressures inside both cylinder chambers start from an initial value that is higher than the lower pressure threshold, and the pressure remain higher than the threshold. The system pressure remains low.

0 1 2 3 42

4

6

8

10

time [sec]

Cyl

inde

r Pos

ition

[cm

]

trajectory referencecylinder position

0 0.5 1 1.5 2 2.5 3 3.5 4

2

468

1012

14

time [sec]

Cha

mbe

r Pre

ssur

e [b

ar]

Cap sideRod side

Figure 7. Cylinder position trajectory tracking and the chamber pressures

The control efforts are shown in Figure 8. As designed, the directional control valve does not change direction very frequently, especially after the trajectory is well tracked. The throttling valve is kept fully open most of time, and it starts to close when the trajectory velocity decreases, comes to a stop and switches direction. The throttling valve is also used when the pressure constraint is active, so that the pressures inside both cylinder chambers stay above the pressure lower bound.

0 1 2 3 40

10

20

30

40

time [sec]

Flow

rate

[lpm

]

0 1 2 3 40

50

100

time [sec]

Thro

ttlin

g va

lve

open

ing

%

0 1 2 3 4-1

-0.5

0

0.5

1

time [sec]

Dire

ctio

nal v

alve

Figure 8. Control efforts from variable flow source, throttling valve and directional valve

6. CONCLUSION AND FUTURE WORK

In this paper, the displacement control of a single hydraulic actuator was investigated. An open circuit was proposed to realize direct displacement using one variable flow source, one directional valve, and one throttling valve. A multiple mode control strategy was developed to achieve accurate trajectory tracking with maintaining a low system operating pressure. The trajectory tracking was

based on a nonlinear back-stepping controller. This controller guarantees that neither of the cylinder chambers cavitates or goes unbounded.

An experimental set was being developed. In the next step, we will implement this control strategy on the backhoe with the novel VVDP as the variable flow source.

ACKNOWLEDGMENTS

This material is based upon work performed within the ERC for Compact and Efficient Fluid Power, supported by the National Science Foundation under Grant No. EEC-0540834.

REFERENCES

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3. K. Heybroek, “Saving energy in construction machinery using displacement control hydraulics-concept realization and validation”, PhD dissertation, 2008.

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Mechanical Engineers, The Fluid Power and Systems Technology Division, American Society of Mechanical Engineers, New York, NY 10016-5990. IMECE2006-14973

10. H. Tu, M Rannow, M Wang, P Li, T, Chase, “ Modeling and validation of a high speed rotary PWM on/off valve” Proceedings of the ASME Dynamic Systems and Control Conference 2009, DSCC2009, n PART A, p 629-636, 2010, Proceedings of the ASME Dynamic Systems and Control Conference 2009, DSCC2009

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15. H K. Knaill “Nonlinear Systems”. Third Edition, Upper Saddle River, NJ: Prentice-Hall, Inc.,2002. pp. 588-589.

CONTACT

Meng Wang, Haink Tu, and Mike Rannow: graduate students with Center for Compact and Efficient Fluid Power, Department of Mechanical Engineering, University of Minnesota.

Email: {wang134, tuxxx021, rann0018}@me.umn.edu

Dr. Perry Y Li: professor with Center for Compact and Efficient Fluid Power, Department of Mechanical Engineering, University of Minnesota.

Email: pli@me.umn.edu

Dr. Thomas R. Chase: professor with Center for Compact and Efficient Fluid Power, Department of Mechanical Engineering, University of Minnesota.

Email: trchase@me.umn.edu