DSCC HYDRAULIC CYLINDER VELOCITY CONTROL WITH ENERGY RECOVERY: A COMPARATIVE SIMULATION STUDY

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HYDRAULIC CYLINDER VELOCITY CONTROL WITH ENERGY RECOVERY: A COMPARATIVE SIMULATION STUDY

Ned A. Troxel Graduate Student

School of Mechanical Engineering Purdue University

West Lafayette, Indiana 47907 Email: ntroxel@purdue.edu

Bin Yao Professor

School of Mechanical Engineering Purdue University

West Lafayette, Indiana 47907 Email: byao@purdue.edu

ABSTRACT

A valve configuration including a hydraulic accumulator for energy recovery is proposed for velocity control of hydraulic cylinders. A control design incorporating a low-level adaptive robust controller and high-level logic is presented. The bene- fits of independent cylinder pressure control, regeneration flows, and the proposed energy recovery system are compared. Simu- lation results show the proposed configuration provides signifi- cant energy savings compared to the other system configurations following the same velocity trajectory. An explanation of the ad- vantages of the proposed configuration over previous configura- tions is given, showing why the proposed configuration makes increased recycling of system flows possible. Results for con- stant pressure source and a load-sensing pump show that differ- ent control objectives are appropriate for different supply pres- sure setups. Additional applications and further study of the pro- posed configuration are discussed.

1 INTRODUCTION

Hydraulic excavators, wheel loaders, and other mobile hy- draulic machinery typically have several hydraulic actuators which are controlled by the operator. In many traditional applica- tions, the operator controls the velocity of hydraulic cylinders or motors by directly controlling the spool position of a 3-position, 4-way directional valve. Hydraulic cylinders with this configu- ration have one spool position to control both the flow into and out of the actuator, and so independent control of both cylinder chamber pressures is not possible. Using separate valves to con- trol these flows for significant energy savings is not a new idea.

Address all correspondence to this author.

Figure 1. PROPOSED 6 VALVE SYSTEM CONFIGURATION

Proceedings of the ASME 2011 Dynamic Systems and Control Conference DSCC2011 October 31 - November 2, 2011, Arlington, VA, USA

DSCC2011-6192

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Such independently metering valve configurations have been studied to see how separate valves may be used to increase efficiency and performance. A detailed review of the state of the art for these types of systems is given by Eriksson and Palm- burg [3]. Hu and Zhang integrated five two-way cartridge valves and showed that the configuration could emulate the character- istics of open-center, closed-center, tandem-center, and float- center spool valve geometries and that a regeneration function (for increased extension speed) could be realized [5].

Regeneration is the process of recycling hydraulic fluid flowing out of one chamber into the other chamber. Shenouda studied the potential for energy savings using normal and regen- eration operation modes on a 4-valve configuration [9] similar to that studied by Hu and Zhang. Liu and Yao presented a system with a 5-valve configuration which added a valve to control flow directly between the cylinder ports and demonstrated its ability to save energy [8]. This configuration was different from that stud- ied by Hu and Zhang since their fifth valve was used as to provide relief and open-center functions and does not allow cross port re- generation flow. The principles behind independent metering and regeneration will be discussed in more detail later.

Other papers which deal with similar valve configurations are found in [1, 2, 7]. There are many patents relating to indepen- dent metering valves, regeneration flows, and applicable control methods [4, 6, 10, 11]. Industrial applications of independent me- tering valves are currently on the market.

This paper will show the benefits of adding an energy re- covery system to further increase efficiency. A double-acting, single-rod hydraulic cylinder is used as an example, and the pro- posed system configuration is shown in Fig. 1 with a constant pressure supply setup.

2 SAVING ENERGY IN HYDRAULIC SYSTEMS

Increasing the efficiency of any system means reducing the total input energy required to perform a given task. The energy provided to a system on the interval [t0,t1] may be calculated by:

Es= ˆ t1

t0

ps(t) Qs(t) dt (1)

where ps(t) is the supply pressure and Qs(t) is the flow rate into the system. It is clear that the energy used by the system can only be reduced by lowering the supply pressure or reducing the flow provided. This is made possible by reducing the energy dissipated by the system.

The main sources of energy dissipation in hydraulic systems are mechanical friction, throttling losses, and leakage. For valve- controlled systems, the throttling loss is often the largest of these three components and can be most influenced by the system con- figuration and control algorithm. Throttling losses are caused by friction between the hydraulic oil and the flow passage and by

viscous shear forces within the fluid. The flow path obstruction created by a valve results in permanent pressure (and energy) loss. The power dissipated by oil flow through a valve is the product of the flow rate and the pressure drop (i.e. P = ∆p · Q).

Thus, the most efficient way to supply a given flow is with the smallest pressure drop possible. In general, the minimum pres- sure drop for a given flow occurs when a valve is fully open.

Load-sensing (LS) pumps maintain a slightly higher supply pressure than the maximum cylinder chamber pressure. Thus, when the highest chamber pressure decreases, so does the supply pressure and less energy is input to the system as compared to a constant pressure supply. Because the pressure drop between the source and the chamber pressures is reduced, the throttling losses are also reduced and the same performance can be achieved with lower input energy. By setting one chamber pressure to a low level, the maximum chamber pressure can be reduced. When such a strategy is combined with a LS pump, the required input energy is significantly reduced.

If a constant pressure source is used, then no matter how the system pressures change, the energy supplied for two different situations will be equal if the flows are equal. The only way to save energy is to reduce the flow from the pump. This may be accomplished by recycling flow from the system, as occurs when regeneration is used.

Regeneration can theoretically be used whenever the flow leaving one chamber has a higher pressure than the other cham- ber. This commonly occurs during deceleration periods or in the presence of an overrunning load (e.g. lowering a heavy load).

Shenouda showed that for a 4-valve setup, flow could be regener- ated from one chamber to the other through the return valves [9].

This is equivalent to flow through valves #2 and #5 in Fig. 1. It should be noted that Shenouda’s system employed a check valve in the return line which supported a slight pressure drop before opening, thus maintaining positive pressure. This regeneration flow is driven by the overrunning load and saves energy by re- ducing the required supply flow.

For a single rod cylinder, regeneration may be possible during extension of the rod due to the significant difference in the rod and head side piston areas. When the required load force is low, the the rod chamber pressure can exceed that of the head chamber. This type of regeneration has been used with a four valve configuration by allowing the flow to pass from one chamber to the other through the supply valves (equivalent to flow through valve #4 and then valve #1 in Fig. 1). In order to do this, the rod chamber pressure must exceed the source pressure.

This type of regeneration can boost the maximum extension speed, but usually requires significantly higher source pressure (and hence greater energy consumption) than normal operation, as observed by both Shenouda and Hu and Zhang [5, 9]. When true cross port flow is possible, as in the system used by Liu and Yao [8], the pressures can be much lower, allowing this technique to provide high flow without a drastic pressure increase or to save energy by reducing the supply flow.

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The proposed configuration includes an accumulator in the regeneration flow path. The effect of this modification is to de- couple the regeneration flows, since flow can be stored in the accumulator. Thus, the regeneration flow out of the high pres- sure chamber need not equal the regeneration flow into the low pressure chamber, as is required in normal regeneration. The ac- cumulator may be charged any time the flow out of a cylinder has higher pressure than the accumulator, and flow from the ac- cumulator can be used to replace flow from the pump whenever the flow is into a chamber at a lower pressure than the accumu- lator.

Figure 2. ENERGY RECOVERED BY REDUCING THROTTLING LOSSES

The accumulator reduces the throttling losses by acting as a second flow source or sink. Flow out of a high pressure cylinder chamber can be directed to the accumulator rather than simply throttled to the tank. The associated throttling loss is lower be- cause of the lower pressure drop. Figure 2a illustrates the situa- tion where a flow Q from a chamber at pressure pcylis throttled to the tank, and Fig. 2b shows the case when it flows into an accumulator at pressure pac. The shaded areas in the diagrams represent the power loss due to throttling and the power stored in the accumulator. When the accumulator is charged with fluid, the stored energy may be reused when the pressure in at least one cylinder chamber is below pac. The accumulator then acts as a secondary pressure source to supply flow, replacing the flow from the pump. Of course, for a very slight pressure drop, the maximum achievable flow through a control valve may be less than the amount required. In such cases, the accumulator can act as a source or sink in parallel with the main pressure source or the tank, which still provides a portion of the benefits seen when the accumulator provides or receives the entire flow.

3 CONTROL DESIGN

The objective of the controller is to calculate a set of valve commands such that the load velocity tracks a desired velocity trajectory vd(t). This paper assumes that vdhas been determined and that two of its derivatives are known. The task of defining the trajectory will not be addressed. A very simple way to obtain vd is to filter the user command (e.g. a joystick signal) with a linear filter of relative degree of two or more. A more sophisti- cated approach would take the system’s limitations into account explicitly.

The available measurements are the piston position x, piston velocity v, the head and rod chamber pressures pAand pB, and the pressures of the accumulator, supply, and return line (pac, ps, and pt respectively). The dynamics of the load motion and cylinder chamber pressures are given by:

m˙v(t) = pL(t) − bv (t) + d (t) , pL= AApA(t) − ABpB(t) (2) VA(t)

βe

˙

pA(t) = −AAv(t) + QA(t) ,VB(t) βe

˙

pB(t) = ABv(t) + QB(t) VA= VAmin+ AAx(t) , VB= VBmin+ AB(xmax− x (t))

where m is the effective load mass, v is the load velocity, b is a coefficient of viscous friction, and d (t) is a the lumped uncertain- ties term. The uncertainties are bounded such that |d (t)| < dM

for all time for some dM> 0. The load force on the piston is pL. AAand AB are the head side and rod side piston areas, respec- tively. VAmin and VBmin are the minimum cylinder volumes (i.e.

inefficient volume), and xmaxis the stroke length of the cylinder.

The flow rates QAand QBare regarded as virtual control inputs for lower-level controller design purposes, while the actual con- trol inputs are the valve commands.

The controller used in this study has two-levels, as illustrated in Fig. 3. A low-level adaptive robust flow rate controller similar to that used by Liu and Yao [8] calculates desired cylinder flow rates for precise motion control. A high level algorithm decides how pressures should be specified and how the flow should be distributed to the valves for maximum efficiency. This flow dis- tribution and the pressure measurements are used by another low level controller to determine the appropriate valve commands via inverse flow maps.

Figure 3. OVERALL CONTROLLER STRUCTURE

3.1 High Level Decision Controller

In order to control the motion of the cylinder precisely, only the load force pL needs to be regulated. Theoretically pAor pB may be specified arbitrarily and the other pressure may be used to achieve the desired load force. Based on the desired load force pLd from the flow rate controller, a decision is made to regulate either pAor pBand the appropriate set point is calculated. For ex- ample, pBdcould be chosen to be slightly above the accumulator pressure during extension so flow from the rod chamber can flow

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into the accumulator. When a LS pump is used, a good strategy is to achieve pLdwith the lowest pressures possible.

To provide the desired flow rates QAd and QBd calculated by the low level controller, appropriate flow rates for each valve must be specified. A type of priority flow distribution is imple- mented, so that flow to and from the accumulator is used when- ever the system pressures make it possible. Thus, when the de- sired flow rate into a chamber is positive, the corresponding ac- cumulator valve supplies either the total flow or as much as is possible given the pressure drop. The remaining flow is supplied from the source. Similarly, it is always better to charge the accu- mulator than to throttle flow to the tank, so when a flow rate out of a chamber is specified, all the flow or as much as is possible is directed to the accumulator and any remainder is throttled to the tank. This scheme reduces the required supply flow and charges the accumulator as much as possible for the given QAdand QBd.

3.2 Low Level Flow Rate Controller

A nonlinear ARC algorithm calculates the desired flow rates based on the desired velocity trajectory and the position, velocity and cylinder pressure measurements.

The disturbance force d (t) may be broken into its constant and time varying parts as: d (t) = d0+ ˜d(t). Denote the discrep- ancy from the commanded flow rates as ∆QAand ∆QB, such that QA= QAd+ ∆QAand QB= QBd+ ∆QB. The unknown parame- ter set is θ =1

m b m

d0

m βeβeQAβeQB. The possible range of values for each parameter is known, such that for each compo- nent i, θmin,i< θi< θmax,i. Denote the estimate of θ as ˆθ and the estimation error as ˜θ = ˆθ − θ.

A discontinuous projection is included in the parameter adaptation law, which is defined by:

θ = Proj˙ˆ ˆθ(Γτ) , Projˆθi(•i) =





0 i f ˆθi= θi,minand•i< 0 0 i f ˆθi= θi,maxand•i> 0

i else

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where Γ is a diagonal, positive definite adaptation rate matrix and τ is the adaptation function to be specified later. A diagonal Γ allows the projection to be defined and applied for each compo- nent separately. This projection mapping ensures that the param- eter estimates always lie between the known bounds, and hence the estimation error is uniformly bounded by

˜θ

≤ |θmax− θmin|.

This fact is necessary for the design of robust control functions to be introduced later.

The system model in Eq. (2) may be rewritten in terms of the unknown parameters as follows:

˙

v= θ1pL− θ2v+ θ3+ θ1

˙

pL = θ4ψL− θ4

 A2A VA+A2B

VB

 v+ θ5

AA VA− θ6

AB

VA (4)

where ψL=AVA

AQAdAVB

BQBd. The function ψL can be specified exactly since it depends only on known constants and the desired flow rates. It will be used as a virtual input later on. It is clear from Eq. (4) that the system has unmatched uncertainties and disturbances since only pL can counteract the effect of ˜d and parameter estimation error in θ1, θ2 and θ3, but only ψL may be directly controlled. The backstepping design technique will be applied to overcome this problem. Two design steps will be required.

Step 1:The velocity tracking error is defined as z1= v − vd. In the first step, pLis treated as a virtual input. The virtual control law, pLd, to regulate z1is given by:

pLd= pLa+ pLs, pLa= 1

ˆθ1d+ ˆθ2v− ˆθ3

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pLs= pLs1+ pLs2, pLs1= − k1 θmin,1

z1

where k1is a positive gain and pLs2is a robust control function.

The function pLaprovides model compensation while pLs1pro- vides a nominally stable dynamics for z1. The synthesis of pLs2 will be discussed later.

Denote the discrepancy of the actual load force from the vir- tual control law as z2= pL− pLd. Noting (5), the dynamics of z1 may be written as:

˙z1= θ1(pLd+ z2) − θ2v+ θ3+ θ1d˜− ˙vd

= − θ1

θmin,1

k2z2+

θ1pLs2+ θ1d˜− φT1˜θ + θ1z2 (6)

where

φ1= pLa−v 1 0 0 0T

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If pL were the actual input to the system, then the adaptation function would be given by τ1= φ1z1. This function will be used later in defining the final parameter adaptation law. The robust control function pLs2must satisfy the following 2 properties:

z1

θ1pLs2+ θ1d˜− φT1˜θ ≤ ε1 (8)

z1pLs2≤ 0 (9)

where ε1is a positive design parameter related to the guaranteed final tracking error and can theoretically be arbitrarily small, but is limited in practice by the physical response speed of the valves.

The property in Eq. (8) assures that pLs2will dominate the para- metric uncertainties (φT1˜θ) and uncertain nonlinearities ( ˜d) to a

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prescribed level. The second property (9) assures that the robust feedback will not interfere with the adaptation process.

Step 2: The next step will design a virtual control law for ψL to regulate z2. To do this ˙pLd must be considered, but this derivative is not fully calculable due to unknown parameters and disturbances. Denoting the calculable and incalculable compo- nents of ˙pLdas ˙pLdcand ˙pLdu, the z2dynamics are expressed as:

˙z2= θ4ψL− θ4

 A2A VA+A2B

VB

 v+ θ5

AA VA− θ6

AB

VA− ˙pLdc− ˙pLdu

˙

pLdc= ∂ pLd

∂v ˆ˙v +∂ pLd

∂z1

ˆ˙z2+∂ pLd

∂t

+∂ pLd

∂ ˆθ θ˙ˆ

= 1

ˆθ1d(t) + ˆθ2ˆ˙v − 1 ˆθ1φT1θ +˙ˆ



− k1 θmin,1

+∂ pLs2

∂z1

 ˆ˙z1

˙ pLdu=

∂ pLd

∂v +∂ pLd

∂z1



−˜θ1pL− ˜θ2v+ ˜θ3+ θ1d˜

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= ˆθ2

ˆθ1

− k1 θmin,1

+∂ pLs2

∂z1

!

−˜θ1pL− ˜θ2v+ ˜θ3+ θ1d˜ ˆ˙v = ˆθ1pL− ˆθ2v+ ˆθ3, ˆ˙z1= ˆ˙v− ˙vd

The acceleration estimate ˆ˙vis related to the acutal acceler- ation by ˙v= ˆ˙v− ˜θ1pL− ˜θ2v+ ˜θ3+ θ1d˜. Treating ψL from Eq.

(4) as a virtual input, ˙pLdc is used in model compensation while robust feedback mitigates the effects of ˙pLdu. The virtual control law is given by:

ψL = ψLa+ ψLs ψLa= 1

ˆθ4



−ˆθ1z1− ˆθ5

AA VAv+AA

VAˆθ6+ ˙pLdc

 + A2A

VA+A2B VB

 v

ψLs = ψLs1+ ψLs2, ψLs1= − k2

θmin,4

z2 (11)

The final adaptation function is given by τ = φ1z1+ φ2z2

where φ2is defined as:

φ2=

z1− pL

∂ pLd

∂ ˙x +∂ pLd

∂z2



∂ pLd

∂ ˙x +∂ pLd

∂z2

 v

−

∂ pLd

∂ ˙x +∂ pLd

∂z2

 ψLa−A2

A

VA +AV2B

B

 v

AA VA

AVB

B

The function ψLs2 must satisfy robust conditions similar to (8) and (9):

z2



θ4ψLs2− φT2˜θ − θ1

∂ pLd

∂v +∂ pLd

∂z1

 d˜



≤ ε2 (12) z2θ4ψLs2≤ 0 (13)

where ε2is a positive design parameter.

The final task of the flow controller is to calculate the de- sired cylinder flow rates, QAd and QBd. The high-level decision controller will specify whether pAor pBshould be regulated and to what set point. For an example, assume that a set point pBdis given for pB. A simple proportional feedback is used to drive the pressure to that value, since high accuracy is not necessary. The flow rates are then fully specified as follows:

QBd = −kpVB(x) ˆθ4

(pB− pBd) − ABv−ˆθ6

ˆθ4

QAd = VA(x)

AA ψLd+VA(x) AA

AB

VB(x)QBd (14)

4 SIMULATION RESULTS

Four different valve configurations were simulated. Similar strategies and techniques as presented in Section 3 were used to design a controller for each configuration. These configurations are described in Tab. 1. Each configuration was simulated with a constant pressure source and with a load-sensing pump. This section presents and explains the results obtained.

Table 1. VALVE CONFIGURATIONS Configuration

Name Description

PD Valve 3-position, 4-way proportional directional valve. This configuration is commonly used because of its simplicity.

4-Valve Four 2-position 2-way valves, equivalent to the proposed configuration if valves #3 and #6 in Fig. 1 are kept closed.

5-Valve

Five 2-position 2-way valves (a single valve is added to the 4-valve configuration to allow regeneration flow

directly between the two cylinder chambers)

6-Valve The proposed configuration uses a regeneration path with an accumulator and two 2-way valves (see Fig. 1).

4.1 Model Parameters and Setup

The parameters in Eq. (2) used for simulation were m = 2000 kg, b = 300Nsm, AA= 2 × 10−3m2, AB= 1.1 × 10−3m2, βe= 8.2 × 108Pa, VAmin= VBmin= 1.3 L, xmax= 0.3. Friction is

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modeled with Stribeck, Coulomb, and viscous components. The Coulomb friction magnitude is 200 N and the maximum Stribeck force is 10 N. The disturbance d (t) is created by the two unmod- eled friction components.

For the constant pressure cases, pSwas held constant at 69 bar. The LS pump is modeled as an ideal source which main- tains ps a fixed amount (∆pLS) higher than the maximum cylin- der chamber pressure with a first order lag of bandwidth ωLS. Explicitly, the source pressure changes according to:

s= ωLS(max (pA, pB) + ∆pLS) − ωLSps (15)

The source pressure was saturated at 69 bar. For all cases, 100

rad

s was used for ωLS. A value of 10 bar was used for ∆pLS, except for the directional valve which required 20 bar to generate sufficient flow to follow the trajectory. The tank pressure was held constant at 0 bar. The accumulator is modeled as:

f = QAac+ QBac

Vf =

0, pac< ppr

Vtot

 1 −p

pr

pac

1k

pac≥ ppr (16)

where Vf is the accumulator oil volume, Vtotis the capacity, ppr is the precharge pressure, pacis the accumulator oil pressure, and kis the polytropic gas constant. If the pressure pacdrops below ppr, then its dynamics change and pacchanges in response to the pressure to which it’s connected (pAand/or pB). For the constant pressure supply, ppr was set to 15 bar, while for the LS pump, a lower value of 4 bar was used. For both pressure supplies Vtot was 1.0 L and 1.4 was used for k, which models an adiabatic condition in the accumulator. This is reasonable given the rather rapid pressure changes experienced. The same desired velocity command (shown in Fig. 6a) is input to the controllers for all cases.

4.2 Energy Usage Results

This paper does not consider the effect of pump or motor efficiency on power consumption, but restricts its focus to the energy supplied to the system as in Eq. (1). For all cases, the sup- plied power is plotted in Figs. 4 and 5 for the constant pressure source and LS pressure source, respectively. The energy con- sumed, average efficiency, and mean absolute error are shown in Tabs. 2 and 3 for the constant pressure and LS pump, respec- tively. The average efficiency is calculated by dividing the total energy supplied to the load by the total energy consumed:

η =

´tf

t0 |pL(t) v (t)| dt

´tf

t0 ps(t) QS(t) dt (17)

The low values for efficiency reflect the low (on average) force required to drive the system. A large percentage of the desired trajectory is constant velocity motion, requiring high flow but a very low net force. The efficiencies would be higher for a trajec- tory with a larger percentage of accleration and deceleration or in the presence of larger disturbance forces.

Figure 4. POWER CONSUMPTION FOR CONSTANT PRESSURE SOURCE

Table 2. CONSTANT PRESSURE SUPPLY RESULTS System

Configuration

Net Energy Consumed (kJ)

Average Efficiency

mean absolute error (m/s)

PD valve 8.58 7.90% 0.0061

4 valves 8.56 7.86% 0.0023

5 valves 5.88 11.4% 0.0027

6 valves 3.52 19.1% 0.0036

For a LS supply, the energy required is greatly reduced by using the lowest pressure possible, but for a constant pressure supply, reducing the system pressures gives no benefit in terms of efficiency. As may be seen from Tab. 2, the energy required for the PD valve and 4-valve configurations is nearly identical for the constant pressure case. These configurations do not use regeneration flows, and thus use the same amount of source flow.

The 4-valve configuration lowers the back-pressure in the return chamber to a very low level, and the resulting chamber pressures are much lower than those of the PD valve. This results in a lower source pressure and significantly lower energy consumption than the PD valve for the LS case.

A comparison of the LS and constant pressure supply re- sults shows that the LS pump reduced the energy required for each configuration by 36-64% from the corresponding constant

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pressure case. It may be seen that the benefit of the 6-valve sys- tem over the 5-valve system is much greater when a constant pressure source is used than when a LS pump is used. This is natural, since one function of the accumulator is to save the ex- cess energy which results when the supply pressure is higher than required (see Section 4.3 for how this is done). A LS pump elim- inates this excess to a large extent, reducing the opportunity for the accumulator to save energy.

Figure 5. POWER CONSUMPTION FOR LOAD-SENSING PRESSURE SOURCE

Table 3. LOAD-SENSING PUMP RESULTS System

Configuration

Net Energy Consumed (kJ)

Average Efficiency

mean absolute error (m/s)

PD valve 5.42 12.6% 0.0083

4 valves 3.04 22.1% 0.0025

5 valves 2.67 25.2% 0.0030

6 valves 2.27 29.7% 0.0029

4.3 Comparison of 5- and 6-Valve Configurations Figure 6 shows pressure and flow variables for the 5-valve and 6-valve configurations with constant pressure source. A de- tailed comparison of the results will illustrate the difference be- tween the two configurations and explain why the proposed con- figuration requires less energy. First, the flow terms shown in Fig. 6d and Fig. 6e will be explained and then the operation of the 5- and 6-valve systems will be analyzed.

Qsis the total flow from the pressure source. By comparing the velocity (Fig. 6a), it can be seen whether the flow is into the head chamber (for v > 0) or rod chamber (for v < 0). Similarly, Qtis the total flow into the tank. For the 5-valve configuration, a

Figure 6. COMPARISON OF 5-VALVE AND 6-VALVE CONFIGURA- TIONS

single regeneration valve controls the cross port flow (QAB) from the head chamber at pressure pAto the rod chamber at pB. In Fig. 6d, QAB< 0 implies the flow is from pB to pA. In Fig.

6e, the flows QAacand QBacrepresent flows into the accumulator from the head chamber (pA) and rod chamber (pB), respectively.

If QAac< 0, then the flow is from the accumulator to the head chamber. Similarly, QBac< 0 indicates a discharge from the ac- cumulator to the rod chamber.

There are two situations where the 5-valve system uses re- generation flow: constant velocity extension (v > 0) and decel- eration. During extension with constant velocity, the net force required to maintain speed is quite low. During such times, pB> pAeven though the net force is still positive. This occurs because AA> AB. It can be seen from Fig. 6d that there is a large amount of flow from the rod to head chamber during these times.

Some flow from the pump is required to supplement the regen-

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eration flow because of the larger head chamber area. During deceleration, the flow out of one of the cylinders is restricted and the pressure rises, providing a braking force. During these times, regeneration flow is also used by the 5-valve configuration.

The 6-valve system also saves energy during the constant velocity extension period, but while the 5-valve still requires sig- nificant pump flow, the 6-valve system provides the flow almost entirely from the accumulator. This causes the pressure in the accumulator to drop significantly (see Fig. 6c, 0 < t < 1s). The 6-valve system can also charge the accumulator during periods of constant velocity retraction. Because of the low net force re- quired, pA can exceed pac so that flow from the head chamber can be directed to the accumulator rather than the tank. Regener- ation flow is never possible for the 5-valve configuration during such times. The 6-valve configuration also utilizes deceleration periods to charge or to provide flow to the low pressure chamber.

To summarize, the proposed configuration is able to recycle more flow than the 5-valve configuration. This can be explained in two ways. First, the accumulator may be said to decouple the regeneration flow. Thus, the accumulator can supply more flow than it takes in or take in more flow than it supplies. Second, the accumulator may be viewed as an additional flow source or sink, which can allow flow which would normally be throttled to the tank to instead be used to charge the accumulator. The accumulator acts as a low pressure source to replace the pump flow for light loads.

5 EXTENSIONS

There is much promise for further development of the pro- posed configuration. Several practical issues have not been ad- dressed. Reducing the pressure drop across a control valve re- duces the throttling loss, but in practice it may increase the diffi- culty of precisely controlling the flow. Unless high performance can be preserved, increased efficiency is often meaningless, so experimental results are necessary to show that the increased ef- ficiency shown by the simulation results is attainable in practice.

The valve position calculations performed by the controllers require inverse flow maps (look-up tables were used for this study). Such flow mappings are not easy to obtain experimen- tally and the actual flow characteristics may differ considerably from manufacturer’s data. It may be possible to improve the flow mappings online using adaptation.

No effort has been made in this paper to explain how to se- lect accumulator parameters (e.g. capacity, precharge pressure and typical working pressure) for optimum performance. Also, more detailed accumulator models could be used to examine the effect of thermal losses, which would be significant for longer charging and discharging times.

The analysis presented assumes a desired velocity trajec- tory has been specified. In reality, for step-like reference com- mands, the selection of the trajectory has a large effect on the effi- ciency, so the trajectory planning should be considered explicitly to achieve optimal performance and efficiency. Cases where d (t)

is large should also be considered, since lifting machinery such as hydraulic cranes and excavators commonly operate against large gravitational forces which are constant or piecewise con- stant (due to payload changes, for example). Large amounts of energy could be recovered when heavy loads are lowered.

An additional area of great promise for the current research is that of multi-actuator systems controlled by a single pressure source. Even when load-sensing equipment is used, the supply pressure is regulated to the highest system pressure, so throttling losses are significant for actuators requiring lower pressures. An accumulator could increase the system efficiency in these cases, in the same way as when a high constant pressure source is used.

If all actuators were connected with the accumulator, energy re- covered by one actuator could be supplied to another.

6 CONCLUSION

A new valve configuration including an energy recovery ac- cumulator was proposed for velocity control of hydraulic cylin- ders. A control design for this configuration was presented.

Comparative simulation results have shown that increased flow recycling allows the proposed configuration to follow a given ve- locity trajectory with lower energy usage than three other previ- ously studied valve configurations.

ACKNOWLEDGMENT

The work is supported in part by the US National Science Foundation (Grant No. CMMI-1052872).

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