valves coordinate control of the independent

Automation in Construction 57 (2015) 98–111

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Automation in Construction journal homepage: www.elsevier.com/locate/autcon

Pump/valves coordinate control of the independent metering system for mobile machinery Bing Xu a,⁎,1, Ruqi Ding b, Junhui Zhang a, Min Cheng a, Tong Sun a a b

The State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, China School of Mechatronic Engineering, East China Jiaotong University, China

a r t i c l e

i n f o

Article history: Received 7 August 2014 Received in revised form 4 April 2015 Accepted 23 April 2015 Available online xxxx Keywords: Independent metering system Proportional directional valve (PDV) Electrical controlled pump Coordinate control Energy saving

a b s t r a c t The independent metering system is an alternative to the conventional valve control system by decoupling the meter-in and meter-out orifices. With a number of features such as flow recuperation or regeneration, and simultaneous control of speed and pressure, the energy saving performance can be improved. Nevertheless, independent metering systems make the control more complex. The current control design focused on the two-level controller: mode switch in upper level, and velocity and pressure control in lower level. However, pump control is seldom considered and the coordinate control of pump and valves briefly couples electronic load sensing (ELS) with the twolevel controller. The contribution of this paper is to design a three-level controller to improve the energy efficiency. The upper level determines the operating mode in terms of the current system states and desired motion trajectory. The lower level contains the meter-out flow/pressure valve control and the open-loop displacement pump control. A coordinate level is added to incorporate the pump control into the valve control. By the coordinate control of the pump and valves, the meter-in valve opens maximally and the pressure losses across the valves can be minimized. The problems caused by the maximal opening of the meter-in valve are described and then solved by three parts: pressure matching, configuration of flow/pressure valve control and damping compensator. The proposed controller is applied to a mini-excavator. The experimental results of boom and arm motions show that the three-level controller is able to address dual objectives of energy saving and control performance improvement. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Due to the advantages of high power weight ratio and high load capability, fluid power transmission technology has been used for a long time in all sorts of mobile machinery, for example construction, forestry and agricultural machines [1,2]. Because of the environmental and economic problems, energy efficiency and energy saving in mobile working machines are highly topical issues [3–6]. Therefore, even small improvements in system efficiency often have a significant economic impact on the total life-cycle cost. In traditional hydraulic systems, the two ports of an actuator are controlled by the traditional valve with one single control signal, the position of the spool in a control valve. With this kind of valve, the inlet (meter-in) and outlet (meter-out) orifices are mechanically connected. This coupling makes the system highly robust and easy to control, but inefficient. Mobile hydraulic applications distinguish themselves from other hydraulic applications because more than one function is supplied by one single pump. Also, pressure and flow demands vary greatly with ⁎ Corresponding author. Tel.: +86 571 87952505; fax: +86 571 87952507. E-mail addresses: [email protected] (B. Xu), [email protected] (R. Ding), [email protected] (J. Zhang), [email protected] (M. Cheng), [email protected] (T. Sun). 1 Postal Address: No.38 Zheda Road, Hangzhou, 310027, China.

http://dx.doi.org/10.1016/j.autcon.2015.04.012 0926-5805/© 2015 Elsevier B.V. All rights reserved.

time and different functions [7], for example, loads mostly appear in both positive and negative directions. Owing to these characteristics, the disadvantages of traditional hydraulic systems such as low efficiency are more pronounced in this application because the mechanical coupling between the inlet and outlet causes undesirable large losses at meter-out orifices and poor flexibility under overrunning load. In order to improve the efficiency of mobile hydraulic systems, independent metering system is applied. In this system, the meter-in orifice and the meter-out orifice are independently controlled [7]. By decoupling the meter-in and meter-out orifices, the energy saving performance can be improved by flow recuperation or regeneration, together with independent control of the flow and pressure. Nevertheless, independent metering systems make the control more complex. The control strategies for the system are usually divided into two levels: upper level for mode switch to determine the valve distribution and lower level for valve control to independently control the flow and pressure. Many researches highlighted the independent control strategies of flow and pressure [8–19]. Other researches highlighted the mode switch and valve distribution [20–23]. It is concluded that previous researches about the independent metering system focused on the valve control. However, the pumps in a system have also to be controlled somehow, as well as the valves. Hence, the paper focuses on a more complex control structure than the two-level controller, which takes advantage of incorporating the pump control into the independent metering system control to save energy.

B. Xu et al. / Automation in Construction 57 (2015) 98–111

Following the hydraulic load sensing (HLS) systems, close-loop pressure control (e.g. electronic load sensing, ELS) was developed to deal with the problems of HLS systems including oscillations and high pressure margin [24–29]. The conventional coordinate control of the pump and valves for independent systems is ELS pump control coupled with the two-level control strategy. However, the energy efficiency has not been maximized due to large pressure losses at the valve orifices. Another efficient pump control method was open-loop displacement control (e.g. electronic flow matching, EFM) [30–34]. Kim proposed a concept of displacement control to save energy in construction machinery [35]. In this research, each actuator was controlled by an electrically controlled open circuit over-center pump coupling with four separate proportional poppet valves. The coordinate control of pump and valves focused on the mode switch. Seldom researches focused on the flow and pressure control under selected modes in this paper. Sitte et al. studied the independent metering system consisting of an electrically controlled pump and two proportional valves with primary pressure compensator (P-IPC) [36]. The authors employed EFM strategy to control the pump and the meter-out strategy to control valves. However, the switch of flow or pressure control by valves was not mentioned in this article. Besides, the system stability was another problem in the meter-out valve control due to the maximal opening of the meter-in valve. On the basic of these previous researches, the paper proposes a complete control strategy for the independent metering system. Compared to the two-level controller in the current researches, a three-level controller is proposed, of which a coordinate control level is added to associate the pump control with the valve control. The coordinate control is of major concerns for addressing dual objectives: saving energy, as well as improving the control performance. The rest paper is organized as follows: In Section 2, the problem of pump/valves coordinate control is demonstrated in detail. In Section 3, the energy-saving independent metering system is developed. The three-level control method for the system is designed. In Section 4, the control strategies are applied for controlling the boom and arm motions of a mini-excavator. Conclusion and future work is given in the last section. 2. Problem statement Energy consumption for a hydraulic system is defined as: Z E¼

t1 t0

Z ps Q s dt ¼

t1 t0

ðpLs þ Δpd Þ ðQ L þ Q c Þdt

ð1Þ

where E represents the hydraulic energy used for a certain task from t0 to t1; ps, pLs, and Δpd are the hydraulic supply pressure, load pressure and pressure loss respectively; Qs, QL, and Qc are the flow rates of the pump, load and other flow rate such as leakage respectively. Reducing the energy consumption is equivalent to reducing the power, the integrand ps·Qs. It is obvious that there are the following two ways to save energy [15]: (1) reduce the supply pressure ps, which can be realized by the decrease of pressure loss in valves; (2) reduce the pump flow rate Qs, which can be realized by the flow regeneration with a differential hydraulic circuit. In load-sensing systems, the pump pressure margin pm is set to overcome the losses in the hoses and the directional valve. Therefore, the worst working conditions should be taken as the reference to choose the pre-set pressure margin pm,ref in order to satisfy requirements of all operating points [32]. For the independent metering system, the control strategy of the load sensing can be designed as Fig. 1. By means of the ELS, the pressure losses in the directional valve can be reduced by optimizing the setting of pressure margin pm according to the operating flow rate. In spite of this, the pressure margin pm is unable to be set perfectly due to the uncertainty of pressure losses in the hoses. In order to provide sufficient pressure losses for the hoses and valves, the pre-set pressure margin pm,ref is always higher than the actual pressure losses. As a result, the unnecessary pressure losses in the valve still exist and flow control is implemented in the meter-in valve. The meter-out valve opens as large as possible to save energy. Instead of ELS control, the paper employs the open loop displacement control approach shown in Fig. 2, the pressure drop between the pump and load is given by the resistance in the hoses and valves, rather than a pre-set pressure margin pm,ref [32]. Coupling with this pump control approach, the meter-in valve can be opened fully to reduce pressure losses in the valves. However, there are some problems caused by the maximal opening of the meter-in valve, which goes against the objectives of energy saving and control performance improvement simultaneously. Firstly, the meter-out valve can be performed as both flow control and pressure control for each actuator. Considering the different operating modes of independent metering system, it is difficult to deal with the conflicts between the flow distribution and the reduction of energy consumption of the meter-out valve in the multi-actuator system. Secondly, the system damping would be reduced, which leads to the pressure and velocity oscillations of the actuators., Thirdly the mismatch between the load pressure and pump pressure would cause the load drops in the startup stage. The complete control strategy for the system will be designed in the next section.

Loss in valve 1 Useful energy Loss in valve 2

v Pa

Pb Max.open u2

u1

99

Meter-in flow control

Ps,max Pressure Ps

Pm=Pm,ref

Pa

Pm, +

PLS

G2(s)

,ref

Pb Pr

Fig. 1. Schematic diagram of ELS control associating with meter-in valve control.

qa flow

100


Loss in valve 1 Useful energy Loss in valve 2

v Pa Pb Meter-out control u2

Max.open

u1

Ps,max Pressure Ps Pa Min. Pm

Ps

Qs,ref

G1(s)

s,ref

Pb Pr

Pr

qa flow

Fig. 2. Schematic diagram of open loop displacement control associating with meter-out valve control.

3. Control system design An independent system is designed to improve the energy efficiency, as shown in Fig. 3. It mainly consists of two proportional directional valves (PDVs) for one actuator coupling with an electronic pump. The two PDVs are able to control the inlet and outlet orifices of an actuator individually, which decouples the mechanical connection of two orifices compared to traditional single PDV system. In order to distinguish the two valves in the following section, the one in the head side is defined as valve 1, and the other in the rod side is defined as valve 2. The controller receives the signals including pressures of actuator chamber, pump and drain line. Based on these feedback signals, the controller supplies the most efficient control configurations including valve opening and pump displacement, which is the main focus of this paper. The difficulties in the coordinate control of the independent metering valves and electronic pump for energy saving are to be dealt with through the following controllers, as illustrated in Fig. 4. The controller is composed of three levels. Mode switch (upper level) selects the most efficient operating mode in terms of the current system states and desired motion trajectory, and then controls the transitions between different modes. The selected mode determines the distributions

of the independent metering valves and the action of the electronic pump that would enable significant energy saving without the loss of hydraulic circuit controllability for precise motion tracking. Under the selected operating mode, the flow and pressure control are carried out by the valve control and pump control (lower level). Unlike the twolevel controller in many previous researches, the control design is more complex because a coordinate control level is proposed to associate the pump control with the valve control.

3.1. Upper level control—mode switch 3.1.1. Mode selection The operating mode is selected according to the load quadrants, which are defined by the four combinations of the axial direction of load force and actuator velocity, as shown in Fig. 5. If the directions of the force and velocity vectors are the same, the quadrant is defined as overrunning; otherwise it is defined as a resistive quadrant [35]. In order to choose the corresponding operating mode automatically in real-time work, the load force is calculated by the head and rod chamber pressures: Fl = paAa–pbAb. The velocity direction is determined by the reference velocity instead of the actual velocity.

Fl1 v1 pb1 u2

pa1

Fl2 v2 pb2

Boom u1

Arm

pa2

u2

u1 T

T ps Xpc-Target Controller

up

pr T

Fig. 3. Schematic diagram of independent metering system.


101

Mode switch

Q1,ref Q2,ref

u1 u2

Coordinate control

Valves

v1 Actuators

Ps Pr Pa Pb

up

Valve control

v2

Pump

Pump control

Fig. 4. Schematic diagram of control system.

For the same couple of force and velocity, there might be several operating modes. In these cases, the most energy efficient mode must be determined. Besides, the force-velocity capability should be considered except the efficiency.

the most efficient one for quadrant II. However, the velocity is limited by the drain pressure pr instead of the pump flow limit. f F LSRR ; vLSRR g ¼

3.1.1.1. Quadrant I. PE (Power Extension) mode is a traditional one which can be implemented by the conventional PDV system. The limits in load force FPE and cylinder velocity VPE are given based on the pump maximum pressure and flow by Eq. (2): f F PE ; vPE g ¼

qs; max ps; max Aa ; : Aa

ð2Þ

HSRE (High Side Regeneration Extension) mode is a novel mode which cannot be implemented by the PDV system. The pump flow can be reduced together with the increase of pressure. In mobile machinery, this mode is preferred for the lower load in the multi-actuator motion system. The limits in load force FHSRE and cylinder velocity VHSRE are given by Eq. (3): f F HSRE ; vHSRE g ¼

qs; max : ps; max ðAa −Ab Þ; Aa −Ab

ð3Þ

3.1.1.2. Quadrant II. In LSRR (Low Side Regeneration Retraction) mode, the cylinder can be used as a pump to generate the pressure oil due to the overrunning load. Flow and pressure are not required from the pump, and there are not limits for the force. Therefore, LSRR mode is

Fl

quadrant I

Fl

Fl v -

v quadrant IV

quadrant III

Fl v

Fl -

v

Fig. 5. Definition of the load quadrants.

qLSRR Ab

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðpr −pb Þ ¼ C q Av u2; max ρ

ð4Þ

ð5Þ

where pb usually is controlled to approximate 1–2 bar to avoid the cavitation. If the reference velocity exceeds the limit of LSRR mode, then the traditional LSR (Low Side Retraction) mode should be used. The velocity is limited by the pump maximum flow in the mode. f F LSR ; vLSR g ¼

Fl;

qs; max Ab

ð6Þ

3.1.1.3. Quadrant III. This quadrant is less complicated than the others because only one mode PR (Power Retraction) can be chosen. The limits in load force FPE and cylinder velocity VPE are also given based on the pump maximum pressure and flow by Eq. (7): f F PR ; vPR g ¼

qs; max : ps; max Ab ; Ab

ð7Þ

3.1.1.4. Quadrant IV. The overrunning load still exits in the quadrant. In LSRE (Low Side Regeneration Extension) mode, the cylinder can also be used as the pump to generate the pressure oil. Although it is the most efficient mode in this quadrant, it only can be operated in strict conditions. Firstly, excess return flows from other cylinder are necessary to build up the drain line pressure pr. Secondly, the overrunning force should be high enough. Therefore, the velocity is limited by both of the drain pressure pr and load force Fl.

+

quadrant II

qLSRR

Fl;

+v

f F LSRE ; vLSRE g ¼

q q F l ; min LSRE1 ; LSRE2 Aa Ab

ð8Þ

The first velocity limit is determined by the pressure drop of valve 1. qLSRE1

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðpr −pa Þ ¼ C q Av u1; max ρ

ð9Þ

where pa usually is controlled to approximate 1 ~ 2 bar to avoid the cavitation in this mode.

102


case, the relative valve spool displacement must cross zero. Therefore, switching between modes may cause the instability of velocity and pressure, and thereby causes frequent switch around zero or threshold value. To overcome this problem, a zero-order hold is used to filter the high-frequency mode switch signals. The transfer function between the input mode and output mode of the zero-order hold is given as Eq. (12). Gm ðsÞ ¼

Modein 1−e−T Z s ¼ Modeout s

ð12Þ

3.2. Lower level control—valve/pump control

Fig. 6. Mode selection for different load quadrants.

The second velocity limit is determined by the pressure drop of valve 2.

qLSRE2

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi u Fl u −pr u2 t Ab ¼ C q Av u2; max : ρ

ð10Þ

As depicted by Eqs. (8)–(10), the threshold force between LSRE mode and HSRE mode in quadrant IV is determined in terms of the reference velocity and drain pressure. If the actual load force Fl is beyond the threshold value, it means the cylinder cannot work in the LSRE mode. Then the HSRE mode should be chosen. Although flows from the pump are still required, it is reduced by the regeneration. Besides, the pump only provides low pressure to drive the motion and therefore the force is not limited. The force-velocity capability in this case is given by Eq. (11).

F HSRE ; vHSRE ¼

Fl;

qs; max Aa −Ab

3.2.1. Valve control-flow/pressure control Due to the maximal opening of the meter-in valve, the flow or pressure of each actuator should be controlled by the meter-out valve. The schematic diagrams of two valve control approaches are depicted in Fig. 7. For the velocity tracking, the closed loop flow control via flow sensors or velocity control via displacement (or angle) sensors have been excluded, since they are too expensive or too sensitive for practical use so far [36]. Therefore, the paper employs the calculated flow rate feedback control based on the pressure feedback to implement the velocity tracking. The control signal of the meter-out valve is given by Eq. (13) based on the difference between the reference flow and the actual flow. Z u2 ¼ K p Q e ðt Þ þ K i

Considering the load force and velocity limits, the most efficient modes for different quadrant are shown in Fig. 6. 3.1.2. Mode transition Actuator velocities and load forces crossing the mode borders require a specific control strategy. Load forces crossing zero or threshold valve may occur either at positive or negative actuator velocity. In either

t0

Q e ðt Þdt þ K d

dQ e ðt Þ dt

ð13Þ

where Qe = Qref–Qactual. Usually, the actual flow is calculated through Eq. (14). Q actual

ð11Þ

t1

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Δp2 ¼ C q Av2 ðu2 Þ ρ

ð14Þ

Except for pressure difference through the valve, the parameters in Eq. (14) are hard to estimate precisely. Hence, a flow mapping of the proportional directional valve, shown in Fig. 8, is tested to calculate the actual flow. The calculated flow rate feedback control eliminates the non-linear dependency of load pressure. It means that the flowpressure gain of the valve approximates to zero. For the pressure tracking, the closed loop pressure control is implemented by means of PID controller, as shown in Eq. (15).

Fig. 7. Schematic diagram of valve control.

Flow rate (L/min)


103

80 60 40 20 0 10

Inp

15

ut v

olta 5 ge (v

10

)

Fig. 8. Experimental valve flow mapping.

t1 t0

pb;e ðt Þdt þ K d

dpb;e ðt Þ dt

ð15Þ

where pb,e = pb,ref–pb. 3.2.2. Pump control—open loop displacement control In the pump control, an open loop algorithm is implemented to map a flow reference to a pump displacement. The pump pressure is determined by the load pressure. By using the open loop algorithm, the pressure margin between the pump and meter-in valve is able to be minimized. The pump swash control signal is given by Eq. (16): θs;re f ¼

5

Pa) e (M

ur Press

Fig. 9. Experimental pump flow mapping.

Z u2 ¼ K p pb;e ðt Þ þ K i

0

θs; max X Q i;re f V p np

the load would drop at first due to the maximal opening of meter-in valve. To overcome this problem, the pump pressure must firstly meet the load pressure prior to open the load holding valve, otherwise large pressure peaks and velocity decline will occur. For this purpose, the pump pressure increases to the load pressure by means of a pre-set pump displacement command. The valves don't open until the pump pressure approximately equals to the load pressure. The logics between the pump and valves are shown in Fig. 10. To simplify this controller, the algorithm without pressure feedback is applied.

ð16Þ

However, due to the leakage, the pump flow cannot match the reference flow precisely. The leakage flow mainly depends on the displacement, pressure, rotational speed and oil temperature. Assuming that the oil temperature and the rotational speed are constant during operation (np = 1500 r/min, T = 30°C), the pump flow is determined by the displacement and pressure, as given by Eq. (17). Q s ¼ V p np −ps C p

ð17Þ

Substituting Eq. (16) to Eq. (17), the actual pump swash control signal is given as: θs;re f ¼ θs; max

X

Q i;re f þ ps C p V p np

:

ð18Þ

To cancel out the non-linear dependency of the pump pressure, a flow mapping of pump has to be provided. The test pump flow mapping is given in Fig. 9. Based on the flow mapping, the leakage flow with respect to the swash angle and pump pressure can be estimated. 3.3. Coordinate control As mentioned above, there is a coordinate controller between the upper level and lower level to incorporate the pump control into the valve control. The flowchart of the control strategy is described in Fig. 10. 3.3.1. Pressure matching The valves hold the load when there is no command signal. In this state the pump should maintain a relatively low standby pressure in order to minimize the viscous drag losses. The pressure is much less than the load pressure. Whenever actuation is commanded to move,

Fig. 10. Coordinate control concept for pump and valves.

104


Valve-based damping control

Pump-based damping control v

v HP Khp

u2

+-

ucom

PLs

PLs

Meter-out

Max.open by Meter-out Pr or Ps

Khp

Qs,ref

up G1(s) +

HP

Max.open by Pump control Ps

ucom Pr

Fig. 11. Dynamic pressure feedback damping control.

Fig. 12. Photograph of mini-excavator using the developed system.

3.3.2. Configuration of flow/pressure valve control After pump matching, the valve starts to open to control the motion of actuators. As demonstrated in the valve control, the meter-out valve is able to control the flow or pressure of actuators. Three steps are listed below to configure the valve control to distribute the flow and reduce the system pressure in the multi-actuator system.

the drain line. It is beneficial to avoid the cavitation. The pressure is always controlled as low as possible to save energy. Step 3 For each actuator with low load, the meter-out flow control is chosen to control the velocity of the actuator. In this case, the pressure level is raised to the pump pressure due to the maximal opening of meter-in valve. The meter-out valve performs as the

Step 1 Decide whether there are actuators operating under the regeneration mode. For the regeneration mode containing LSRR and LSRE, the pump is not required to supply flow. Due to the overrunning load, the valve in high pressure side always controls the flow and the valve in low pressure side opens maximally to save energy. Therefore, the meter-out flow control is chosen. In HSRE mode, the valve control also selects meter-out flow control under the consideration of system damping. The damping of the cylinder drive increases because the hydraulic spring stiffness is increased significantly by the higher pressure level [36]. Step 2 Among the actuators under normal modes (non-regeneration modes), the controller decides which actuator operates with the highest load. For the actuators with highest load, the meter-out pressure control is chosen to keep pressure drop in

Fig. 13. Comparison of boom cylinder velocity using pressure matching control.


105

Fig. 14. Boom cylinder head side pressure without pressure matching control.

Fig. 17. Comparison of boom cylinder velocity using DPF.

Meanwhile, the meter-out valve always controls the low pressure side and opens as large as possible to save energy. Therefore, the damping compensator will be saturated by means of valve-based damping control, and the capability of this approach will be suppressed. To overcome this drawback, a pump-based damping control approach is used, as shown in Fig. 11. It is seen that the pump displacement, instead of the meter-out orifice, is controlled to damp instabilities, which has avoided the saturation of damping compensation. The compensation control signal derived by DPF can be expressed as:

Fig. 15. Boom cylinder head side pressure with pressure matching control.

flow distribution. Then, the velocity of the highest load is determined by the Eq. (19). X Q high ¼ Q s − Q i;low

ucom s ¼ K hp : s þ ωhp pLs

ð20Þ

ð19Þ

3.3.3. Damping compensator In the proposed valve control and pump control, the electrical pressure compensator has been employed to achieve less influence on the flow from the load pressure. A drawback with this method is that the load will be poorly damped [37], which is exacerbated by the maximal opening of meter-in valve. Dynamic pressure feedback (DPF) is an effective approach to damp instabilities. Currently, DPF is implemented by sensing the load pressure with high-pass filter (HP) signal and compensating an output ucom to the valves [37–39], such as valve-based damping control in Fig. 11. In the independent metering system, this approach is still suitable for mainly valve-controlled modes such as LSRE and LSRR modes. However, for the open loop pump control coupled with meter-out valve control, the meter-in orifice opens maximally and thereby it is excluded to provide damping to the system.

case A

The control parameters contain the cut-off frequency of the filter ωhp and feedback gain Khp. ωhp is set to be below the resonance frequency of the system [40]. The feedback gain Khp is set to obtain reasonable stability margins [40]. 4. Experiment Experiments are done to test the proposed three-level control system in the mini-excavator shown in Fig. 12. The experimental studies are conducted in three parts: (1) a comparison concerning with the pressure matching control for the startup stage of boom motion; (2) a complete single actuator motion using the proposed controller in comparison to the ELS coupled with meter-in valve control strategy; (3) a complete multi-actuator motion using the proposed controller in comparison to the ELS coupled with meter-in valve control strategy.

case B

Fig. 16. (a) Comparison experimental motion trajectories; case A:Boom motion trajectory; (b) Comparison experimental motion trajectories; case B: Arm motion trajectory.

106


Fig. 18. Comparison of boom cylinder pressure using DPF.

Fig. 21. Cylinder pressure for case A using ELS & meter-in control.

4.2. Single actuator motion Two motion trajectories are tested in this section: (1) boom firstly moves upward and then moves downward; (2) arm firstly extends and then retracts (Fig 16). The reference pressure margin pm,ref in ELS control is set as 0.8 MPa considering the pressure loss across hoses and valves. It is lower than hydraulic-mechanical load sensing system, which always sets the pressure margin ranging from 1.5 MPa to 2 MPa.

Fig. 19. Comparison of boom cylinder velocity for case A.

4.1. Startup stage With the reference velocity 50 mm/s, the actual velocity of boom cylinder with and without pressure matching is given in Fig. 13. The results show that by means of the pressure matching, an abrupt falling, which is dangerous for mobile machinery, is avoided. Concerning with the head side pressure and pump command signal in Fig. 14, the pump and valve open simultaneously as soon as the specified reference velocity is given, and therefore a pressure drop of load pressure appears. In contrast, as shown in Fig. 15, the pump firstly receives a relative high command signal to pressure the system. The valve doesn't open until the pump pressure approximative equals to the load pressure.

Fig. 20. Cylinder pressure for case A using proposed controller.

4.2.1. Case A The velocity and pressure of the boom cylinder are exhibited from Figs. 17 to 21 respectively. According to the operating condition, PE mode is chosen for the upwards motion and LSRR mode is chosen for the downwards motion. The comparison of results in Figs. 17 and 18 exhibits effect of proposed damping compensator. According to the principle of the damping compensator parameters mentioned above, the cut-off frequency of the filterωhp for the system is 0.5 Hz, while the feedback gain Khp is 5e-8. The velocity and head side pressure of boom cylinder reveal that the damping compensator reduces the oscillations and makes the machine more stable for both upwards and downwards motion. It means that a higher damping is obtained compared to the original control without damping compensator. The comparison of results using proposed controller and ELS & meter-in control are described in Figs. 19, 20 and 21. Fig. 19 shows that the velocity overshoot caused by the proposed controller is larger than the one using ELS & meter-in control. It can be explained that the

Fig. 22. Comparison of arm cylinder velocity for case B.


107

motion. There is no energy consumption for the downwards motion because the overrunning load is used to drive the cylinder under the LSRR mode.

4.2.2. Case B The velocity and pressure of arm cylinder are exhibited from Figs. 22 to 24. According to the operating condition, PR mode is chosen for the extension motion and LSRE mode is chosen for the retraction motion. The comparisons of results using two controllers are in accordance with the boom motion of case A. The pressure margin pm using proposed controller is only 0.2 MPa, much lower than the 0.4 MPa for the boom motion. It can be explained that the velocity of the arm cylinder is lower than that of boom cylinder, which means that less pressure losses across the valves and hoses. There is no energy consumption for the retraction motion because the overrunning load is also used to drive the cylinder under the LSRE mode. Fig. 23. Cylinder pressure for a case B using proposed controller.

4.3. Multi-actuator motion

Fig. 24. Cylinder pressure for case B using ELS & meter-in control.

meter-in orifice opens maximally and the response of the pump displacement is directly determined by the reference velocity for the proposed control, while the meter-in orifice opens partly and the pump displacement is regulated gradually by the pressure. Except for this, the performances of the two controllers are approximately consistent. In regard to the energy consumption, Fig. 20 shows that the pressure margin pm using proposed controller is approximately 0.4 MPa, lower than the one using ELS & meter-in control shown in Fig. 21. It leads to a reduction of pump pressure and energy saving during the upwards

The complete multi-actuator experiment is implemented for the multi-actuator motion. The experimental motion trajectory case C is shown in Fig. 25. Figs. 26 and 27 depict the velocity and pressure variations of the arm and boom cylinder. The boom cylinder operates under PE mode and the arm cylinder operates under PR mode. When the two actuators move simultaneously, the boom cylinder drives the high load, and thereby the pressure in the rod side is reduced to 0.2 MPa by the meter-out pressure control. The pressure level in the rod side of the arm cylinder is raised to the pump pressure due to the maximal opening of meter-in valve, and the meter-out valve controls the flow of arm cylinder until the boom cylinder stops moving. A control switch from meter-out flow control to pressure control is expected because the high load turns to the arm cylinder in the case of the boom stopping. By means of the switch, the head side pressure of arm cylinder reduces to approximately 0.3 MPa, along with a peak velocity during the switch process. It reveals that the proposed controller can eliminate excess energy consumption of the meter-out valve and consequently save the system energy. Results depicted in Figs. 28 and 29 exhibit the velocity and pressure of the arm and boom cylinder using the ELS &meter-in control. Both the arm and boom cylinders always operate by the meter-in flow control. The velocity overshoot of boom cylinder by the proposed controller is larger than the one using ELS & meter-in control as the case A and case B. In addition, the peak velocity of the arm cylinder is lower when the boom cylinder stops to move. Except for this, the performances of the two controllers are approximately consistent. However, pump pressures of the ELS & meter-in control are much higher than the one using the proposed controller.

Boom upwards Arm extension

Arm extension

Boom stop

Fig. 25. Multi-actuator experimental motion trajectory, case C.

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Fig. 26. Arm and boom cylinder velocity for case C using proposed controller. Fig. 29. Arm and boom cylinder pressure for case C using ELS & meter-in control.

using proposed controller and ELS & meter-in control respectively, the energy saving ratio is given as: rE ¼

Fig. 27. Arm and boom cylinder pressure for case C using proposed controller.

4.4. Comparison of energy consumption The energy consumptions calculated in terms of Eq. (1) are shown in Fig. 30. They have been determined over 6 s, 8 s and 5.5 s time periods for case A, B, C respectively. Defining E1 and E2 as the energy consumptions

E2 −E1 100%: E2

ð21Þ

As depicted in Figs. 1 and 2, the reductions of energy consumptions using the proposed controller come from the decreases of pressure loss in the meter-in valve pm, therefore the ratio rE depends on the operating conditions, such as pre-set pressure margin pm,ref, pump pressure ps and the reference flow Qref. In the case of B and C, the ratios rE are 21.3% and 9.2% respectively. It is proved that the proposed controller provides a meaningful reduction of energy consumption. The ratio rE for case B is fairly high owning to two reasons: one is that Qref of arm is lower and thereby the decrease of pm using proposed controller is larger, as shown in Figs. 23 and 24; another is that the pump pressure ps of case B is lower and then the energy saving caused by the decrease of pm is fairly remarkable. The ratio rE for the case A is approximately 2.4%, which is not as noticeable as case B and C. This is because the response of the pump flow by the ELS control is slow (shown in Fig. 19), and then weakens the energy saving performance by the reduction of pressure margin pm. For a longer period task of case A the energy saving performance will also be obvious because when the boom lift upwards, the pump pressure ps decreases by approximately 0.4 MPa comparing Figs. 20 to 21. 5. Conclusion and future work In this paper, a three-level control system is proposed for the independent metering system for addressing dual objectives of energy saving and

Fig. 28. Arm and boom cylinder velocity for case C using ELS & meter-in control.

Fig. 30. Comparison of energy consumption.


control performance improvement. Compared to the two-level control strategy in the other research presented to date, the contribution of this paper is to add a coordinate level to incorporate the pump control into the valve control. By the coordinate control of pump and valve, the meter-in valve opens maximally and the pressure losses across the valve can be minimized. Meanwhile, the problems caused by the maximal opening of the meter-in valve are solved by three parts: pressure matching, configuration of flow/pressure valve control and damping compensator. The results shows that higher energy efficiency and few reductions of motion performance can be obtained compared to the conventional coordinate control strategy, which simply couples ELS with the two-level Appendix A Table I The operating modes coupled with their energy consumption.

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controller. The proposed controller can be applied for the mobile machinery to perform motion control and save energy. The future work will focus on more experimental studies on the control strategy. Also, it is expected that the two-spool PDV will be developed as a key component to replace the two independent PDVs. Acknowledgment This work was supported by the National Basic Research Program of China (973 Program) Grant No.2014CB046400 and the National Natural Science Foundation of China Grant No. 51375431.

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Appendix B Notation Aa Ab Av Cp Cq E E1 E2 FPE FHSRE FLR FLSRR FPR FLSRE ⁎ FHSRE Kd Ki Khp Kp np pa pa1 pa2 pb pb1 pb2 pLs pm pm,ref pr ps pin ps,max Δp1 Δp2 Δpd qPE qHSRE qLSR qLSRR qPR qLSRE q⁎HSRE qs,max Q actual Qc Qe Q high Q i,ref Q i,low QL Q ref Qs Q s,ref u1 u1,max u2 u2,max ucom up t0

head side area of cylinder (m2) rod side area of cylinder (m2) orifice area of proportional valve (m2) leakage coefficient discharge coefficient hydraulic energy consuming (J) energy consumptions using proposed controller (J) energy consumptions using ELS & meter-in control (J) force limit for PE mode (N) force limit for HSRE mode (N) force limit for LR mode (N) force limit for LSRR mode (N) force limit for PR mode (N) force limit for LSRE mode (N) force limit for HSRE* mode (N) differentiation coefficient integration coefficient gain of dynamic pressure feedback control proportion coefficient rotational speed of pump (r/min) pressure in head side chamber (Pa) pressure in head side chamber of boom cylinder (Pa) pressure in head side chamber of arm cylinder (Pa) pressure in rod side chamber (Pa) pressure in rod side chamber of boom cylinder (Pa) pressure in rod side chamber of arm cylinder (Pa) load pressure (Pa) pressure margin between pump and load (Pa) pre-set pressure margin between pump and load (Pa) drain pressure (Pa) pump pressure (Pa) the inlet pressure of orifice (Pa) pump pressure limit (Pa) pressure difference of valve 1 (Pa) pressure difference of valve 2 (Pa) pressure loss (Pa) flow limit for PE mode (N) flow limit for HSRE mode (N) flow limit for LR mode (N) flow limit for LSRR mode (N) flow limit for PR mode (N) flow limit for LSRE mode (N) flow limit for HSRE* mode (N) pump flow limit (m3/s) calculated flow (m3/s) leakage flow (m3/s) flow difference between reference flow and calculated flow (m3/s) flow for the actuator with highest load (m3/s) reference flow for different actuators (m3/s) flow for different actuators with low load (m3/s) load flow (m3/s) reference flow (m3/s) pump flow (m3/s) reference flow for pump (m3/s) control voltage of valve 1 (v) max. control voltage of valve 1 (v) control voltage of valve 2 (v) max. control voltage of valve 2 (v) compensation voltage from dynamic pressure feedback control (v) control voltage of pump (v) starting time for a task (s)

t1 Tz Vp v1 v2 θs,ref θs,max ρ ωhp

end time for a task (s) time constant of Zero-Order Hold (s) pump displacement (m3/r) velocity of boom cylinder (m/s) velocity of arm cylinder (m/s) reference angle of pump swash plate (rad) max. angle of pump swash plate (rad) density of oil (kg/m3) cut-off frequency of dynamic pressure feedback control (Hz)

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