High Tracking Control for a New Independent Metering Valve System Using Velocity-Load Feedforward and Position Feedback Methods

Abstract

The new configuration of independent metering valve (NIMV) system uses three proportional valves that gave been effectively proven to be energy saving compared with a conventional independent metering valve system in the fixed load condition. However, the variable load condition completely affects the accuracy and energy consumption during the operation of excavators. To improve the motion tracking precision and reduce the energy consumption of the NIMV system, a novel control method based on the coordinated control of the pump and the valve is proposed. In detail, the valve is controlled by considering velocity, load force, and position feedback of the cylinder. Meanwhile, velocity feedforward and position feedback methods are used to control the speed of the pump. In addition, a switching mode for the NIMV system is designed to flexibly select the metering modes based on the load and velocity conditions. To confirm the effectiveness of the proposed control method, the co-simulation model is built by using the AMESim and MATLAB software. From the results, the proposed method not only has high trajectory tracking precision with the displacement error of the cylinder at around 3.6% but also achieves up to 6.4% energy saving.

1. Introduction

Currently, energy and environmental pollution are the most pressing problems in the world, while fossil fuels are depleting, the demand for use is increasing. Moreover, the high urbanization rate leads to environmental problems and global warming due to CO₂ emissions, which are emitted from activities of machinery equipment in the fields such as construction, mining, and other industries [1,2,3,4]. Among them, earth-moving machinery is most commonly used, especially in the construction industry [5,6,7]. The earth-moving machines such as hydraulic excavators consume a huge amount of fossil fuels and emit a lot of CO₂ emissions during operation [8,9,10]. Therefore, reducing energy consumption in hydraulic excavators saves fossil energy sources and protects the environment.

Conventional excavators use a lot of energy to work, but only about 50% of the energy is delivered to the cylinder, the remaining 50% of the energy is lost in the pump, pipes, and valve [11,12,13]. As a widely used device in the excavators to control flow, a conventional four-way proportional directional control valve is one of the main problems causing losses. To overcome this problem, the independent metering valve (IMV) has been proposed and proved its effectiveness compared with conventional proportional directional valves [14,15,16]. By replacing the conventional valves with four 2/2-way proportional valves, the IMV system allows the flow rate at the inlet and outlet of the cylinder to be independently managed according to five metering modes specially designed for the hydraulic excavators [17,18,19]. In particular, when applied to the boom excavator, the IMV system can save up to 44% of energy by using gravitational potential energy [20,21,22]. However, the IMV system has two problems that make it meet an obstacle for applying in practice. Firstly, the cost of the proportional valve causes a high cost for the system [23]. Secondly, controlling four valves is particularly challenging because of various types of nonlinearities in hydraulic systems [24]. Therefore, reducing the number of proportional valves and developing control methods are current research trends [25,26].

The solution of proportional valves is always more expensive than that of conventional proportional directional valves, while the conventional IMV (CIMV) system uses up to four proportional valves [27]. Thus, reducing the number of proportional valves in the CIMV system leads to cost savings in the system. Ahamad et al. [28] proposed a configuration of IMV system that used three electro-hydraulic poppet valves ((EHPV) a kind of 2/2-way proportional valve) and applied the equivalent valve coefficient equation to estimate the valve conductance of those valves based on the metering modes. Although, the cost of this system was cheaper and saved more energy compared with the CIMV system due to removing one proportional valve and a check valve, the approach with the equivalent valve coefficient made the control system complicated. Moreover, during the operation, friction and leakage occurred, leading to low tracking performance of the boom cylinder. Shi et al. [29] used two 4/3-way proportional direction valves for the IMV system and proposed the velocity feedforward and position feedback (VFPB) for the control method. With the same approach, Zhang et al. [30] used two 3/3-way proportional direction valves to replace four proportional valves in the IMV system. Moreover, the system was controlled by velocity and position of the boom cylinder based on the difference between the feedback signal and the target signal control. Their results showed that the control method helped the system operate smoothly and achieve high position precision. However, the use of two proportional direction valves made the system become more expensive due to their high cost. In a different approach, Ding et al. [11] presented an energy management algorithm based on the IMV configuration using a single-edge meter-out control valve (one proportional valve) to enhance the energy efficiency and reduce investment costs of the hydraulic excavator. The coordinated control between the pump and valve was designed with two-level control for the valve (flow/pressure control) and three-level control for the pump (pressure/flow/hybrid control) for motion characteristic tracking and saving energy on the system. This proposed algorithm showed that the energy saving efficiency reached up to 28% compared with the load-sensing system. Especially, by fully opening the meter-in valve and only controlling the meter-out valve can reduce the energy loss of the system. Nevertheless, multiple control strategies for valves and pumps cause complexity in system control. Moreover, open-loop control at flow control mode for the pump can make a lack of flow in the cylinder due to the leakage of the pipes and the valves. Generally, the above studies have reduced the number of proportional valves and provided a reasonable control strategy for the IMV system, but the load factor has not been considered, especially influence of the variable load during the operation of the system.

In our previous studies, the investigation of NIMV system in the boom excavator showed that this system was efficient in terms of energy saving and investment costs. With a configuration that uses three EHPV, the NIMV system reduced one proportional valve and the check valve on the CIMV while ensuring the working performance across the metering modes. Moreover, applying the VFPB control for the meter-out valve and position feedback control (PFC) for the pump helped the system to operate stably, increase tracking precision, and save up to 6.5% energy compared with the CIMV system [31,32]. However, this study was only focused on the case of a fixed load condition. In fact, the cylinder was always under the influence of a variable load during operation, this was effect to the accuracy and the energy consumption of the NIMV system.

To solve the above problem, this paper proposes a novel control method for the NIMV system. The proposed control method is the cooperation between the pump and valve control for the boom system under variable load. The main contributions of the article are presented as follows:

• The velocity-load feedforward and position feedback (VLFPB) control method is applied for meter-out valve control, and the velocity feedforward and position feedback (VFPB) methods are used for the speed control of the pump for the purpose of enhancing the tracking precision of the cylinder under variable load;
• Depending on the working conditions, a switching mode based on the load and the velocity of the cylinder is presented to select the suitable mode to improve the energy saving of the system.

Moreover, the co-simulation model by using the LMS AMESim and MATLAB software is built to demonstrate the effectiveness of the proposed control method. The simulation results of the proposed method are compared with the previous study based on two criteria, namely energy consumption and tracking precision. In detail, the displacement error of the boom cylinder can be reduced by 3.6% compared with the previous study. In addition, energy consumption is reduced by 6.4%.

The rest of this paper is organized as follows: Section 2 presents the metering modes of the NIMV system. Control strategy that includes valve control, pump control and switching mode of the proposed control method is provided in Section 3. Meanwhile, the co-simulation and result are discussed in Section 4. Moreover, the conclusions are shown in Section 5.

2. System Description

The NIMV system which is developed from the conventional IMV system is shown in Figure 1. In the detail of the hydraulic circuit, the NIMV system uses three proportional valves (K_sa, K_ab, K_bt), combines with one directional valve (K_d) to control the boom cylinder. Moreover, a main pump driven by an electric motor is used to provide the flow rate to the system under the protection of a check valve. The maximum pressure of the system can be guaranteed through a relief valve. The NIMV system that applies to the boom cylinder has four metering modes including power extension mode (PE), power retraction mode (PR), high-side regeneration extension mode (HSRE), and low-side regeneration retraction mode (LSRR) [31,32]. Depending on the working conditions, a suitable metering mode is selected to operate the cylinder. The working principle of the four metering modes is described in Figure 2 and the valve conductance of each mode is shown in

Table 1. The conductivity of valves on four metering modes.

Mode	Ksa	Kab	Kbt	Kd
PE	Fully open	Closed	Control	Right side
PR	Fully open	Closed	Control	Left side
HSRE	Fully open	Control	Closed	Right side
LSRR	Closed	Control	Fully open	Right side

.

3. Control Strategy Design

In the previous study, the pump/valve coordinate control strategy for the NIMV system was chosen under the fixed load condition [31,32]. Therefore, the control method was not too complicated, such as velocity feed forward control (VF) for the valve and PFC for the pump, or VFPB for the valve and PFC for the pump (VF + PID). However, in this study, the variable load and the switching mode are applied to the NIMV system during the boom moving up and down. Therefore, it is necessary to include two factors, load and speed, of the cylinder into the control strategy. Moreover, the PFC method using the proportional integral derivative (PID) controller is not suitable when applying it to the variable load condition. This PID controller is operated based on the displacement error that is feedback from the cylinder, wherein the gain parameters are selected appropriately and fixed setting in the controller in the fixed load condition. However, when the system suddenly changes the load during operation, the displacement error is quickly changed. At this time, the PID controller does not respond in time, causing large errors in the pump and valve control. Hence, the VLFPB method is proposed to apply to the valve and the VFPB method to apply to the pump (VLF + FLC), shown in Figure 3. In this case, the PB method is replaced by the Fuzzy logic controller (FLC).

3.1. Valve Control

In the NIMV system, the movement of the cylinder is independently controlled by two metering valves including meter-in and meter-out. However, controlling two metering valves at the same time causes more throttling loss. To solve this problem, one metering valve is fully opened and one metering valve is controlled. In the case of controlling the meter-in valve, not only the throttling loss from the valve but also loss from the pump due to the pressure difference between the pump and the cylinder chamber occur [15]. Therefore, to reduce energy loss, controlling the meter-out valve is used via the VLFPB method meanwhile the meter-in valve is fully opened.

The valve control signal $U_K$ (K = sa, ab or bt) from the VLFPB method is obtained by the combination of two control signals. In which, the velocity-load feedforward signal $U_K^{VLC}$ is calculated from the velocity requirement, the load force, and the pressure of the system. Meanwhile, a position feedback signal $U_K^{PB}$ obtained from the FLC is added to improve the tracking position of the cylinder and compensates for the energy loss in the valve. The mathematical modeling of the VLFPB method on each mode is described as follows:

The valve control signal of valve can be calculated by Equation (1).

$$U_K=U_K^{VLF}+U_K^{PB}$$

(1)

According to the Newton’s Law, the dynamics of the boom cylinder can be provided by Equation (2).

$$p_a{A}_a-p_b{A}_b-mg-B_v\dot{x}=m\ddot{x}$$

(2)

where $p_a,p_b$ are the pressure at the bore and rod chamber, $A_a{,}^{}{A}_b$ are an area of the bore and rod side of the piston respectively, $m$ is the load, $B_v$ is the viscous friction coefficient, and $x$ is the target displacement of the cylinder. Depending on each mode, the pressures at the bore and rod chamber are different.

3.1.1. Mathematical Modeling of the Velocity-Load Feedforward on the Metering Modes

In the PE mode, the K_sa valve is fully opened and the K_bt valve is controlled. The flows across the inlet and outlet orifice of the cylinder are provided by the following orifice equations:

$$Q_a=\left|\dot{x}\right|A_a=C_d{A}_{sa}\sqrt{\frac{2\left(p_s-p_a\right)}{\mathsf{\rho }}}=K_{sa}\sqrt{p_s-p_a}$$

(3)

$$Q_b=\left|\dot{x}\right|A_b=C_d{A}_{bt}\sqrt{\frac{2\left(p_b-p_r\right)}{\mathsf{\rho }}}=K_{bt}\sqrt{p_b-p_r}$$

(4)

where $Q_a{,}_{}{Q}_b$ are the flow rate at the bore and rod chamber, $C_d$ is a coefficient of discharge, $\mathsf{\rho }$ is the density of the fluid, $A_{sa{,}_{}ab{,}_{}{\mathrm{or}}_{}bt}$ is the area of orifice, $K_{sa{,}_{}ab{,}_{}{\mathrm{or}}_{}bt}$ is the valve conductance of the proportional valve, and $p_s{,}_{}{p}_r$ are the pressure at the outlet of the pump and the pressure at the tank. By rearranging Equations (3) and (4), the chamber pressure of the cylinder can be written as:

$$p_a=p_s-{\left(\frac{\left|\dot{x}\right|A_a}{K_{sa}}\right)}^2$$

(5)

$$p_b=p_r+{\left(\frac{\left|\dot{x}\right|A_b}{K_{bt}}\right)}^2$$

(6)

By substituting Equations (5) and (6) into Equation (2), can be obtained:

$$\left[p_s-{\left(\frac{\left|\dot{x}\right|A_a}{K_{sa}}\right)}^2\right]A_a-\left[p_r+{\left(\frac{\left|\dot{x}\right|A_b}{K_{bt}}\right)}^2\right]A_b-mg-B_v\dot{x}-m\ddot{x}=0$$

(7)

Following the control strategy and the valve operation in PE mode (shown in Table 1), the signal control of the K_sa valve is always fixed at the maximum value. Meanwhile, the K_bt valve is always adjusted so that the cylinder operates according to the design strategy. Therefore, there exists a ratio factor k which varies depending on the velocity, pressure, and load of the system during operation. The relationship between valve K_sa and valve K_bt is shown as follows:

$$k_{PE}=\frac{K_{sa}}{K_{bt}}=\frac{U_{sa}^{VLF}}{U_{bt}^{VLF}}$$

(8)

where $k_{PE}$ is the ratio factor of the PE mode. From Equations (7) and (8), the ratio factor $k_{PE}$ is calculated as the following equation:

$$k_{PE}=\sqrt{\frac{\left(p_s{A}_a-p_r{A}_b-mg-B_v\dot{x}-m\ddot{x}\right)K_{sa}^2-{\dot{x}}^2{A}_a^3}{{\dot{x}}^2{A}_b^3}}$$

(9)

Using the same approach as in PE mode, the mathematical analysis of HSRE mode can be described as shown in Figure 2b. However, the flow of the bore chamber is the combination between the flow from the rod chamber and the flow from the pump through the K_sa valve. Therefore, the orifice equations of valve K_sa and valve K_ab are difference based on the structure of the hydraulic circuit. Similarly with PE mode, the chamber pressure, and the ratio factor $k_{HSRE}$ of the HSRE mode are obtained as:

$$\begin{array}{l}{p}_a=p_s-{\left(\frac{\left|\dot{x}\right|\left(A_a-A_b\right)}{K_{sa}}\right)}^2\\ p_b=p_s-{\left(\frac{\left|\dot{x}\right|\left(A_a-A_b\right)}{K_{sa}}\right)}^2+{\left(\frac{\left|\dot{x}\right|A_b}{K_{ab}}\right)}^2\\ k_{HSRE}=\sqrt{\frac{\left(p_s\left(A_a-A_b\right)-mg-B_v\dot{x}-m\ddot{x}\right)K_{sa}^2-{\dot{x}}^2{\left(A_a-A_b\right)}^3}{{\dot{x}}^2{A}_b^3}}=\frac{U_{sa}^{VLF}}{U_{ab}^{VLF}}\end{array}$$

(10)

For PR mode, the valve control method is the same with the PE mode. However, the flow through the K_bt valve comes from the bore chamber. In this mode, the pressure of the cylinder chamber and the ratio factor $k_{PR}$ of the PR mode can be calculated as follows:

$$\begin{array}{l}{p}_a=p_r+{\left(\frac{\left|\dot{x}\right|A_a}{K_{bt}}\right)}^2\\ p_b=p_s-{\left(\frac{\left|\dot{x}\right|A_b}{K_{sa}}\right)}^2\\ k_{PR}=\sqrt{\frac{\left(p_s{A}_b-p_r{A}_a+mg+B_v\dot{x}+m\ddot{x}\right)K_{sa}^2-{\dot{x}}^2{A}_b^3}{{\dot{x}}^2{A}_a^3}}=\frac{U_{sa}^{VLF}}{U_{bt}^{VLF}}\end{array}$$

(11)

The LSRR mode is operated by controlling the K_ab valve and fully opening the K_bt valve. In this case, the chamber pressure of the cylinder and PR mode’s ratio factor $k_{LSRR}$ is represented by:

$$\begin{array}{l}{p}_a=p_r+{\left(\frac{\left|\dot{x}\right|\left(A_a-A_b\right)}{K_{bt}}\right)}^2+{\left(\frac{\left|\dot{x}\right|A_a}{K_{ab}}\right)}^2\\ p_b=p_r+{\left(\frac{\left|\dot{x}\right|\left(A_a-A_b\right)}{K_{bt}}\right)}^2\\ k_{LSRR}=\sqrt{\frac{\left(-p_r\left(A_a-A_b\right)+mg+B_v\dot{x}+m\ddot{x}\right)K_{bt}^2-{\dot{x}}^2{\left(A_a-A_b\right)}^3}{{\dot{x}}^2{A}_a^3}}=\frac{U_{bt}^{VLF}}{U_{ab}^{VLF}}\end{array}$$

(12)

3.1.2. Fuzzy Logic Controller

During actual operation, the noise and throttling loss can affect the valve control signal, leading to errors in the system, especially the displacement accuracy of the cylinder. For this reason, the FLC with the position feedback control is added to eliminate the noise and throttling loss in the valve during operation, as shown in detail in Figure 4. Two input variables are used in this FLC, namely the displacement error of cylinder e(t) and the derivative of the error de(t), while the voltage U_FLC is the output variable. Figure 5 depicts the specifics of the input and output in the FLC with triangular-type membership functions which are characterized by different colors. Moreover, the inputs and output membership functions are divided into seven groups and considered as: “neg-big” (NB) as an acronym for “negative small in size”, “neg-middle” (NM), “neg-small” (NS), “zero” (Z), “pos-small” (PS) is the “positive small in size”, “pos-middle” (PM), and “pos-big” (PB). According to linguistic variables, the logic rules related to the inputs and outputs are developed and shown in

Table 2. Rule table of FLC for valve.

RFCL for Valve		e
		NB	NM	NS	Z	PS	PM	PB
de	NB	NB	NM	NM	NS	NS	NS	Z
	NM	NM	NM	NS	NS	NS	Z	PS
	NS	NM	NS	NS	NS	Z	PS	PS
	Z	NS	NS	NS	Z	PS	PS	PS
	PS	NS	NS	Z	PS	PS	PS	PM
	PM	NS	Z	PS	PS	PS	PM	PM
	PB	Z	PS	PS	PS	PM	PM	PN

.

The output range and logic rule of FLC is flexibly designed for each metering mode, this means that one controller is needed for one mode. However, using multiple FLC complicates the control system and makes the system take longer to process. For this reason, one FLC for all metering modes is designed. Moreover, the gains of output $g_i$ (i = PE, PR, HSRE or LSRR) for each mode are added to adjust the range for flexibility in each mode. Therefore, the $U_K^{PB}$ signal can be obtained as:

$$U_K^{PB}=g_i{U}_{FLC}$$

(13)

where $U_{FLC}$ is the output of FLC, $g_i$ are chosen from the experiments.

3.2. Pump Control

To ensure the working performance of the cylinder and energy saving, the VFPB method is applied into the pump by controlling the speed of the motor. This signal is combined by two control signals, the velocity feed forward signal $U_P^{VF}$ and the position feedback signal $U_P^{PB}$. In which the $U_P^{VF}$ signal is the required speed to guarantee that the cylinder receives the requisite amount of oil to move in accordance with the design trajectory. The $U_P^{VF}$ signal can be calculated as follows:

$$U_P^{VF}=\frac{Q_{need}}{D_p}$$

(14)

where $D_P$ is the pump displacement, and $Q_{need}$ is the requisite amount of oil to supply on the cylinder. Depending on the metering mode, the amount of oil required is different to ensure energy saving and can be calculated as provided by Equation (15):

$$Q_{need}={\{\begin{array}{c}\left|\dot{x}\right|A_a\\ \left|\dot{x}\right|A_b\\ \left|\dot{x}\right|\left(A_a-A_b\right)\end{array}}_{}\begin{array}{cc}& \end{array}\begin{array}{c}\mathrm{PE}\mathrm{mode}\\ \mathrm{PR}\mathrm{mode}\\ \mathrm{HSRE}\mathrm{mode}\end{array}$$

(15)

In addition, the position feedback signal $U_P^{PB}$ is added by using FLC to compensate for the effect of various factors such as leakage, friction, delayed response of the pump, etc. This fuzzy set has two inputs as the displacement error of cylinder e(t) and the target velocity v_r(t); an output variable which is the motor speed, shown in Figure 6 and Figure 7 depicts the specifics of the triangular-type membership functions, in which “neg-big” (NB), “neg-middle” (NM), “neg-small” (NS), “zero” (Z), “pos-small” (PS), “pos-middle” (PM), and “pos-big” (PB) are used for displacement error input, whereas “neg-small” (NS), “zero” (Z), and “pos-small” (PS) are described for velocity input. The membership function of the output of FLC is divided into “zero” (Z), “pos-small” (PS), “pos-middle” (PM), “pos-big” (PB), and “pos-large” (PL).

Table 3. Rule table of FLC for pump.

RFCL for Pump		e
		NB	NM	NS	Z	PS	PM	PB
vr	NS	PL	PB	PM	PS	Z	Z	Z
	Z	Z	Z	Z	Z	Z	Z	Z
	PS	Z	Z	Z	PS	PM	PB	PL

shows the logic rule of this FLC based on the linguistic values corresponding to the membership functions.

3.3. The Switching Mode

In the NIMV system, each metering mode has a different operating condition, for example the PE mode can extend the cylinder with the high load and low speed, while HSRE mode can extend with high speed but low load. In this study, the variable load is applied to the NIMV system during operation. Therefore, to operate the system with lower energy consumption, the switching mode of the NIMV system is proposed, in which the target velocity of the cylinder and the load are the conditions to select the suitable mode for the system.

3.3.1. Switching Mode for Extension

In the NIMV system, the PE and HSRE modes are two extension modes typically employed for the boom excavator. To switch between these two modes, it is necessary to find out the limited velocity of cylinder and load capability of each mode. In this case, the limited cylinder’s velocity is determined by the maximum oil which is supplied by the pump. Moreover, the load capability is the maximum load that the cylinder can lift at the maximum pressure supplied from the pump and at a specified velocity. The limitation of the cylinder’s velocity is described as follows:

$${\dot{x}}_{PE}=\frac{Q_{max}}{A_a}$$

(16)

$${\dot{x}}_{HSRE}=\frac{Q_{max}}{\left(A_a-A_b\right)}$$

(17)

Substituting Equations (16) and (17) for Equation (2), respectively. The load capability of the PE and HSRE mode can be written as:

$$m_{PE}=\frac{p_s{A}_a-p_r{A}_b-B_v{\dot{x}}_{PE}}{g+{\ddot{x}}_{PE}}$$

(18)

$$m_{HSRE}=\frac{p_s\left(A_a-A_b\right)-B_v{\dot{x}}_{HSRE}}{g+{\ddot{x}}_{HSRE}}$$

(19)

From Equations (18) and (19), the load-velocity curve of cylinder for PE and HSRE mode are drawn at the maximum pressure of 100 bar and maximum flow rate at 12.45 L/min as shown in Figure 8 where the blue and black regions are selected for the PE mode, the red region represents for the HSRE mode. Based on the Figure 8, the maximum load that the cylinder can lift, and the maximum velocity are determined. In detail, the PE mode can push the maximum load of 1267 kg and obtain a limited velocity of 0.165 m/s. Meanwhile, the HSRE mode can only lift the capability load of 320 kg, but the maximum velocity which can achieve at 0.66 m/s is much larger compared with the velocity of the PE mode. Based on the velocity-load condition, and combined with the energy saving element, the PE and HSRE modes are flexibly switched to ensure the system working in the suitable mode.

3.3.2. Switching Mode for Retraction

In the retraction process, the PR and LSRR modes are used for the NIMV system. While the LSRR mode uses the energy potential gravitation from the load to retract the cylinder, the PR mode uses energy from the pump to move the cylinder. If energy saving is the primary concern, the LSRR mode is chosen to operate the cylinder. However, the LSRR mode has its limitation, while the gravity of the load retracts the cylinder, the viscous friction and pressure drop from the cylinder to the K_ab valve to obstruct the movement of the cylinder. Thus, LSRR mode has a minimum load capability. For this reason, the switching mode of the PR and LSRR modes needs to be studied.

The maximum velocity capability of the LSRR and PR mode is represented as:

$${\dot{x}}_{LSRR}={\dot{x}}_{PR}=\frac{Q_{max}}{A_a}$$

(20)

In both modes, the load capacity is considered based on the maximum pressure at the bore chamber, which is generated by closing the meter-out valve while the system is holding the load. This pressure must not be over the maximum pressure setting on the system. Therefore, the load capability can be provided as follows:

$$m_{LSRR}^{max}=m_{PR}=\frac{p_{max}{A}_a}{g}=\frac{p_s{A}_a}{g}$$

(21)

where $p_{max}$ is the maximum pressure at the bore chamber, in this case $p_{max}=p_s$. Moreover, the minimum load capability of the LSRR mode can be calculated by Equation (23):

$$m_{LSRR}^{\min }=\frac{\mathrm{\Delta }{p}_{ab}{A}_a-B_v{\dot{x}}_{LSRR}}{g+{\ddot{x}}_{LSRR}}$$

(22)

where $\mathrm{\Delta }{p}_{ab}$ is the pressure drop from the cylinder to the K_ab valve.

Figure 9 describes the cylinder’s load-velocity curve for retraction modes of the NIMV system at the maximum flow rate of 12.45 L/min and pressure of 100 bar. Although both modes have the same velocity range and the maximum load capability that is shown at the overlap region, the limit of the minimum load capability of the LSRR mode is the point that distinguishes between the two modes. Based on the condition of the system, the load capability of LSRR mode is from 97 to 1280 kg at the velocity of 0.165 m/s and the PR mode is from 0 to 1280 kg. Moreover, improving energy saving is one of the main priorities of this research.

From the above results, the control strategy of the NIMV system is proposed for the boom excavator (shown in Figure 10). The target displacement and velocity signal are estimated by the joystick and sent to the controller along with the load signal, which is measured by the load cell. Based on the condition of the switching mode, the metering mode is chosen to operate the system. Through the VLFPB method for the valve and the VFPB method for the pump, the control signal is sent to the hydraulic valves and electric motor in the NIMV circuit, leading to the cylinder being operated.

4. Simulation and Results

In order to demonstrate the effectiveness of the control method of the NIMV system, the simulation model was built for the boom system. Figure 11 describes the co-simulation between the LMS AMESim (2020) and the MATLAB software (2017), in which the model components are represented in different color blocks and shown as follows: the hydraulic components are illustrated in blue blocks, the mechanical parts are depicted in the green blocks and the red blocks are the control signal ports. The setting parameters of the NIMV system for the AMESim model are shown in

Table 4. The setting parameter of the NIMV system.

Components	Specification	Value
Cylinder	Bore chamber	40 mm
	Rod chamber	20 mm
	Length of Stroke	500 mm
	Viscous friction coefficient	2000 N/(m/s)
Pump	Displacement	8.3 cc/rev
	Max. speed	1500 rpm
	Volumetric efficiency	0.9
	Torque efficiency	0.95
Relief valve	Cracking pressure	100 bar
Proportional valve	Max. signal control	10 Voltage
	Max. flow rate	26.5 L/min
	Corresponding pressure drop	10 bar
Directional valve	Max. flow rate	60 bar
	Corresponding pressure drop	10 bar

. Moreover, the simulation results are compared with the previous study to prove the effectiveness of the proposed control method based on tracking performance and energy consumption.

The co-simulation is designed with two driving cycles that are used to test the performance of the NIMV circuit along with four working modes. During the operation, the external force of the boom cylinder which mimics the weight of the boom system is changed from 70 kg to 1000 kg, and the velocity is adjusted from 0.1 m/s to 0.2 m/s.

Figure 12 illustrates the tracking performance of the proposed control method (VLF + FLC) compared with the previous method (VF + PID) on four metering modes (PE, PR, HSRE, and LSRR). In detail, the PE mode operates from 2 to 7 s with a velocity of 0.1 m/s and the load varies from 500 kg to 1000 kg (shown in Figure 12a), the PR mode retracts the cylinder from 9 to 12.5 s at 0.143 m/s in the changed load from 100 kg to 70 kg. While from 14 to 16.5 s is the HSRE mode, which extends at the velocity of 0.2 m/sec with the effect of loads from 100 kg to 150 kg, and the final is the LSRR mode which moves the cylinder down under the loads from 1000 kg to 500 kg at the velocity 0.125 m/s from the time 19 to 23 s. Under the same variable load, the displacement and velocity results of the proposed method have better performance and higher tracking precision than the VF + PID method, especially in the PE, PR, and LSRR modes (as shown in Figure 12b,c). In this case, the tracking precision is considered based on the root means square error (RMSE) method that is applied to analyze the displacement error on both methods, as shown in

Table 5. Root means square error for metering modes on both control methods.

Mode	VLF + FLC	VF + PID
PE	0.776	1.766
PR	0.369	9.082
HSRE	3.694	3.563
LSRR	0.351	14.466

. The RMSE method can be calculated by Equation (23) provided below.

$$RMSE=\sqrt{{\displaystyle \sum _{i=1}^n\frac{e_i^2}{n}}}$$

(23)

The comparisons of the valve control signal and system pressure in the two methods are shown in Figure 13. In the valve control signal, both methods have the same signal at the K_sa valve, but the difference is mostly shown in the K_ab and K_bt valves. In PE mode the U_bt signal of the VLF + FLC method is smaller but controls the system better than the VF + PID method. The U_ab signal of the VLF + FLC method is smooth in LSRR mode, while the signal in the VF + PID method is high in fluctuation.

In addition to the high tracking precision, energy consumption is also one of the criteria to evaluate the effectiveness of the proposed control method. The energy consumption of the system can be calculated based on the energy consumption of the electric motor, which drives the main pump of the NIMV system, and is provided by Equation (24).

$$E={\displaystyle \int T\omega dt}$$

(24)

where E is the energy consumption of the electric motor, T is the torque and $\omega$ is the angular velocity which converts from the speed of the motor.

Based on Equation (24), the comparison of the energy consumption of both control methods is provided in Figure 14. In addition, the detailed energy consumption of each metering mode is presented in

Table 6. Energy consumption on both control methods (kJ).

Mode	VLF + FLC	VF + PID
PE	4.638	4.608
PR	0.76	0.12
HSRE	1.74	2.9
LSRR	0	0

. The result shows the energy consumption in the PE mode is the same, but the motor speed after 4.5 s of the VF + PID method fluctuates when changing the load. This is the limitation of the PID controller on the VF + PID control method when applying the variable load. Moreover, in PR mode, the energy consumption of the VLF + FLC (0.76 kJ) is higher than in the previous control method (0.12 kJ) by about 84% because the proposed method uses the energy to ensure reduction in the displacement error; therefore, the motion tracking precision of the proposed method is 95% higher compared with the previous method (shown in Table 5). In the HSRE mode, the VLF + FLC method consumes less energy (1.74 kJ), it achieves approximately 40% energy saving. The VFPB method is applied to the pump control while the VF + PID method (2.9 kJ) only uses the PB method. The p_s pressure at the HSRE mode on both control methods can be seen in Figure 13b, while the p_s of the VLF + FLC is decreased after 15 s, p_s of the VF + PID method maintain high pressure until the end of the mode, leading to energy loss via the relief valve. From all the above results, the proposed method can perform well in the metering modes of the NIMV system, not only ensuring high accuracy but also lower energy consumption.

To prove the advantages of the proposed switching mode, some simulations with changing the load and velocity while the cylinder is in operation are carried out as shown in

Table 7. Switching mode over two cycles of the NIVM system.

Mode	Timeline (s)	Load (kg)	Velocity (m/s)
Cycle 1
HSRE	From 2 s to 3 s	200	0.25
PE	From 3 s to 7 s	750	0.0625
PR	From 9 s to 11 s	100	0.143
LSRR	From 11 s to 12.5 s	500	0.143
Cycle 2
PE	From 14 s to 17 s	1000	0.1
HSRE	From 17 s to 18 s	150	0.2
LSRR	From 19 s to 21.5 s	1200	0.125
PR	From 21.5 s to 23 s	75	0.125

. Figure 15 describes the behavior of the switching mode in two operating cycles of the NIMV system. At switching points, a transient response occurs, which causes unstable and unsmooth switches in the system [18]. However, this problem is overcome by the proposed method. The load and target velocity are the two factors that are used in the control algorithm of the system; hence, when the switching mode takes place, the control signals are adjusted quickly to respond promptly to changes in the system. In conclusion, the proposed control method enhances the tracking precision not only in the variable load condition but also in the switching mode condition.

5. Conclusions

This paper proposed an intelligent control method for the NIVM system under variable load on the boom excavator, the VLFPB method for the valve, and the VFPB method for the pump. The proposed method considers the load factor into the valve control algorithm to accommodate variable load conditions. Moreover, the fuzzy controller was used for position feedback control, thereby the system operated smoothly with high tracking precision accuracy. To operate the system flexibly and choose the appropriate mode for operation, the switching mode of the NIMV system was designed based on the load condition and target velocity of the system. The co-simulation in the AMESim and MATLAB software was built to prove the effectiveness of the proposed control method compared with the previous study based on the tracking precision and energy consumption criteria. The results demonstrated that the proposed control method had high tracking precision with lower displacement error which was always in the range of 3.6%. In the energy consumption, after 25 s working with four metering modes, the proposed method can save up to 6.4% energy compared with the previous study. Consequently, the proposed method can not only achieve high tracking performance but also reduce the energy consumption. In future work, with the goal of saving more energy, the combination between the hydraulic accumulator and the NIMV system will be developed to store the recovered energy and reuse it, especially in the recovered energy from LSRR mode. Moreover, the proposed method will be applied to enhance tracking precision and energy saving efficiency.