Working Performance Improvement of a Novel Independent Metering Valve System by Using a Neural Network-Fractional Order-Proportional-Integral-Derivative Controller

Abstract

In recent years, reducing the energy consumption in a hydraulic excavator has received deep attention in many studies. The implementation of the novel independent metering valve system (NIMV) has emerged as a promising solution in this regard. However, external factors such as noise, throttling loss, and leakage have negative influences on the tracking precision and energy saving in the NIMV system. In this paper, a novel control method, simple but effective, called a neural network-fractional order-proportional-integral-derivative controller is developed for the NIMV system. In detail, the fractional order-proportional-integral-derivative (FOPID) controller is used to improve the precision, stability, and fast response of the control system due to the inclusion of non-integer orders in the proportional, integral, and derivative terms. Along with that, the auto-tuning algorithm of the neural network controller is applied for adjusting five parameters in the FOPID controller under noise, throttling loss, and leakage. In addition, the proposed controller alleviates the amount of calculation for the system by using model-free control. To verify the effectiveness of the proposed controller, the simulation and experiment are conducted on the AMESim/MATLAB and a real test bench. As a result, the proposed controller not only operates the NIMV system accurately in the target trajectory but also reduces energy consumption, saving up 23.33% and 29.25% compared to FOPID and PID in the experimental platform, respectively.

1. Introduction

Nowadays, due to a high power-to-weight ratio, high load capabilities, and robustness, construction machinery plays an important role in infrastructure development, especially hydraulic excavators [1,2,3]. Hydraulic excavators (HEs) are versatile heavy equipment commonly used in many fields of industry, such as building, digging, moving, drilling, mining, and other industries for various earth-moving tasks. They possess several distinctive characteristics that make them suitable for a wide range of applications: providing high force and torque, multi-functional use, high flexibility, and work in harsh environments [4,5]. However, consuming a lot of fossil fuels and emitting a lot of pollutant emissions into the environment are challenges that still exist in HEs [6,7,8]. Hence, reducing energy consumption in hydraulic excavators is one of the important tasks.

One of the widely used solutions today is the energy regeneration system (ERS) that is used to store and reuse the potential energy in the HEs. In particular, the boom system contains the biggest potential energy up to 51% of total recoverable energy due to the gravitational force during the lowering process [9,10,11,12]. The ERS can be classified into three main types, namely electric ERS, mechanical ERS, and hydraulic ERS. In the mechanical ERS structure, a flywheel, the hydraulic pump/motor, and the clutch were the main components. The hydraulic energy was converted to rotation energy with the hydraulic motor when the boom cylinder moved down and stored in the flywheel. Then, through clutch adjustment, the hydraulic pump was driven by the stored energy and supplied the oil to operate the system in the next cycle [13,14]. The structure of the electric ERSs was composed of a hydraulic motor, which was connected to an oil return line to the tank, used to drive a generator to convert the gravitational potential energy into electricity and store it in a battery or capacitor. After that, this electricity power was used to operate the electric motor or supply to other electric devices in the HE, leading to a significant energy consumption reduction [15,16,17]. In the approach of hydraulic ERS, the gravitational potential energy was stored in the hydraulic accumulator through the valve, a booster cylinder, or a transformer system and reused for the system via auxiliary devices [18,19,20]. Overall, the ERSs are a highly effective solution for minimizing energy consumption on the HEs. However, adding recovery, storage, and reuse components increases investment costs. At the same time, it also leads to increasing hardware size and complexity in controlling elements.

An independent metering valve system (IMV) is known as another effective solution for reducing the energy consumption in the HEs [21,22,23]. By connecting four proportional valves logically, the IMV system takes advantage of the gravitational potential energy to lower the boom cylinder without energy from the pump, resulting in saving up to 30% of energy consumption in the system [24,25,26]. Moreover, the original IMV systems do not use energy storage and reuse components, leading to lower investment costs and being more compact than the ERSs. Nonetheless, the IMV system still has certain limitations that warrant improvement. These include the continued use of many proportional valves; the issues of tracking precision stemming from factors like leakage, throttling loss, and noise; and further strides in energy-saving efficiency.

To solve the above problem, a coordination control method between the pump and valve has been developed [27]. In detail, the valve control plays the role of controlling the tracking performance while the pump control helps improve the energy saving in the system. Along with that is the development of advanced controllers to enhance the effectiveness of the IMV system. Lyu et al. [28,29,30] proposed the high-performance adaptive robust control approach for the IMV system with the configuration that combines the hydraulic accumulator to guarantee tracking precision and energy saving. Through experimental verification, this control method not only demonstrated remarkable tracking performance but also led to a reduction in energy consumption by approximately 35–47%. Ding et al. [31] presented a management algorithm that combined meter-out valve control and pump control based on the pressure and flow rate in the system. In detail, the inverse flow mapping approach was used for flow control, and the proportional integral derivative (PID) was applied for pressure control, or a combination of both methods based on the working condition. The experiment result showed that this proposed algorithm had a high stability and fast response while saving up to 28% energy compared to the load-sensing system. Shi et al. [32] proposed the velocity feed forward and position feedback control (VFPB) method for the boom and arm of HEs. In this, the velocity feed forward control was built based on the target trajectory and the model base of the valve or pump (open-loop control) while displacement error between the target position and the real position of the cylinder was used for position feedback control (closed-loop control). The results indicated the system could meet the smooth and high precision during the use of low energy consumption. The common feature of these studies is to build a controller based on the model-based control of the system, which provides robustness control and high accuracy for the system [33,34]. However, the hydraulic system is a complex and non-linear system, so determining the exact model of the system takes a lot of time and makes calculations difficult. In addition, model-based controllers also need a lot of sensors to control the system, causing high costs. Meanwhile, model-free control is still frequently applied in industry, especially on hydraulic systems, such as PID controllers [35,36], or FOPID controllers [37,38,39]. In this case, the FOPID had superior advantages over PID controllers when easily applied in complex systems, because it was capable of processing the delay and the noise in the system due to the fractional-order dynamics [40,41,42]. Nevertheless, when the IMV system frequently faces negative factors, such as leaks and throttling losses on the hydraulic system, the control performance of the FOPID controller is reduced. Consequently, the auto-tuning methods for the FOPID controller were developed for hydraulic systems to deal with negative factors in the system. Although several studies focused on adjusting the parameters of FOPID by using a fuzzy logic control, only three parameters could be tuned [43,44]. In addition, compared to fuzzy logic, neural networks could learn and adapt better to the negative factors mentioned above; in addition, it could also adjust five parameters of the FOPID controller. Despite these advantages, the application of this tuning method remains constrained, particularly in the field of hydraulic systems.

Based on the above analysis, in this paper, a novel control method has been proposed, a neural network-fractional order PID controller (NNFOPID). Specifically, the neural network was used to tune five parameters in the FOPID controller under the effect of external factors such as noise, leakage, and throttling loss. In addition, the proposed controller was applied to the NIMV, which utilized three proportional valves and a directional valve to control the boom cylinder (the NIMV system has been demonstrated to not only better track precision and energy saving but also work similarly to the IMV system in our previous studies [45,46]). The primary contributions of this study are outlined as follows:

• For the first time, the NNFOPID controller was applied to a real test rig that mimics the motion of the boom cylinder of a hydraulic excavator. The advantage of this controller was used for the system without identifying the model of the system (model-free), resulting in minimizing the amount of computing and hardware of the controller on the NIMV system.
• The tuning method of five parameters based on the neural network algorithm was applied to the FOPID controller to enhance the tracking precision and energy saving.
• Both co-simulation and experimental platforms were employed to validate the effectiveness of the proposed controller.
• Compared with the PID and FOPID controllers, the proposed controller not only achieved high tracking precision but also used less energy consumption, saving up to 23.33% and 29.25% under experimental conditions, respectively.

The rest of the paper is arranged as follows: The description of the system is presented in Section 2 and the control algorithm is designed in Section 3. Subsequently, the verification with the co-simulation and experiment is shown in Section 4. Finally, conclusions and future work are discussed in Section 5.

2. System Description

2.1. The Novel Independent Metering Valve System

Due to the high energy-saving efficiency demonstrated in previous studies [45,46], the NIMV system continues to be used to investigate the effectiveness of the proposed controller. Figure 1 displays the NIMV system consisting of the following components: an electric motor (1) that drives the main pump (2) to supply the oil for the system, the NIMV circuit (5) with three proportional valves (K_sa, K_sb, K_ab) and a directional control valve (K_d), a relief valve (3) for protecting the system from excessive pressure, a check valve (4) to protect the pump from system return pressure, a boom cylinder (6), and the controller (7). In addition, four metering modes are utilized for controlling the boom cylinder’s operation, including the power extension (PE) and high-side regeneration extension (HSRE) modes that are applied for the boom-up mode and power retraction (PR) and low-side regeneration retraction (LSRR) modes that are used for the boom-down mode.

2.2. Analysis of Energy Consumption of the System

According to Newton’s Law, the force acting on the boom cylinder can be expressed as follows [47]:

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

(1)

where $p_a$, $A_a$, $p_b$, and $A_b$ are the pressure and area of the bore and rod chamber, respectively, m is the weight of the load, x is the cylinder displacement, and $\beta$ is the viscous friction coefficient. To reduce throttling loss in the valve, a control strategy that involves adjusting the meter-out valve and fully opening the meter-in valve is employed [48]. Therefore, the pressure at the pump outlet $p_s$ can be given as follows:

$$p_s=\left\{\begin{array}{cc}{p}_a=\frac{m\ddot{x}+\beta \dot{x}+mg+p_b{A}_b}{A_a}& \mathrm{at} \mathrm{PE} \mathrm{mode}\\ p_b=\frac{p_a{A}_a-m\ddot{x}-\beta \dot{x}-mg}{A_b}& \mathrm{at} \mathrm{PR} \mathrm{mode}\\ p_a=p_b=\frac{m\ddot{x}+\beta \dot{x}+mg}{A_a-A_b}& \mathrm{at} \mathrm{HSRE} \mathrm{mode}\\ 0& \mathrm{at} \mathrm{LSRR} \mathrm{mode}\end{array}\right.$$

(2)

Based on the cylinder’s velocity v, the required flow rate $Q_s$ from the pump to the cylinder chamber is calculated as follows:

$$Q_s=\left\{\begin{array}{cc}{A}_{a}v& \mathrm{at} \mathrm{PE} \mathrm{mode}\\ A_{b}v& \mathrm{at} \mathrm{PR} \mathrm{mode}\\ \left(A_a-A_b\right)v& \mathrm{at} \mathrm{HSRE} \mathrm{mode}\\ 0& \mathrm{at} \mathrm{LSRR} \mathrm{mode}\end{array}\right.$$

(3)

From Equations (2) and (3), the torque and rotation speed at the pump shaft are represented as follows:

$$T_p=\frac{D_p{p}_s}{2\pi }$$

(4)

$${\omega }_p=\frac{Q_s}{D_p}$$

(5)

where $D_p$ is the pump’s displacement; $T_p$ and ${\omega }_p$ are the torque and rotation speed of the hydraulic pump, respectively. From that, the hydraulic energy required to control the hydraulic boom cylinder can be written as

$$E_p={\displaystyle \int T_p{\omega }_{p}dt}$$

(6)

where $E_p$ is the energy required for the pump. In addition, the energy consumption of the system can be determined with the energy consumption of the electric motor, which replaces the internal combustion engine to drive the hydraulic pump. The energy consumption of the system $E_m$, which is calculated based on the torque $T_m$ and the rotation speed ${\omega }_m$ of the electric motor, is given with the following [49]:

$$E_m={\displaystyle \int T_m{\omega }_{m}dt}$$

(7)

From Equations (6) and (7), the energy consumption efficiency of the NIMV system can be obtained as follows:

$${\eta }_E=\frac{E_p}{E_m}·100\%$$

(8)

where ${\eta }_E$ is the energy consumption efficiency. In addition, the energy saving of the proposed method compared with another control approach, such as PID and FOPID, is calculated as follows [45]:

$${\eta }_{save}=\frac{E_{con}-E_{pro}}{E_{con}}·100\%$$

(9)

where ${\eta }_{save}$ is the energy-saving efficiency, $E_{con}$ is the energy consumption in the NIMV system of the compared controller (PID and FOPID controller), and $E_{pro}$ is the energy consumption of the NIMV system that is controlled with the NNFOPID controller.

3. Control Algorithm

To enhance the tracking precision and energy saving in the NIMV system, the coordination control between the pump and valve is conducted with the NNFOPID controller. In detail, valve control plays the role of taking over the tracking performance of the cylinder through adjusting the area of the orifice of the proportional valve. Meanwhile, the pump control performs the function of managing the energy consumption in the system. The structure of the NNFOPID controller is depicted in Figure 2, and its detailed functionality is described in the subsequent section.

3.1. Fractional Order PID

The general representation for the fractional calculus of the fractional order integration and differentiation operator is as follows [43]:

$${}_{a}D_b^{\alpha }=\left\{\begin{array}{ccc}\frac{d^{\alpha }}{d{t}^{\alpha }}& & \Re \left(\alpha \right)>0\\ 1& & \Re \left(\alpha \right)=0\\ {{\displaystyle {\int }_a^b\left(dt\right)}}^{-\alpha }& & \Re \left(\alpha \right)<0\end{array}\right.$$

(10)

where ${}_{a}D_t^{\alpha }$ represents the fractional calculus, a and b are the lower and upper limits of the operation, and α is the fractional order $\left(\alpha \in \mathbb{R}\right)$. Additionally, the definitions for fractional calculus that are frequently employed are Grunwald–Letnikov and Caputo, and particularly the Riemann–Liouville fractional integral formulation. It is described as follows:

$${}_{a}D_b^{\alpha }=D^n{J}^{n-\alpha }f\left(t\right)=\frac{1}{\mathsf{\Gamma }\left(n-\alpha \right)}{\left(\frac{d}{dt}\right)}^n{\displaystyle {\int }_a^b\frac{f\left(\tau \right)}{{\left(t-\tau \right)}^{\alpha -n+1}}d\tau }$$

(11)

where $\mathsf{\Gamma }$ is the Gamma function, J represents the integral operator, and n denotes the integer value ($n-1<\alpha <n$). The Gamma function can be calculated as follows:

$$\mathsf{\Gamma }\left(x\right)={\displaystyle {\int }_0^{\infty }{t}^{x-1}{e}^{-t}dt{,}_{\hspace{1em}}{}_{}\Re \left(x\right)>0}$$

(12)

In this paper, for fractional integral and derivative calculation, the Riemann–Liouville definition is applied. In addition, the fractional-order modeling and control (FOMCON) toolbox is used to simulate the FOPID controller in MATLAB/Simulink software [50]. The formulation of the FOPID controller that is applied to the pump and valve is presented as follows:

$$U_n\left(t\right)=K_{P}e\left(t\right)+K_I\frac{d^{-\lambda }e\left(t\right)}{d{t}^{-\lambda }}+K_D\frac{d^{\mu }e\left(t\right)}{d{t}^{\mu }}$$

(13)

where $U_n\left(t\right)$ is the output of the FOPID controller at the sampling period t; $K_P$, $K_I$, $K_D$, λ, and μ are the coefficients of the FOPID controller, namely the proportional, integral, derivative coefficients, the order of fractional integration, and the fractional derivative, respectively. $e\left(t\right)$ is the displacement error, which is calculated based on the design trajectory ($r_d$) and the real trajectory ($y_r$) from the cylinder, and is given as follows:

$$e\left(t\right)=r_d\left(t\right)-y_r\left(t\right)$$

(14)

In the FOPID controller, besides setting $K_P$, $K_I$, and $K_D$ for the controller, it is necessary to specify two parameters, λ and μ, because they determine the orders of fractional integration and fractional differentiation, respectively. Notably, the range for adjusting λ and μ can extend from 0 to 2, as illustrated in Figure 3. By tuning these two additional fractional orders (λ and μ), the controller becomes more flexible and stable, meaning the performance of the system can be enhanced. However, it is important to acknowledge that these parameter settings are fixed. External factors such as noise, throttling loss, or system leakage alter the working environment conditions, leading to the controller’s performance being degraded. To address this challenge, a neural network (NN) controller can be employed to tune the five parameters of the FOPID controller. This approach ensures that the system performs effectively even under the influence of external factors, promoting its robustness and reliability.

3.2. Neural Network FOPID Controller Design

The schematic of the NNFOPID controller is represented in Figure 2 and the structure of NNs is shown in Figure 4. To tune the FOPID parameter, the gradient descent (GD) method is used for the weight-updating procedure of NNs [51]. This method is a fundamental and powerful optimization method for neural networks. It provides the necessary tools to efficiently train neural networks, optimize their parameters, and improve their performance on the system. Below is the presentation of the tuning parameter and the learning algorithm of the proportional coefficient; the remaining parameters are calculated similarly.

The performance index function is shown with the following equation:

$$E_P\left(t\right)=\frac{1}{2}{\left[\Delta K_P\left(t\right)-K_P\left(t\right)\right]}^2=\frac{1}{2}{e}_P^2\left(t\right)$$

(15)

where $\Delta K_P$ is the tuning parameters of the proportional and $K_P$ is the proportional coefficient after the update of the NNFOPID controller. According to the GD method, the learning algorithm is established as follows:

$$\Delta {\mathit{w}}_P\left(t\right)=-\eta \frac{\partial E_P\left(t\right)}{\partial w_P\left(t\right)}=\eta e_P\left(t\right){\mathit{h}}_P\left(t\right)$$

(16)

where $\eta$ is the learning rate, ${\mathit{h}}_P=\left[h_j\right]$ with $h_j$ is the Gaussian function value for neural net $j$ in the hidden layer, and $h_j$ can be calculated as

$$h_j=\exp \left(-\frac{{‖\mathit{x}\left(t\right)-{\mathit{c}}_j‖}^2}{2b_j^2}\right)$$

(17)

where $\mathit{x}=\left[x_i\right]$ is the input vector, $\mathit{c}=\left[c_{ij}\right]$ reflects the coordinate value of the center point of the Gaussian function of neural net j for the i-th input, and $b_j$ is the width value of the Gaussian function. Finally, the weight update value of $K_P$ is defined as follows:

$${\mathit{w}}_P\left(t\right)={\mathit{w}}_P\left(t-1\right)+\Delta {\mathit{w}}_P\left(t\right)+\alpha \left[{\mathit{w}}_P\left(t-1\right)-{\mathit{w}}_P\left(t-2\right)\right]$$

(18)

where α is the momentum factor. From Equations (8) and (9), the tuning parameter of the proportional coefficient can be expressed in Laplace form with the following equation:

$$\Delta K_P\left(t\right)={\mathit{w}}_P{\left(t\right)}^T·{\mathit{h}}_P\left(t\right)$$

(19)

The remaining coefficients, i.e., $\Delta K_P{,}_{}\Delta K_I{,}_{}\Delta K_D{,}_{}\Delta \lambda$, and $\Delta \mu$, are similarly calculated as the calculation of $\Delta K_P$. Now, the output of the NN will be described as follows:

$$U_{NN}\left(t\right)=\Delta K_P\left(t\right)e\left(t\right)+\Delta K_I\frac{d^{-\Delta \lambda \left(t\right)}e\left(t\right)}{d{t}^{-\Delta \lambda \left(t\right)}}+\Delta K_D\frac{d^{\Delta \mu \left(t\right)}e\left(t\right)}{d{t}^{\Delta \mu \left(t\right)}}$$

(20)

where $\Delta K_P{,}_{}\Delta K_I{,}_{}\Delta K_D{,}_{}\Delta \lambda$, and $\Delta \mu$ are the tuning parameters of the proportional, integral, derivative coefficients, the order of fractional integration, and the fractional derivative for the FOPID controller, respectively. Hence, the output of the NNFOPID can be written as

$$U\left(t\right)=U_{NN}\left(t\right)+U_{FOPID}\left(t\right)=\left[K_{P0}+\Delta K_P\left(t\right)\right]e\left(t\right)+\left[K_{I0}+\Delta K_I\left(t\right)\right]\frac{d^{-\left[{\lambda }_0+\Delta \lambda \left(t\right)\right]}e\left(t\right)}{d{t}^{-\left[{\lambda }_0+\Delta \lambda \left(t\right)\right]}}+\left[K_{D0}+\Delta K_D\left(t\right)\right]\frac{d^{{\mu }_0+\Delta \mu \left(k\right)}e\left(t\right)}{d{t}^{{\mu }_0+\Delta \mu \left(k\right)}}$$

(21)

where $K_{P0}$, $K_{I0}$, $K_{D0}$, ${\lambda }_0$, and ${\mu }_0$ are the initial setting values of the FOPID controller, namely the proportional, integral, derivative coefficients, the order of fractional integration, and the fractional derivative, respectively.

4. Simulation and Experiment Results

In this section, the effectiveness of the proposed controller is evaluated based on two criteria: tracking precision and energy consumption of the system. To assess the tracking precision, the displacement error of the cylinder is evaluated using the root mean square error (RMSE) and the mean absolute error (MAE). The RMSE and MAE methods allow for a quantitative comparison of the proposed controller and other controllers, enabling informed conclusions about their effectiveness in achieving accurate and precise control over the cylinder’s displacement. The RMSE and MAE methods are defined as follows:

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

(22)

$$MAE=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|e_i\right|}$$

(23)

where n is the sample’s number of displacement errors $e$$\left(e_i{,}_{}i=1{,}_{}2{,}_{}3,\dots {,}_{}n\right)$.

4.1. Simulation Study

4.1.1. Simulation Model

To validate the effectiveness and reliability of the proposed controller, the co-simulations on four working modes of the NIMV system were performed in the commercial software AMESim 2022 and MATLAB 2017a with the simulation model as presented in Figure 5. The main parameter of the simulation model was installed based on the real test bench, and their specifications can be found in

Table 1. The main parameter of the NIMV system was used for the simulation and experiment.

Description	Remark and Unit	Value
Boom cylinder	Model	D140H-LA40B-N500
	Stroke length (mm)	500
	Piston diameter (mm)	40
	Rod diameter (mm)	20
Hydraulic pump	Type	Gear Pump SAP20-8.0
	Displacement (cc/rev)	8.3
	Max. speed control (rpm)	1500
	Volumetric efficiency *	0.9
	Torque efficiency *	0.95
Proportional valve	Type	EHPV SP10-24
	Max. flow (L/min)	26.5
	Max. pressure (bar)	207
	Pressure drops (bar) *	10
Directional control valve	Model	RPE3-063Z11/24V
	Max. flow (L/min)	80
	Max. pressure (bar)	350
	Pressure drops (bar) *	10
Relief valve	Model	VPN1-06-MP-32S
	Cracking pressure (bar)	100
	Max. flow (L/min)	70
	Max. pressure (bar)	320
Load	(kg)	100

* This parameter is exclusively used for the simulation model.

. This ensures that the simulation model closely aligns with the characteristics of the actual NIMV system. Furthermore,

Table 2. The valve’s conductivity and operating time on four working modes.

Working Mode	Ksa	Kab	Ksb	Kd	Time
PE	Fully open	Closed	Control	Kd2	1 to 9
PR	Fully open	Closed	Control	Kd1	11 to 16
HSRE	Fully open	Control	Closed	Kd2	18 to 23
LSRR	Closed	Control	Fully open	Kd2	25 to 33

provides the valve’s conductivity and operating time for each of the four working modes of the NIMV system. These values play a crucial role in defining and distinguishing the various operating modes within the system. Finally, the simulation results of the proposed controller will be compared with the PID and FOPID controllers under the same condition simulation. Notably, the noise signal, which is shown in Figure 6, is used to simulate external factors affecting pumps and valves such as throttling loss, or system leakage. This comparative analysis aims to evaluate and highlight the advantages of the suggested controller in terms of performance and efficiency. The PID controller is used in the comparison as shown as follows:

$$U_{PID}\left(t\right)=K_{P0}e\left(t\right)+K_{I0}{\displaystyle \underset{0}{\overset{t}{\int }}e\left(t\right)dt}+K_{D0}\frac{de\left(t\right)}{dt}$$

(24)

Remark 1.

To facilitate a fair comparison, it is worth noting that the control coefficients for the PID, FOPID, and proposed controllers have been carefully configured to have the same parameter values. These coefficients have been appropriately selected based on the specific working characteristics of each mode, and their corresponding values can be found in

Table 3. The control coefficients were installed for the simulation.

Component	Mode	${\mathit{K}}_{\mathit{P}0}$	${\mathit{K}}_{\mathit{I}0}$	${\mathit{K}}_{\mathit{D}0}$	${\mathit{\lambda }}_0$	${\mathit{\mu }}_0$
Valve	PE	1	1	0.1	0.3	0.6
	PR	−2	−0.5	−0.01	0.3	0.6
	HSRE	0.05	0.01	0.001	1.5	0.5
	LSRR	−1.5	−0.1	−0.01	0.8	1.05
Pump	PE	60	15	1	1.2	0.6
	PR	−35	−5	−1	1.5	1.2
	HSRE	20	5	1	0.5	0.5

.

4.1.2. Simulation Result

Figure 7 illustrates the comparison of the displacement and error of the boom cylinder on three controllers under the same effect of disturbance (as shown in Figure 6) on the time of 35 s. During the lifting and lowering of the cylinder, the FOPID and NNFOPID controllers have better tracking than the PID controller. It is obvious that the fractional order components allow for better handling of noise in the system, enabling more robust control. Meanwhile, through the tuning of five control coefficients in the FOPID controller, the proposed controller with the NN technique not only achieves the highest tracking precision but also exhibits a faster convergence rate. Notably, it shows a detail from time 20–23 s on the HSRE mode and the zoom in 25–27 s on the LSRR mode. In addition, to ensure fairness in comparison, the RMSE and MAE calculation results of the three controllers are presented in Figure 8 and Figure 9. It is evident from these results that the RMSE of the proposed controller consistently yields as lower compared to the other two controllers, especially in the LSRR mode, about 75.7% and 74.5% of those from FOPID and PID controllers, respectively. Moreover, MAE results are similar to RMSE results when the MAE value of the proposed controller is the smallest. This proves that the accuracy tracking of the system has been improved through the process of tuning the control coefficients.

Most of the time, the proposed controller always has better tracking precision. This advantage is achieved through the seamless coordination between the valve and the pump control. Figure 10 shows the comparison of the valve control signal in three controllers and Figure 11 represents the rotation speed, torque, and energy consumption of the electric motor. The most notable disparities appear prominently in PE, HSRE, and LSRR modes when the valve control signal and motor speed have been significantly changed during operation. This is because the fractional order integral component and tuning of their parameters allow the controller to respond more quickly to changes in the system’s behavior, resulting in faster adjustments to the control signal. Particularly detailed is the LSRR mode, where the valve control signal of the NNFOPID controller rapidly increases to 10 V upon entering the mode, only gradually declining to 4 V once the system stabilizes. In contrast, in PID and FOPID controllers, the signal control only fluctuates at about 4 V when opening this mode.

In addition to the criterion of tracking precision, energy consumption serves as another pivotal measure in evaluating the effectiveness of the proposed controller. In Figure 11, the energy consumption of the three controllers is almost the same in the PE and PR mode, especially in the zoom of 6–7 s when the curves are very close together. However, when delving into a more specific energy consumption analysis for each mode (depicted in Figure 12), the NNFOPID controller consumes 0.005 kJ more energy than the PID controller but 0.021 kJ less than the FOPID controller in the PE mode. In the PR mode, it consumes 0.013 kJ more energy compared to the PID controller, and equivalently to the FOPID controller. While it does require slightly more power in these modes, the difference is relatively minor. The most notable differentiation emerges in the HSRE mode, where the NNFOPID controller showcases remarkable efficiency. Consuming a mere 4.289 kJ to lift the cylinder, it significantly outperforms the FOPID controller’s consumption of 4.787 kJ and the PID controller’s 6.053 kJ. In conclusion, the proposed controller demonstrates high energy-saving performance for the NIMV system, particularly in the HSRE mode.

In summary, the simulation results offer a comprehensive evaluation of the NNFOPID controller performance in the NIMV system. Under complex noise, the proposed controller not only ensures high tracking accuracy but also saves energy admirably across four working modes, saving 10.4% energy when compared with the FOPID controller and 29.14% compared with the PID controller.

4.2. Experiment Verification

4.2.1. Experiment Setup

The real test bench of the NIMV system was used to demonstrate the effectiveness and practical applicability of the NNFOPID controller. Figure 13 portrays the experimental setup meticulously designed to emulate the hydraulic boom excavator within the laboratory conditions. The proposed controller was configured in the program computer (1), operating through Simulink Desktop Real-Time on the MATLAB/Simulink software. The control signals were subsequently transmitted to the control box (2) via the PCI card, thereby orchestrating the actions of the servo motor (8) and valve’s conductance. In conjunction, the torque sensor (9) and rotational speed sensor (10) were affixed to the motor shaft to facilitate data acquisition for energy consumption calculations. Simultaneously, the linear sensor (7) was integrated with the cylinder to measure its tracking position. An enumeration of devices employed within the experimental setup is itemized in Table 1 and

Table 4. Device setting of the test bench system.

Description	Remark and Unit	Value
Linear sensor	Model	TLH−0500
	Linearity (±)	0.05%
Amplifiers for EHPV	Mode	KURP−9502
	Power supply (VDC)	24
	Input range (VDC)	0 to 10
	Output range (VDC)	0 to 24
Pressure sensor	Model	PMCE0200BDAA
	Pressure range (bar)	0 to 200
	Power supply (VDC)	24
	Output range (VDC)	0 to 5
Torque transducer	Model	YDR−5KM
	Capacity (Nm)	49.03
Rotational speed sensor	Model	MP-981
	Power supply (VDC)	12
	Output waveform (V)	5 ± 0.5 or less
Servo motor	Model	FMACN22−AB00
	Power (kW)	2.2
PCI card 1	Type	NI PCI−6221
	Resolution	16AI/2AO: 16 bits
PCI card 2	Type	NI PCI−6703
	Resolution	16AO: 16 bits

.

As the same in the simulation section, three controllers were compared to demonstrate the advantage of the proposed controller for application in the real practice of the NIMV system. In addition, the trial-and-error strategy was used to find the suitable parameter for the experiment, as chosen in

Table 5. Control coefficients are applied to the experimental system.

Component	Mode	${\mathit{K}}_{\mathit{P}0}$	${\mathit{K}}_{\mathit{I}0}$	${\mathit{K}}_{\mathit{D}0}$	${\mathit{\lambda }}_0$	${\mathit{\mu }}_0$
Valve	PE	1	0.05	0.005	1.55	0.1
	PR	−5	−1	−0.01	0.6	0.5
	HSRE	0.04	0.02	0.005	1.25	0.8
	LSRR	−0.08	−0.03	−0.005	1.1	0.9
Pump	PE	25	10	1	1.2	0.4
	PR	−40	−5	−1	2	1.2
	HSRE	20	5	1	1.2	1.5

.

4.2.2. Experimental Results

The tracking position results in the NIMV system of the three controllers, which are shown in Figure 14, Figure 15 and Figure 16. Following this result, the proposed controller provides better tracking performance when compared with the PID and FOPID controllers on four working modes with a maximum error held less than 0.062 m, as shown in Figure 14. In addition, the proposed controller has a faster response time in the PE and HSRE modes and a rapid convergence rate in all modes thanks to the advantages of tuning the control parameters in the NNFOPID controller. This result is further reinforced in Figure 15 and Figure 16 when the proposed controller always gives the lowest RMSE and MAE values during operation.

In addition, the input control signal of the valve and pump are shown in Figure 17 and Figure 18a. As shown in Figure 17, in the HSRE mode, the signal control of the K_ab valve (U_ab) of the proposed controller increases quickly to 1.2 V when the system starts in this mode, higher than the other two controllers (detail on the zoom-in of 17.8–18 s), resulting in the cylinder being operated earlier than the rest of the controllers. Meanwhile, the signal of the U_ab increment up to 3.4 V in the LSRR mode from 25 to 26 s helps the proposed controller to close more closely to the reference signal. In contrast to HSRE and LSRR modes, the tracking performance in the PE and PR modes is decided by the pump control signal. In the PE mode, the valve control signal of the K_sb valve is at the maximum (U_sb = 10 V) for 1 to 4 s, and gradually decreases to control the accuracy after that. With the advantage of the proposed controller, the speed of the motor is increased rapidly from 1 to 1.4 s (detail on zoom-in of 1.1–1.4 s, Figure 18a), leading to the faster response time of the cylinder in this mode. While in the PR mode, the K_sb valve is fully open during the operation time. The motor speed rises quickly to 850 rpm from 11 to 11.6 s in the proposed controller, resulting in displacement error reducing faster.

Finally, the comparison of the energy consumption is presented in Figure 18c and Figure 19. By using the NNFOPID controller, the NIMV system consumes less energy in four working modes, saving up 23.33% and 29.25% compared with the FOPID and PID controllers, respectively. Figure 19 shows in detail the energy consumption of the NIMV system of each mode. In general, the energy used in PE and PR modes is relatively similar, the difference only occurs in the HSRE mode due to the fast response ability of the NNFOPID controller.

From the above results, the proposed controller not only effectively extinguishes disturbance factors (noise, throttling loss, or system leakage) but also has high tracking precision and energy saving in the NIMV system. Through experimental verification, the NNFOPID controller shows high efficiency in practical application to the NIMV system on the boom excavator.

5. Conclusions

In this paper, the control method of NNFOPID was proposed for the NIMV system to enhance the tracking performance and energy saving in the boom excavator. Specifically, the fractional order derivative and integral component of the FOPID contribute to precision, stability, and fast response for the system. In addition, five parameters of the FOPID controller were automatically tuned using the NN controller to ensure the performance of the system under the influence of external factors. From the simulation and experimental results, the proposed system proved excellent control ability under complex influence conditions from noise, leakage, to throttling loss. As a result, the NIMV system provided better tracking performance and energy saving, saving up 23.33% and 29.25% compared to FOPID and PID in the experimental platform, respectively. Future endeavors will focus on optimizing the cylinder response time in the NIMV system to enhance the tracking precision for hydraulic excavators. Additionally, we will explore the potential for storing and reusing gravitational potential energy from the NIMV system, aiming to enhance energy-saving capabilities even further.