A Novel Hydraulic Interconnection Design and Sliding Mode Synchronization Control of Leveling System for Crawler Work Machine

Abstract

To address the issues of easy overturning and poor safety of crawler work machines operating on steep slopes in hilly and mountainous areas, this study develops a structural design scheme based on a “three-layer frame” structure. An omnidirectional leveling system with hydraulic interconnection is designed to maintain platform stability by ensuring a stationary central point during leveling. Furthermore, a sliding mode synchronization control method based on a disturbance observer is proposed to reduce the synchronization error of the hydraulic cylinders and enhance leveling precision. The system’s performance is validated through an AMESim-MATLAB/Simulink co-simulation platform, demonstrating significant improvements over traditional PID control. Specifically, both lateral and longitudinal leveling times are reduced, rise time decreases by 21.8% on average, and overall leveling time is reduced by 35.5%, with synchronization errors maintained within ±6 × 10⁻⁴ m. Finally, physical prototype testing further confirms the system’s effectiveness, achieving an average body inclination error of 2.55% and a hydraulic cylinder synchronization error of 8.2%. These findings validate the feasibility and superiority of the proposed omnidirectional leveling system for the crawler work machine in hilly and mountainous regions.

1. Introduction

Hilly and mountainous regions are characterized by uneven terrain and challenging transportation conditions, leading to poor operational stability and low efficiency of agricultural machinery [1,2,3]. These issues are further exacerbated by the high risk of rollovers during operations on steep slopes. Therefore, optimizing the structural design of agricultural machinery for such terrains [4,5] and innovating leveling systems have become critical priorities [6,7,8]. To ensure efficient and safe operations in these complex environments, it is imperative to develop advanced leveling structures and intelligent control strategies tailored to the demands of uneven terrains [9,10,11].

In recent years, the development of leveling technologies for agricultural equipment has made notable progress. Dettù, F. et al. introduced a cascade control method for the attitude adjustment of combine harvesters, leveraging sensor fusion and precise attitude estimation algorithms to achieve efficient leveling under diverse terrain conditions. This method significantly improved operational stability and efficiency [12]. Lv, X.R. et al. designed a tractor leveling mechanism tailored for hilly and mountainous terrains, incorporating adaptive control algorithms that enable rapid posture adjustment to cope with complex topographies, while also minimizing mechanical vibrations and energy loss [13]. Xie, X. et al. optimized the design of dynamic chassis systems and conducted extensive field testing, demonstrating their quick responsiveness and high reliability on dynamic terrains, providing an essential reference model for intelligent leveling in agricultural machinery [14]. Furthermore, Jeon, C.W. et al. developed an autonomous leveling system for paddy field operations, integrating high-precision path planning algorithms and real-time dynamic adjustments. This system adaptively optimized operational routes based on terrain variations, achieving higher levels of automation and precision [15]. Zhang, Y. et al. investigated a chassis leveling control system for a three-wheeled agricultural robot, utilizing a PID control algorithm to achieve precise leveling adjustments. Their study emphasized the role of PID-based feedback mechanisms in maintaining chassis stability and improving operational efficiency in agricultural tasks [16]. Lastly, Hu, J. et al. developed an attitude-adjustable crawler chassis for combine harvesters, incorporating an adaptive fuzzy control algorithm to implement real-time leveling adjustments under varying terrain conditions. Their work demonstrated the effectiveness of such systems in ensuring stability and efficiency for machinery operating on complex terrains [17].

Despite advancements, the body leveling of crawler work machines remains a significant challenge in both theoretical research and engineering applications. Existing leveling systems exhibit notable deficiencies in adaptability and stability, particularly on steep slopes and complex terrains [18,19,20]. Regarding control strategies, while PID control algorithms are widely employed in agricultural machinery [21,22,23], they face limitations such as difficult tuning, poor adaptability, and susceptibility to external disturbances, resulting in reduced robustness [24,25,26]. To address these challenges, innovative and adaptable mechanical structures and control strategies are essential for improving operations on uneven terrains in hilly and mountainous regions.

To tackle these issues, this study focuses on the crawler work machine and proposes an innovative “three-layer frame” crawler work machine structure. By employing hydraulic interconnection, the system achieves moment balance between the frames, overcoming the traditional rigid structure’s limitations in dynamically adapting to steep slopes. This design enhances the machine’s leveling capability and resistance to overturning.

Theoretical research was conducted to focus on the design and control principles of the proposed system. A sliding mode synchronization control method based on a disturbance observer was developed. Compared to traditional PID control, sliding mode control demonstrates greater robustness against external disturbances, while the incorporation of a disturbance observer significantly improves the system’s dynamic response and control precision. The “three-layer frame” structure with hydraulic interconnection ensures moment balance and enhances platform stability, addressing the challenges of existing leveling systems in hilly and mountainous terrains.

Experimental research was then carried out to validate the system’s performance. Simulation analyses and prototype testing were conducted to evaluate the dynamic response, leveling precision, and operational stability of the crawler work machine. The results demonstrate that the omnidirectional leveling system achieves significant improvements in leveling performance and resistance to overturning on steep slopes.

The novelty of this research lies in the introduction of the “three-layer frame” structure with hydraulic interconnection, coupled with a sliding mode control strategy enhanced by a disturbance observer, which collectively ensure superior leveling performance and operational stability on complex terrains. Through combined simulation analyses and prototype testing, the omnidirectional leveling performance and reliability of this crawler work machine are validated, providing a valuable reference for the intelligent development of agricultural machinery tailored to hilly and mountainous terrains.

2. Materials and Methods

2.1. Design of the Omnidirectional Leveling System

2.1.1. Design Scheme and Working Principle

The omnidirectional leveling structure of the crawler work machine utilizes a “three-layer frame” design, which enables independent leveling in both the lateral and longitudinal directions, as illustrated in Figure 1. The upper frame (9) represents the main body of the crawler work machine, which is connected to the intermediate frame (10) via two triangular articulated structures and four lateral leveling cylinders (3). These cylinders are symmetrically arranged relative to the machine’s lateral and longitudinal central planes. During lateral leveling, the symmetrical lateral leveling cylinders (3) extend and retract equally, ensuring that the geometric center of the machine body remains stationary throughout the process. The intermediate frame (10) serves as a connection between the upper (9) and lower frames (11), facilitating the articulation mechanism and supporting the leveling cylinders. The lower frame (11) forms the chassis of the crawler work machine and is connected to the intermediate frame (10) via two triangular articulated structures and two longitudinal leveling cylinders (4). These cylinders are symmetrically positioned about the lateral central plane. During longitudinal leveling, the symmetrical longitudinal leveling cylinders (4) extend and retract equally, similarly maintaining the geometric center of the machine body in a fixed position. The track (5) is mounted on the lower frame, with key components including the driving wheel (6), supporting wheels (7), and the tensioning wheel (8). These components ensure that the crawler work machine maintains stability and traction on steep and uneven terrains. This symmetrical arrangement of the lateral (3) and longitudinal hydraulic cylinders (4) enables a center-immobile leveling process, significantly enhancing the overall stability of the crawler work machine during operation. By ensuring that the geometric center remains stationary, the machine achieves improved safety and reliability when working on steep slopes.

The control process of the omnidirectional leveling system for the crawler work machine is depicted in the updated Figure 2. The information detection module utilizes a dual-axis inclination sensor to measure the angular positions of the crawler work machine in both the lateral and longitudinal directions. By continuously monitoring the inclination angles of the machine body in real time, the dual-axis inclination sensor provides precise lateral and longitudinal inclination data to the leveling controller. These data are subsequently transmitted to the leveling controller, which independently processes the lateral and longitudinal inclination information obtained from the information detection module. Based on the variations in the lateral and longitudinal angles, the leveling controller calculates the required adjustments for each direction separately, ensuring that the leveling actions in both directions operate independently of each other. This design enhances the stability and precision of the control system. Finally, the leveling controller outputs control signals to the leveling module, achieving coordinated control of the six hydraulic cylinders within the leveling module.

2.1.2. Design of Hydraulic Interconnection Circuit

The design of the hydraulic leveling system’s functional principles is a key component of the crawler work machine system. The choice of a hydraulic system is due to the advantages of hydraulic transmission, including small size, light weight, and compact structure, which make it well-suited to meet the needs of complex and dynamic working environments [27,28,29]. The hydraulic circuit in this system adopts an open-loop hydraulic circuit design, where the working fluid flows from the oil source to the actuator and then returns to the reservoir without recirculating directly back to the pump. This choice is made considering operational efficiency, simplicity of design, and ease of future maintenance [30]. An omnidirectional leveling hydraulic interconnection circuit is designed, based on symmetrically arranged lateral and longitudinal cylinders, as shown in Figure 3. The system includes the oil source system, lateral and longitudinal leveling cylinders, an electromagnetic proportional directional valve, a stacked hydraulic control check valve, and a stacked double-acting throttle valve. This leveling system’s hydraulic circuit allows for the simultaneous control of all hydraulic cylinders’ extension. The interconnection between symmetrical pairs ensures that the extension lengths of the two cylinders are identical, thus enabling stationary leveling at the center point. To prevent overheating of the hydraulic system, return oil filters and air filters are integrated into the circuit, which enhances the overall stability of the hydraulic system.

As shown in Figure 3, HL1, HR1, HL2, and HR2 represent the lateral leveling hydraulic cylinders located at the left front, right front, left rear, and right rear of the crawler work machine, respectively. ZL and ZR denote the longitudinal leveling hydraulic cylinders at the front and rear. HDC1 and HDC2 are electromagnetic proportional directional valves controlling the lateral leveling cylinders HL1/HR1 and HL2/HR2, respectively, while ZDC controls the longitudinal cylinders ZL and ZR. The hydraulic system operates in the following sequence for each of the four leveling states of the crawler work machine.

• Raising the right side for horizontal leveling: motor starts → hydraulic pump operates → electromagnetic proportional valves HDC1 and HDC2 actuate → hydraulic cylinders HL1 and HL2 (rod chambers fill, rodless chambers empty) → hydraulic cylinders HR1 and HR2 (rodless chambers fill, rod chambers empty) → oil source system.
• Raising the left side for horizontal leveling: motor starts → hydraulic pump operates → electromagnetic proportional valves HDC1 and HDC2 actuate → hydraulic cylinders HR1 and HR2 (rod chambers fill, rodless chambers empty) → hydraulic cylinders HL1 and HL2 (rodless chambers fill, rod chambers empty) → oil source system.
• Raising the right side for longitudinal leveling: motor starts → hydraulic pump operates → electromagnetic proportional valve ZDC actuates → hydraulic cylinder ZL (rod chamber fills, rodless chamber empties) → hydraulic cylinder ZR (rodless chamber fills, rod chamber empties) → oil source system.
• Raising the left side for longitudinal leveling: motor starts → hydraulic pump operates → electromagnetic proportional valve ZDC actuates → hydraulic cylinder ZR (rod chambers fill, rodless chambers empty) → hydraulic cylinder ZL (rodless chambers fill, rod chambers empty) → oil source system.

2.1.3. Hydraulic Interconnected Leveling System Model Establishment

The hydraulic cylinder model built by AMESim is accurate and effective. The hydraulic cylinder drive model in AMESim includes the electromagnetic proportional valve control signal, the electromagnetic proportional valve itself, the hydraulic cylinder, the power source, and the oil tank, as shown in Figure 4.

Based on this, a hydraulic interconnection omnidirectional leveling system is established. In AMESim, the hydraulic interconnection omnidirectional leveling system model shown in Figure 5 is created according to the configuration in Figure 3. Here, 1 represents the hydraulic cylinder load, 2 refers to the hydraulic components of the interconnection system, and 3 denotes the control signals. The omnidirectional leveling hydraulic interconnected system model is integrated with the mechanical model of the crawler work machine. First, the hydraulic cylinder drive model in the hydraulic leveling system is connected to the rotational joint sub-model, establishing the electrical–hydraulic cylinder dynamics sub-model of the crawler work machine, as shown in Figure 6. On this basis, the hydraulic cylinders of the omnidirectional leveling hydraulic interconnected system are correspondingly connected to the rotational joint sub-models of the crawler work machine. This results in the construction of the complete machine model of the crawler work machine, as shown in Figure 7.

2.2. Design of Synchronization Control Strategy

2.2.1. Mathematical Model of Omnidirectional Leveling System

Before designing the controller, it is necessary to establish the mathematical model of the valve-controlled hydraulic cylinder based on the flow equation of the electro-hydraulic proportional directional valve, the dynamic equilibrium equation of the hydraulic cylinder, and the continuity equation of hydraulic cylinder flow. The system state variables are defined as shown in Equation (1):

$${\left[x_{m_1},x_{m_2},x_{m_3},x_{m_4}\right]}^{{\rm T}}={\left[x_f,{\dot{x}}_f,p_{m_1},p_{m_2}\right]}^{{\rm T}}$$

(1)

In the equation, $P_{m_1}$ and $P_{m_2}$ refer to the pressures in the rodless chambers of the left and right hydraulic cylinders and $x_f$ is the piston displacement of the hydraulic cylinder.

The electro-hydraulic proportional directional valve is the key control component of the omnidirectional leveling hydraulic system in the crawler work machine’s electro-hydraulic proportional position system. The flow equation of the valve port is given by Equation (2):

$$\left\{\begin{array}{l}{q}_{m_1}=S\left(u_m\right)k_q{u}_m\sqrt{P_{m_s}-P_1}+S\left(-u_m\right)k_q{u}_m\sqrt{P_{m_1}-P_r}\hfill \\ q_{m_2}=S\left(u_m\right)k_q{u}_m\sqrt{P_{m_2}-P_r}+S\left(-u_m\right)k_q{u}_m\sqrt{P_s-P_{m_2}}\hfill \end{array}\right.$$

(2)

where $S\left(u_m\right)=\left\{\begin{array}{ll}1\hfill & u_m\ge 0\hfill \\ 0\hfill & u_m<0\hfill \end{array}\right.$; $k_q=k_u{C}_{d}w\sqrt{{\displaystyle \frac{2}{\rho }}}$.

In the equation, $k_u$ represents the gain of the electro-hydraulic proportional directional valve, $w$ denotes the spool area gradient of the valve, and $u_m$ is the input voltage signal of the electro-hydraulic proportional directional valve. Variables $P_s$ and $P_r$ represent the supply pressure and return pressure, respectively. $\rho$ denotes the fluid density, and $C_d$ is the flow coefficient of the valve port.

Assuming that the pressure within the hydraulic cylinder chambers is uniform at any position, pipeline resistance losses, piston seal leakage of the hydraulic cylinder, oil temperature variations, and the effects of fluid bulk modulus are neglected. Under these assumptions, the dynamic continuity equation for the internal flow of the hydraulic cylinder can be derived, as shown in Equation (3):

$$\left\{\begin{array}{l}{q}_{m_1}=A_{m_1}{\dot{x}}_f+{\displaystyle \frac{V_{m_1}}{\beta }}{\dot{P}}_{m_1}+C_i\left(P_{m_1}-P_{m_2}\right)\hfill \\ q_{m_2}=A_{m_2}{\dot{x}}_f-{\displaystyle \frac{V_{m_2}}{\beta }}{\dot{P}}_{m_2}+C_i\left(P_{m_1}-P_{m_2}\right)\hfill \end{array}\right.$$

(3)

where $V_{m_1}=V_{01}+A_1{x}_f$, $V_{m_2}=V_{02}-A_1{x}_f$, $C_i$ is the internal leakage coefficient, $V_{01}$ and $V_{02}$ are the initial volumes of the rodless and rod chambers of the hydraulic cylinder, respectively, and $\beta$ is the bulk modulus of the hydraulic oil.

The hydraulic cylinder load includes the gravitational force of the piston rod assembly, the gravitational force of the external load, and the frictional force. The hydraulic cylinder load is a critical factor influencing the dynamic characteristics of the system. The dynamic equilibrium equation of the hydraulic cylinder is derived from Newton’s Second Law, as shown in Equation (4):

$$A_{m_1}{p}_{m_1}-A_{m_2}{p}_{m_2}=m_l{\ddot{x}}_f+B_m{\dot{x}}_f+F_m+d_m(t)$$

(4)

where $A_{m_1}$ is the effective acting area of the rodless chamber, $A_{m_2}$ is the effective acting area of the rod chamber, $m_l$ is the load mass, $B_m$ is the viscous damping coefficient, $F_m$ is the theoretical load, and $d_m(t)$ is the unknown load disturbance.

Based on Equations (1) to (4), the state–space equation for the omnidirectional leveling position control system of the crawler work machine can be established, as shown in Equation (5):

$$\left\{\begin{array}{l}\begin{array}{l}{\dot{x}}_{m_1}=x_{m_2}\\ {\dot{x}}_{m_2}={\displaystyle \frac{1}{m_l}}\left(A_{m_1}{x}_{m_3}-A_{m_2}{x}_{m_4}-B_m{x}_{m_2}-F_m-d_m(t)\right)\end{array}\hfill \\ {\dot{x}}_{m_3}={\displaystyle \frac{\beta }{V_{01}+A_{m_1}{x}_{m_1}}}\left(-A_{m_1}{x}_{m_2}-C_i\left(x_{m_3}-x_{m_4}\right)+q_{m_1}\right)\hfill \\ \begin{array}{l}{\dot{x}}_{m_4}={\displaystyle \frac{\beta }{V_{02}-A_{m_2}{x}_{m_1}}}\left(A_{m_2}{x}_{m_2}+C_i\left(x_{m_3}-x_{m_4}\right)-q_{m_2}\right)\\ y_m=x_{m_1}\end{array}\hfill \end{array}\right.$$

(5)

2.2.2. Design of Nonlinear Disturbance Observer

During the actual operation of the leveling system, various uncertainties may affect the system, reducing its control accuracy and stability [31]. To address this, this paper proposes a disturbance observer to effectively compensate for the omnidirectional hydraulic leveling system of the crawler work machine, improving the control accuracy and disturbance rejection capability of the system. The disturbance estimation error is defined as shown in the following equation:

$${\tilde{d}}_m(t)={\widehat{d}}_m(t)-d_m(t)$$

(6)

where ${\tilde{d}}_m(t)$ is the estimated disturbance value,

$$d_m(t)=-m_l{\dot{x}}_{m_2}+\left(A_{m1}{x}_{m_3}-A_{m_2}{x}_{m_4}\right)-B_m{x}_{m_2}-F_m$$

By compensating the estimated value with the disturbance error and assuming that the derivative of the disturbance with respect to time is bounded, we can write

$${\dot{\widehat{d}}}_m(t)=-l_0{\tilde{d}}_m(t)$$

(7)

where $l_0$ is the linear gain of the disturbance observer, which is always positive.

From Equation (6), it is known that a nonlinear relationship exists between the state variables $x_{m_2}$ and the unknown disturbances in the system. To effectively address this nonlinear disturbance and further enhance the dynamic performance and disturbance rejection capability of the crawler work machine’s omnidirectional leveling control system, a nonlinear gain term closely related to the state variables $x_{m_2}$ is introduced in the design of the disturbance observer. The nonlinear disturbance observer is defined as follows:

$$\left\{\begin{array}{l}{\widehat{d}}_m(t)=z_i+l_s{x}_{m_2}\hfill \\ {\dot{z}}_i=-l_x\left(z_i+l_s{x}_{m_2}\right)+l_x\left(A_{m1}{x}_{m_3}-A_{m_2}{x}_{m_4}-B_m{x}_{m_2}-F_m\right)\hfill \end{array}\right.$$

(8)

where $l_s$ is the nonlinear gain and $z_i$ is the auxiliary state variable.

To validate the system’s stability, a semi-definite Lyapunov function is selected as follows:

$$V_0={\displaystyle \frac{1}{2}}{\tilde{d}}_m{(t)}^2$$

(9)

Taking the derivative of $V_0$, based on Equations (6), (7) and (9), we obtain

$$\left\{\begin{array}{c}{\dot{V}}_0={\tilde{d}}_m(t){\dot{\tilde{d}}}_m(t)={\tilde{d}}_m(t)\left({\dot{\widehat{d}}}_m(t)-{\dot{d}}_m(t)\right)\\ ={\tilde{d}}_m(t)\left(-l_0{\tilde{d}}_m(t)-{\dot{d}}_m(t)\right)\\ =-l_0{\tilde{d}}_m{(t)}^2-{\tilde{d}}_m(t){\dot{d}}_m(t)\\ \le -\left(l_0-{\displaystyle \frac{C}{2}}\right){\tilde{d}}_m{(t)}^2+{\displaystyle \frac{1}{2C}}{\lambda }^2\\ \le -(2l_0-C){\tilde{d}}_m{(t)}^2+{\displaystyle \frac{1}{2C}}{\lambda }^2\end{array}\right.$$

(10)

where $\lambda$ and $C$ are arbitrary positive constants. Let $2l_0-C>0$, which satisfies $l_0>C/2$, and since ${\lambda }^2/2C>0$, the disturbance observer is proven to be exponentially stable.

2.2.3. Sliding Mode Synchronous Controller Design Based on Disturbance Observer

In this paper, a cross-coupling method is adopted for the selection of the synchronization control strategy. This method is chosen due to its ability to effectively coordinate the positional synchronization errors between the two hydraulic cylinders, thereby improving the overall control accuracy and system stability. The cross-coupling method has the advantage of dynamically correlating the positional synchronization errors, which allows the system to respond more effectively to uneven loads and external disturbances. This ensures a balanced distribution of control effort across the actuators, reducing the likelihood of instability caused by isolated error corrections [32,33,34]. During lateral leveling, the positional synchronization errors of the two hydraulic cylinders are correlated with each other. In the controller design, the positional synchronization error is introduced into the sliding mode controller as a compensation term, ensuring both the positional control accuracy of the system and the stability and robustness of the system. The block diagram of the sliding mode synchronization controller based on the disturbance observer is shown in Figure 8. Additionally, the nonlinear disturbance observer designed earlier is incorporated into the sliding mode synchronization controller to compensate for the unknown total disturbances, further enhancing the robustness of the system.

Let the displacement errors of the two groups of lateral leveling hydraulic cylinders be, $e_1$ and $e_2$, respectively. If position synchronization error is $e_s$, then:

$$\left\{\begin{array}{l}{e}_1=x_{11}-x_t\hfill \\ e_2=x_{21}-x_t\hfill \\ e_s=e_1-e_2\hfill \end{array}\right.$$

(11)

where $x_t$ is the expected displacement output, $x_{11}$ and $x_{21}$, respectively, are the actual displacement outputs of the two groups of lateral leveling hydraulic cylinders on the same side. Take the coupling sliding form surface as follows:

$$S_m=\left(C_1{e}_1+C_2{\dot{e}}_1+{\ddot{e}}_1\right)+\left(w_1{e}_s+w_2{\dot{e}}_s\right)$$

(12)

where $C_1$ is the error gain, $C_2$ is the error derivative gain, $w_1$ is the synchronization error gain, and $w_2$ is the synchronization error derivative gain.

The sliding mode synchronization controller incorporates the fundamental characteristics of sliding mode variable structure control. The sliding mode approaching gain ${\epsilon }_i$ determines the system’s approaching speed to the sliding mode surface and the chattering amplitude under the constant approaching rate. When ${\epsilon }_i$ is large, the approaching speed increases, but the system experiences more significant chattering. Conversely, although chattering decreases with a smaller ${\epsilon }_i$, the approaching speed also reduces. Furthermore, due to the introduction of the synchronization error term in the sliding mode controller design, the sliding mode switching function becomes more complex. This additional term affects the dynamic performance of the system, influencing both the rapid approaching speed to the sliding mode surface and the stability during the approaching process. To optimize the system’s approaching time to the sliding mode surface and reduce the chattering amplitude after reaching the sliding mode surface, a novel adaptive sliding mode reaching law is designed for the proposed sliding mode synchronization controller. This design aims to balance the trade-off between approaching speed and chattering amplitude, thereby improving the overall performance and stability of the control system. The novel adaptive sliding mode reaching law is shown in Equation (13).

$$\dot{S}=-eq\left(e_i,s\right)\cdot sgn(s)-ks$$

(13)

where

$$eq\left(e_i,s\right)={\displaystyle \frac{k}{\epsilon +\left(1+\frac{1}{e_i}-\epsilon \right)e^{-\delta \left|s\right|}}}$$

(14)

In the equation, $k$ and $\delta$ are constants, $\epsilon$ is a constant between 0 and 1, and $e_i$ represents the system state. When the system state is far from the sliding mode surface, $s$ tends to $k_s$, and the system state converges exponentially to the sliding mode surface. As the system state gradually approaches the sliding mode surface, $eq(e_i,s)$ decreases and converges to $k{e}_i/(1+e_i)$, while the system state $e_i$ tends to 0, thereby suppressing chattering. Based on Equations (5), (13) and (14), we obtain

$$\begin{array}{l}-{\displaystyle \frac{k}{\epsilon +\left(1+\frac{1}{x_1}-\epsilon \right)e^{-\delta \left|s\right|}}}sgn(s)-ks=c_1{\dot{e}}_1+c_2{\ddot{e}}_1+{\stackrel{⃛}{x}}_{m_1}-{\stackrel{⃛}{x}}_t+w_1{\dot{e}}_s+w_2{\ddot{e}}_s=\\ c_1{\dot{e}}_1+c_2{\ddot{e}}_1+{\displaystyle \frac{1}{m_l}}\left[\begin{array}{l}-\left(A_{m_1}^2{\Delta }_1+A_{m_2}^2{\Delta }_2-{\displaystyle \frac{B_m^2}{m_l}}\right)x_{m_2}+A_{m_1}{\Delta }_1{q}_{m_1}+A_{m_2}{\Delta }_2{q}_{m_2}\\ +{\displaystyle \frac{B_m}{m_l}}\left(-A_{m_1}{x}_{m_3}+A_{m_2}{x}_{m_4}\right)+{\displaystyle \frac{B_m}{m_l}}\left(F_m+d_m(t)\right)-F_m^{\prime }\\ -d_m^{\prime }(t)-C_i\left(A_{m_1}{\Delta }_1+A_{m_2}{\Delta }_2\right)\left(x_{m_3}-x_{m_4}\right)\end{array}\right]-{\stackrel{⃛}{x}}_t+w_1{\dot{e}}_s+w_2{\ddot{e}}_s\end{array}$$

(15)

where ${\Delta }_1={\displaystyle \frac{\beta }{V_{01}+A_{m_1}{x}_{m_1}}},{\Delta }_2={\displaystyle \frac{\beta }{V_{02}-A_{m_2}{x}_{m_1}}}$.

According to Equations (7), (8) and (15), the control voltage can be obtained as

$$\left\{\begin{array}{l}{u}_{es}={\displaystyle \frac{-m_l^2\left[-eq\left(e_i,s\right)\cdot sgn(s)-k_s+C_1{\dot{e}}_1+C_2{\ddot{e}}_1-{\stackrel{⃛}{x}}_f\right]}{m_l\left({\Delta }_1{q}_{m_1}+{\Delta }_2{q}_{m_2}\right)}}\\ -{\displaystyle \frac{B_m{F}_m-m_l{\dot{F}}_m+B_m{\widehat{d}}_m(t)-m_l{\dot{\widehat{d}}}_m(t)}{m_l\left({\Delta }_1{q}_{m_1}+{\Delta }_2{q}_{m_2}\right)}}\\ u_{st}={\displaystyle \frac{\left(h_{m_1}{A}_{m_1}+h_{m_2}{A}_{m_2}-B_m^2/m_l\right)x_{m_2}}{{\Delta }_1{q}_{m_1}+{\Delta }_2{q}_{m_2}}}+\\ {\displaystyle \frac{C_i\left(A_{m_1}{\Delta }_1+A_{m_2}{\Delta }_2\right)\left(x_{m_3}-x_{m_4}\right)}{{\Delta }_1{q}_{m_1}+{\Delta }_2{q}_{m_2}}}+{\displaystyle \frac{B_m\left(A_{m_1}{x}_{m_3}-A_{m_2}{x}_{m_4}\right)}{m_l\left({\Delta }_1{q}_{m_1}+{\Delta }_2{q}_{m_2}\right)}}\end{array}\right.$$

(16)

where $u_{es}$ is the switching control voltage. In situations where nonlinear disturbances are produced by the omnidirectional leveling hydraulic system of the crawler work machine, the control mechanism can determine the corresponding parameters based on error and disturbance estimates. This aspect is closely related to the design of the sliding mode reaching rate discussed in this paper. Additionally, $u_{st}$ is state control, which is intimately associated with the condition of the hydraulic cylinder itself.

3. Results and Discussion

3.1. Simulation Analysis

The omnidirectional leveling hydraulic interconnected system model established in Figure 5 is validated, with the parameters of the hydraulic cylinders set as shown in

Table 1. Hydraulic cylinder parameter setting.

Parameters	Landscape	Portrait	Units
Hydraulic cylinder diameter	63	80	mm
Hydraulic cylinder piston rod diameter	35	45	mm
Have rod end piston area	21.55	34.36	mm2
Rodless end piston area	43.64	50.27	mm2
Kinematic viscosity of oil	180	180	mm·s−1
Bulk modulus of oil	1300	1300	MPa

.

The target displacement of the longitudinal hydraulic cylinder is set to 0.3 m and the target displacement of the lateral hydraulic cylinder is set to 0.2 m. The displacement signals of the hydraulic cylinders and the signals of the solenoid valves are obtained through AMESim simulation, as shown in Figure 9.

As shown in Figure 9, the symmetric lateral leveling hydraulic cylinders operate normally, with approximately symmetric displacement variations. Similarly, the symmetric longitudinal leveling hydraulic cylinders also operate normally, with approximately symmetric displacement variations. The solenoid valve port signals tend to symmetry, verifying the correctness of the omnidirectional leveling hydraulic interconnected system model.

To verify the effectiveness of the designed synchronization control strategy for the hydraulic interconnected leveling system, a comparative simulation analysis between the sliding mode synchronization control and PID control was conducted. The leveling performance on a 20° lateral slope and a 25° longitudinal slope was analyzed, and the comparative results are shown in Figure 10.

Figure 10a illustrates the displacement of the hydraulic cylinder pistons under two algorithms during omnidirectional leveling. The trend indicates that piston displacement increases rapidly at the start of operation and then stabilizes. Under PID control, the longitudinal leveling hydraulic cylinder piston reaches a maximum displacement of 0.052 m at 1.24 s and stabilizes at 0.0483 m at 4.46 s. The lateral piston reaches a maximum displacement of 0.04 m at 1.18 s and stabilizes at 0.0368 m at 5.23 s. In contrast, under sliding mode synchronization control, the lateral leveling hydraulic cylinder piston reaches a maximum displacement of 0.039 m at 0.78 s and stabilizes at 0.0372 m at 2.88 s. The longitudinal leveling hydraulic cylinder piston reaches a maximum displacement of 0.048 m at 0.76 s and stabilizes at 0.0468 m at 3.37 s. In summary, the stabilization time for 20° lateral leveling is reduced by 1.6 s, and the stabilization time for 25° longitudinal leveling is reduced by 1.8 s. On average, the rise time is shortened by 18.8%, and the leveling time is reduced by 35.5%. Figure 10b shows the piston velocities of the leveling hydraulic cylinders under the two algorithms during omnidirectional leveling. At the start of leveling, the cylinder velocities are relatively high. Under PID control, the lateral leveling cylinder piston velocity reaches 0.156 m/s, and the longitudinal leveling cylinder piston velocity reaches 0.163 m/s. Under sliding mode synchronization control, the lateral leveling cylinder piston velocity reaches 0.210 m/s, and the longitudinal leveling cylinder piston velocity reaches 0.255 m/s. Subsequently, the piston velocities gradually decrease and stabilize at zero when the machine body becomes level. Figure 10c presents the longitudinal inclination angle changes in the crawler work machine body under the two control algorithms. Under the PID control algorithm, overshoot is observed in both lateral and longitudinal leveling, with a lateral inclination angle overshoot of 2.9° and a longitudinal inclination angle overshoot of 3.7°. In contrast, the sliding mode control algorithm reduces the lateral inclination angle overshoot to 0.76° and the longitudinal inclination angle overshoot to 0.95°, outperforming PID control in both cases. Figure 10d depicts the synchronization error of the lateral leveling hydraulic cylinders under a sinusoidal signal of 1.3 × 10⁻³ sin(0.8 πt). The synchronization position error between the two cylinders under PID control is ±1.25 × 10⁻³ m, which is approximately twice the error under sliding mode synchronization control. The solenoid valve control signals during the simulation are shown in Figure 11.

The simulation results demonstrate that the designed leveling system for the crawler work machine achieves omnidirectional leveling and exhibits superior control performance compared to traditional PID control, validating the effectiveness and advantages of the synchronization leveling control strategy.

3.2. Performance Test

The experimental prototype weighs 728 kg, with a body height of 850 mm, a length of 1560 mm, a width of 1010 mm, and a maximum traveling speed of 15 km/h. Key components of the prototype are shown in Figure 12. The diesel engine adopts a single-cylinder, four-stroke, direct-injection combustion system with a rated speed of 3000 r/min and a rated power of 9.2 kW. The inclination sensor has a maximum range of ±30° and features an aluminum alloy casing, offering high sensitivity, strong stability, and high precision. The control system integrates the main controller of the driving system with the leveling controller and includes a remote-control module. This setup allows the leveling system to operate in either manual control mode or automatic leveling mode, which can be selected via a remote controller. In manual control mode, the hydraulic cylinder actions and the machine’s movement can be directly controlled. The developed physical prototype is shown in Figure 13.

The dynamic performance testing of the crawler work machine’s omnidirectional leveling system includes lateral dynamic performance tests, longitudinal dynamic performance tests, and omnidirectional dynamic performance tests. Figure 14a shows the lateral dynamic performance testing site for the crawler work machine’s omnidirectional leveling system. The travel speed was set to 3 km/h, and data collected during the test was analyzed to observe the changes in the machine’s body inclination angle during automatic leveling. After measuring and calculating the slope of the test terrain for the lateral dynamic performance test, the slope variation curve encountered by the crawler work machine traveling at 3 km/h is shown in Figure 15a. The changes in the body’s lateral inclination angle after leveling during the lateral test are shown in Figure 15b. It can be observed that as the machine enters the terrain, where the slope is steeper, the body’s lateral inclination angle changes significantly, reaching a maximum of 11.8°. As the slope decreases, the machine adjusts its lateral inclination in the opposite direction. Overall, the crawler work machine can maintain a stable lateral inclination angle.

Figure 14b shows the longitudinal dynamic performance testing site for the omnidirectional leveling system. The travel speed was set to 3 km/h, and data collected during the test was analyzed to observe the changes in the machine’s body inclination angle during automatic leveling. To provide more intuitive results, the slope of the test terrain for the longitudinal dynamic performance test was measured, calculated, and estimated as necessary. The slope variation curve encountered by the crawler work machine traveling at 3 km/h is shown in Figure 16a. The changes in the body’s longitudinal inclination angle after leveling during the longitudinal test are shown in Figure 16b. It can be seen that as the machine enters the terrain, where the slope variation is significant, the longitudinal inclination angle of the body changes considerably, reaching a maximum of 13.6°. As the slope increases, the crawler work machine continues to level itself, eventually maintaining a stable horizontal position.

Figure 14c shows the omnidirectional dynamic performance testing site for the omnidirectional leveling system. The travel speed was set to 3 km/h, and data collected during the test were analyzed to observe the changes in the machine’s body inclination angle during automatic leveling. The lateral and longitudinal slope variations in the terrain are shown in Figure 17a,c, respectively. The changes in the body’s lateral inclination angle after omnidirectional leveling are shown in Figure 17b, while the changes in the longitudinal inclination angle are shown in Figure 17d. From the figures, it can be seen that the body’s lateral inclination angle can be controlled within 14°, and the longitudinal inclination angle within 1.5°. Even under conditions of significant slope variations, the inclination angles can be leveled in a short time. Overall, the crawler work machine effectively improves the attitude inclination angle of the body, enhancing travel stability.

4. Conclusions

(1) This study introduces a “three-layer frame” structure for the crawler work machine and designs a hydraulic interconnection leveling circuit. Parameter calculations and component matching were conducted to achieve stationary centralized leveling, which significantly enhances the stability of the crawler work machine. The proposed design effectively addresses the challenge of maintaining machine stability during complex leveling operations in rugged terrains and provides a robust structural and hydraulic foundation for advanced control strategies. Furthermore, this structural design offers the potential for integration with a variety of agricultural machinery, such as transplanting machines and irrigation machines, establishing a versatile and adaptable chassis platform for agricultural applications.

(2) To address unmodeled dynamics in the hydraulic circuit for omnidirectional leveling, a sliding mode synchronous control method based on disturbance observation was developed. Co-simulations of the crawler work machine’s leveling system were conducted using AMESim (2021.1) and Simulink (2021b) software, providing insights into the system’s behavior during leveling operations. Experimental validation demonstrated that the proposed control method achieves more precise and efficient leveling performance compared to traditional methods. These results underline the advantages of the proposed approach in improving the stability, synchronization, and responsiveness of hydraulic control systems.

(3) Experimental testing on a crawler prototype further validated the proposed leveling methods and strategies, confirming their effectiveness in adapting to various terrain conditions. The findings provide valuable reference points for the development of chassis leveling systems, particularly for applications in hilly and mountainous terrains. The adaptability and robustness of the proposed system make it well-suited for a wide range of applications, including agricultural machinery, construction and mining vehicles, military operations on rugged terrain, and disaster response in challenging environments.

(4) Looking forward, future research will focus on improving energy efficiency, reducing emissions, and extending system lifespan to enhance performance and sustainability. The proposed hydraulic control system has significant potential for diverse applications, such as universal chassis platforms for agricultural crawlers operating on steep slopes, construction and mining vehicles in rugged terrains, and disaster response vehicles in earthquake- or landslide-prone zones. By addressing these scenarios, the system can evolve into a more energy-efficient, adaptable, and versatile solution for agricultural, industrial, and emergency use.