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Body Leveling Control Model Establishment and Experiment Analysis
Zhongshan Wang1, Wenxing Ma1, Tongjian Wang1,*, Chunbao Liu1
Published in Applied Engineering in Agriculture 38(2): 243-251 (doi: 10.13031/aea.14501). Copyright 2022 American Society of Agricultural and Biological Engineers.
1 School of Mechanical and Aerospace Engineering, Jilin University, Changchun, China.
* Correspondence: wangtj@jlu.edu.cn
The authors have paid for open access for this article. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License https://creative commons.org/licenses/by-nc-nd/4.0/
Submitted for review on 25 January 2021 as manuscript number ITSC 14501; approved for publication as a Research Article and as part of the Computer Modeling and Statistics for Agriculture Collection by the Information Technology, Sensors, & Control Systems Community of ASABE on 7 January 2022.
Highlights
Abstract. The body leveling control system is the core part of the attitude control of the hilly mountain tractor. It calculates the body posture in real-time according to the body leveling control model and makes corresponding control strategies. The accuracy of the control model directly affects the vehicle leveling accuracy. This article proposes the leveling control model based on tire stiffness and tire mass displacement. The slope road surface excitation information is collected in the field, and the road surface excitation data is processed appropriately. The accurate road surface excitation information is obtained. The input of the simulation model is displacement data. However, the collected road excitation information is the acceleration signal. Thus, the acceleration signal is converted to the displacement signal through the frequency domain integration method. The comparison between the calculated calculation results and the experimentally acquired attitude data indicates that the average pitch angle error is 7.94%, and the average tilt angle error is 4.37%. Accordingly, the vehicle body leveling control model established in this article is compatible with the experimental results and can accurately output the body posture and develop the body tone.
Health monitoring and diagnostic of agriculture vehicles have been considered in the literature (Gupta et al., 2020a, 2020b, 2021). With the continuous improvement of agricultural mechanization levels in mountainous areas of China, the demand for research and development of agricultural machinery suitable for hilly and mountainous areas becomes more and more urgent. Complicated terrain and narrow roads in Hilly and mountainous areas lead to problems such as difficulty, poor quality and easy to topple, which not only affect agricultural production in Hilly areas, but also threaten the personal safety of drivers. In China’s current agricultural machinery market, only a few micro-machines have the leveling function, but due to its size limitation, it still needs more human resources when it is applied to agricultural production, and the production efficiency is low. Therefore, developing a hilly mountain tractor that can automatically level the body is of great significance for improving the agricultural production efficiency in China’s hilly areas (Ding and Xu, 2010).
The automobile body leveling control is mainly realized through mechanical, hydraulic, electronic, and automatic control technologies. When the car body tilts, the sensor can calculate the current body posture by detecting the change of the body tilt angle. The automatic control system can calculate the adjustment amount according to the body posture and control the actuator to level the body (Tan et al., 2005; Wang et al., 2014; Xu et al., 2017). John Deere’s combine harvester (Moline, Ill.) employs an electro-hydraulic automatic leveling system to achieve vehicle body leveling through an appropriate switching of the oil supply circuit (Zhang, 2009). The East 525EX rice combine harvester developed by China Yituo Group Co. Ltd. (Luoyang, China) is equipped with a horizontal control device on the car body, and the car body leveling is realized by the automatic adjustment of the left and right rollers (Irsel and Altinbalik, 2018).
The leveling control system is the core part of the body leveling control, and the accuracy of the control model directly affects the vehicle leveling accuracy (Xia and Cai, 2003; Zhao et al., 2017; Sun et al., 2018; Liu et al., 2018). A fuzzy sliding mode control approach was adopted in Sun et al. (2018) for accurate control of the vehicle height and leveling adjustment system of an electronic air suspension. In Kim and Lee (2011), a sliding mode controller was designed for height and leveling control of an automotive air suspension system. An attitude adjustment device based on a parallel four-bar mechanism was constructed to solve the problems of difficult leveling and poor stability of hill crawler tractors (Sun et al., 2020). In Wang and Xia (2019), a vehicle body attitude adjustment system was established based on a backstepping control algorithm for automatic leveling of the whole vehicle hydro-pneumatic suspension system. A novel model-based control method with slip compensation was presented in Jing et al. (2021) for path tracking control of a global navigation satellite system (GNSS) based tractor-scraper land leveling system.
In this article, the auto-leveling system of auto-body is taken as the research object, and the control model of auto-body leveling is established based on tire stiffness and wheel centroid displacement. A mathematical model based on tire stiffness and wheel centroid displacement is proposed for different sizes of wheels of the front and rear axles in the model. The road surface information data is input into the mathematical model. The calculated simulation results are consistent with the body posture data collected by the road surface experiment. The average pitch angle error is 7.94%, while the average tilt angle error is 4.37%. Compared with the studies performed in the literature, the current study proposes a six-degree-of-freedom motion model for the body leveling control. The model’s validity is demonstrated through the experimental results (not only through physical principles). Moreover, the proposed model directly employs the acceleration signals obtained from the experiment without using any additional sensors. The main contributions of this article are given as follows:
- A six-degree-of-freedom motion model is established for the whole vehicle, compatible with the experimental attitude data. The obtained pitch and tilt angle errors are acceptable.
- Since the simulation model requires the displacement data, the acceleration signal obtained from the acceleration sensor is converted to a displacement signal through the integral property of the Fourier transform. Thus, the displacement sensor is not required in the experiment.
This article is organized as follows. Section 2 describes the body leveling control structure. The mathematical model is introduced in Section 3. Pavement information collection and processing through a frequency-domain approach are described in Section 4. Section 5 introduces the established SIMULINK model and compares the simulation results with the experiments. Finally, Section 6 gives the conclusions and future aspects.
Body Leveling Control Structure
The body leveling control mechanism and body leveling hydraulic system are described in this current section.
Body Leveling Control Mechanism
The sketch of the body leveling mechanism of the hilly tractor and three-dimensional model is shown in figure 1. The leveling is realized by the leveling cylinder installed on the driving axle of the vehicle. The leveling cylinder is rigidly connected with the steering assembly and the driving axle housing (Wang et al., 2014). When the body is tilted, the leveling control system makes a control decision according to the calculated body posture, drives the leveling cylinder to move to the corresponding stroke, and realizes the automatic leveling of the body.
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| Figure 1. Body leveling control mechanism. (1) Axle shell; (2) leveling hydraulic cylinder; (3) steering assembly; (4) wheel reducer; (5) tires. |
Body Leveling Hydraulic System
The body leveling hydraulic system is shown in figure 2, and hydraulic system parameters are shown in table 1. The system is an electro-hydraulic proportional hydraulic system, which consists of leveling cylinder, proportional solenoid valve, high-pressure oil filter, one-way valve, oil pump, oil return filter, electromagnetic relief valve, and other components. The proportional solenoid valve controls the leveling cylinder to generate displacement according to the control signal and level the body (Sun and Chen, 2004; Gao et al., 2005; Liu, 2018).
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| Figure 2. Body leveling hydraulic system. (1) Leveling oil cylinder; (2) proportional solenoid valve; (3) high pressure oil filter; (4) one-way valve; (5) oil pump; (6) oil return filter; (7) electromagnetic relief valve. |
| Table 1. Hydraulic system parameters. | |
| Parameter | Value |
| Front axle hydraulic cylinder stroke | 286 mm |
| Rear axle hydraulic cylinder line | 281 mm |
| Pump | 14.6 mL/r 2000 r/min |
| Minimum body quality | 1260 kg |
| Mass distribution ratio (front/rear axis) | 4:6 |
| Piston diameter | 63 mm |
| Cylinder diameter | 50 mm |
| Oil density | 880 kg/m3 (40°) |
| Electro-hydraulic proportional reversing valve | 25 MPa 43 L/min |
| Maximum system pressure | 16 MPa |
Mathematical Model
Because the driving form of the hilly tractor is a combination of the front drive axle and rear axle box, and the wheels are rigidly connected with the driving axle, the road excitation is transmitted directly to the driving axle through the wheels, and the displacement of the center of mass of the wheels is the road excitation to the body. The front and rear axle wheels of the tractor are different in size, and the parameters such as stiffness and quality are different. The road surface excitation needs to pass through the wheels with different stiffness and weight. The influence of tire stiffness and wheel weight on the model accuracy must be considered in establishing the leveling control model.
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| Figure 3. Body leveling system mode. |
The six-degree-of-freedom motion model of the whole vehicle is shown in figure 3, m is the mass on the whole wheel, z is the displacement of the center of mass of the whole vehicle, f is the body tilt angle, ? is the body pitch angle, a is the distance between the body center of mass and the front wheel, b is the distance between the body center of mass and the rear wheel, c is the distance between the body center of mass and the right wheel, d is the distance between the body center of mass and the left wheel. Z'1, Z'2, Z'3, and Z'4 are the displacements of the vehicle body on each wheel, C1, C2, C3, and C4 are the displacements of each leveling cylinder, m1, m2, m3, and m4 are the masses of each wheel, Z1, Z2, Z3, and Z4 are the center of mass displacements of each tire, k1, k2, k3, and k4 are the stiffness of each wheel, q1, q2, q3, and q4 are the road surface excitation that each wheel receives, and Fr1, Fr2, Fr3, and Fr4 are the forces that each wheel leveling cylinder receives. The dynamics equations of the six-degree-of-freedom motion model are:
- Vehicle dynamics equation
(1)
- Vehicle pitching motion equation
(2)
- Vehicle tilt motion equation
(3)
- Tire centroid motion equation
(4)
where Ft1 is the force applied on each tire.
The body moves at the inclination angle f and the body elevation angle ?. According to the motion law of rigid body, the displacement of the body at all corners of the body can be obtained as:
- Motion equation of vehicle centroid
(5)
Pavement Information Collection and Processing
This section illustrates the practical points in pavement information collection. Moreover, a frequency-domain processing technique is applied to the collected data to transform the acceleration signal into the displacement signal.
Collection of Road Excitation Information
In order to verify the accuracy of the model, it is necessary to apply accurate road excitation information into the model and observe the output results. The accuracy of road excitation signal acquisition affects the accuracy of the results. It is necessary to select the appropriate sampling frequency and data processing method to collect the road surface excitation information. According to Shannon's sampling theorem, when the sampling frequency Fsmax is twice as high as the highest frequency Fmax in the process of converting analog signal to digital signal; that is, when Fsmax >2*fmax, the digital signal after sampling can completely retain the information in the original signal, and generally takes 2~4 times the maximum frequency of the signal. GB 7031-86 stipulates that the pavement wavelength range is from 0.1 to 100 m. It can be seen that when the average test speed of the tractor is 2 km/h, the maximum frequency of road excitation is 5.5 Hz, and the acquisition frequency is set at 20 Hz (Chen et al., 2013).
Acceleration sensors are the AKE392B accelerometer and DCA100T inclination sensor. Acceleration sensors are installed on the four-wheel axle head of the acquisition vehicle, while inclination sensors are installed in the body center. The installation position and acquisition equipment are shown in figure 4. The acceleration sensor collects the road surface excitation data as the excitation input of the vehicle body leveling control model. The inclination sensor collects the body posture data to compare with the model output body posture to verify the model’s accuracy. The road surface was collected as a hard soil road in the mountainous area. The collection time was 80s, and the sampling was repeated three times at a speed of 2 km/h. The road surface and experimental process are shown in figure 5.
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| Figure 4. Sensor mounting position and signal acquisition device. (a) Installation position of accelerometer on the right side; (b) installation position of accelerometer on the left side; (c) installation position of inclination sensor; (d) industrial computer for acquisition. |
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| Figure 5. Road surface spectrum and experimental process. (a) Pavement spectrum acquisition of hard soil pavement; (b) pavement spectrum acquisition of experimental photographs. |
Processing of Pavement Incentive Information
The road excitation information collected in this study is acceleration signal, and the road excitation input by the simulation system is displacement data. Thus, the collected data need to be processed. The acceleration signal is transformed into a displacement excitation signal. The acceleration signal is the displacement signal after two integrations. In time-domain integration, every integration needs a de-trend operation due to the existence of constants. De-trend will lead to the loss of signal energy and signal drift. Therefore, the final result is often not accurate. This article employs the frequency domain integration method to solve this problem.
First of all, Fourier transform is needed for signal integration in the frequency domain. The integral operation is transformed into division operation by the integral operation property of Fourier transform. Then, the inverse Fourier transform is applied, and the real part is taken to obtain the displacement signal (Zhang and Wu, 2011). The details are given as follows
Integral property of Fourier Transform is represented as:
(6)
Then for the acceleration signal a, the Fourier transform is given by 
, the relationship of one integral in the frequency domain is 
, after two integrations, the road excitation can be obtained as:
(7)
where
(8)
where fd and fu are the lower and the upper cut-off frequencies, respectively. X(k) is the Fourier transform of x(n) and ?f is the frequency resolution (Baecker et al., 2015; Kanarachos and Kanarachos, 2015; Bäcker et al., 2016; Sun et al., 2016; Wang et al., 2016, 2018; Chen and Zhou, 2018; Winkler et al., 2018).
Simulation Analysis and Comparison of Experimental Data
This section presents the simulation model established in the SIMULINK and compares the simulations results with the experimental data.
Establishment of SIMULINK Simulation Model
The SimScape tool module in the Simulink simulation system can model and simulate many different types of physical systems. At present, it has been widely utilized in the simulation of automobiles, agricultural machinery, engineering machinery, and other fields and can realize hybrid modeling and simulation of multiple physical systems.
Since the front and rear wheels have different sizes, their weight and stiffness are also different. The main physical parameters of tractors are shown in table 2. The simulation model, including a single wheel subsystem and the vehicle model, are shown in figure 6. Each tire model is packaged as a subsystem, and the subsystem is integrated into the calculation of the vehicle posture according to the motion equation. In the vehicle model, f is the oblique angle, and ? is the pitch angle.
| Table 2. Tractor parameters. | |
| Parameter | Value |
| Wheelbase | 1644 mm |
| Wheel spacing (front/rear wheels) | 1000/1050 mm |
| Minimum ground clearance | 300 mm |
| Minimum quality of use | 1600 kg |
| Quality distribution ratio of front and rear axles (front/rear) | 4:6 |
| Tyre model (front/rear) | 6.00-16/9.50-24 |
Comparison of Simulation Results with the Experimental Data
The pavement information data after data processing and the related parameters of the hilly tractor are input into the mathematical model for simulation. The data of wheel displacement obtained from data processing are employed as the input of pavement excitation. The road surface excitations q1, q2, q3, and q4 obtained after data processing are shown in figure 7.
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| (A) Single wheel subsystem |
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| (B) Vehicle model |
| Figure 6. Simulation model. |
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| Figure 7. Road excitation. (A) left front wheel road excitation; (B) left rear wheel road excitation; (C) right front wheel road excitation; (D) right rear wheel road excitation |
The body pitch angle obtained with simulations is compared with that obtained through the experiment (see fig. 8). The change rule of the body pitch angle curve obtained by simulation analysis is the same as the road surface information collected. As shown in figure 8, the maximum pitch angle error is obtained in 12 to 15 s, 50 to 55 s, and 67 to 75 s. the maximum error is 3.799°, and the average error is 0.3293°.
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| Figure 8. Comparison of pitch angle simulation and experiment. |
The body tilt angle obtained through simulations is compared with that obtained by the experiment (see fig. 9). As shown in figure 9, the variation of the body tilt angle curve obtained by simulation analysis and the body tilt angle curve collected by the road information collection experiment is the same, but the simulation result is slightly larger than the test results within the interval 65 to 70 s. The maximum error is 4.534°, and the average error is 0.3677°.
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| Figure 9. Comparison of tilt angle simulation and experiment. |
The comparative analysis of the experimental results indicates that the tilt sensor is disturbed in the data acquisition process, resulting in more burrs in the body roll and pitch data maps. Overall, the simulation analysis results are consistent with the experimental data. The simulation model can effectively express the attitude of the tractor in the case of road surface excitation.
Conclusions
In this article, by establishing the vehicle body leveling control model and collecting the road excitation information, the body posture calculated by the leveling control model is compared with the collected body posture information. The following conclusions can be drawn:
- The vehicle body leveling control model based on tire stiffness and wheel centroid displacement is established in this article, and the simulation analysis is performed according to the actual road surface information data. The results show that the vehicle body attitude information obtained by the model is consistent with the vehicle body attitude information obtained from the road surface information collection experiment. The average pitch angle error is 7.94%, and the tilt angle average error is 4.37%, which indicates the accuracy and application of the model Six.
- In this article, the frequency domain integration method based on Fourier transform is utilized to process the road excitation signal, which avoids the error caused by the time-domain integration. Accordingly, more accurate road surface excitation data is obtained for the simulation analysis of the vehicle body leveling control model.
Although this article proposes a body leveling control model, designing an advanced controller in a closed-loop form is advised as a future research topic. In this regard, various control strategies can be employed, such as robust and adaptive control strategies to compensate for the uncertainties in the model parameters like the mass and stiffness of each wheel and the measurement noise induced by the sensors. The body leveling control algorithm developed based on this model can be applied to the automatic leveling control of hilly tractors and cars.
Acknowledgements
The authors would like to acknowledge financial support of the National Key Research and Development Program of China: 2016YFD0700403 by the Ministry of Science and Technology, China.
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