# Leveling Control of Hillside Tractor Body Based on Fuzzy Sliding Mode Variable Structure
## 2 Leveling System Design and Control Strategy  
### Leveling System Design  
Here, we explain the designed hillside tractor body four-point leveling system to clarify our method, process, and control system results.  
The tractor motion model subjected to a non-horizontal road surface is established as shown in Figure 1a. In this figure, the body wheelspan is \(a\), the body wheelbase is \(b\), \(\lambda\), \(\mu\) are the distance coefficients from the center of mass to the origin of the coordinate system, the horizontal plane coordinate system of the body in the initial position is \(O\)-\(X_{0}Y_{0}Z_{0}\), the coordinate system of the body in the non-horizontal position becomes \(O\)-\(XYZ\), the rotation angle of the coordinate axis \(X\) is \(\alpha\), and the rotation angle of the coordinate axis \(Y\) is \(\beta\).  
For the non-horizontal state, the functional relationship between the force \(F\) of the rodless cavity of each hydraulic cylinder and the load gravity \(G\) is,  
\[A\cdot F^{T}=B, \tag{1}\]  
where,  
\[A=\begin{bmatrix}1&1&1&1\\ \%&\%&\%&\%&\%\\ \%&\%&\%&\%&\%\\ l_{1}&-l_{2}&l_{3}&-l_{4}\end{bmatrix},F=\begin{bmatrix}F_{1}&F_{2}&F_{3}&F_{4} \end{bmatrix}^{T},B=\begin{bmatrix}G\\ \lambda a\cdot G\\ \mu b\cdot G\\ 0\end{bmatrix}.\]  
Because the initial state of the leveling hydraulic cylinder is the complete recovery state of the cylinder rod, the highest level of the body support point is the target point after excitation from the hilly slope road surface. After analysis and calculation, the displacement of each support point of the tractor is obtained.  
\[\left\{\begin{array}{l}l_{1}=b\cdot\sin\beta\cos\alpha\\ l_{2}=a\sin\alpha+b\sin\beta\cos\alpha\\ l_{3}=a\sin\alpha\\ l_{4}=0\end{array}\right. \tag{2}\]  
Figure 1b shows the working principle of the rear axle. The structure of the front axle is altered so that it has a kingpin tilting angle of \(3^{\circ}\) relative to the rear axle to obtain a front axle hydraulic cylinder stroke 5 mm larger than that of the rear axle hydraulic cylinder; otherwise, the leveling principle is the same for both.  
Figure 1c shows the leveling hydraulic system, which supplies oil through a gear oil pump and stabilizes pressure through a relief valve. By changing the working state of the electromagnetic proportional valve, the corresponding leveling hydraulic cylinder can be extended or retracted [11; 12; 13]. When the tractor encounters a transverse slope during operation, the rodless cavity of the hydraulic cylinder on the lower side of the drive axle begins to charge, causing the hydraulic rod to stretch out to raise the lower side of the tractor and return the posture of the body to a horizontal state to ensure the safety and comfort of the ride.  
Figure 1: Principle, structure and hydraulic system of leveling drive axle: (**a**) The motion model on non-horizontal road surface; (**b**) Three-dimensional structure; and (**c**) Hydraulic system. 1 central transmission assembly; 2 leveling cylinder assembly; 3 steering knuckle assembly; 4 wheel transmission assembly; 5 tire; 6 steering rod; 7 guide pillar; 8 overflow valve; 9 pressure measuring joint; 10 pressure gauge; 11 gear oil pump; 12 hydraulic air filter; 13 liquid level thermometer; 14 oil suction filter; 15 oil tank; 16 electromagnetic proportional directional valve; 17 hydraulic operated check valve; 18 leveling cylinder.