# A Method for Electric Tractor Molding Based on Terminal Sliding Mode Control Algorithm

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. State Equation of the Electric Tractor

#### 2.1. Modular Model

#### 2.1.1. Motor Model

^{2}) for the motor output shaft.

#### 2.1.2. Battery Model

#### 2.1.3. Drive Train Model

^{2}) on the drive shaft, ${T}_{ext}$ is the resistance torque (N·m) when the tractor runs, ${\varpi}_{v}$ is the drive wheel speed (rad/s), and ${b}_{\mathrm{v}}$ is the wind speed coefficient.

#### 2.1.4. Drive Wheel Model

_{q}is the traction force, C

_{n}= CIbd/W, W is wheel load (N), CI is the firmness of the soil, b is tire width, d is tire diameter, and s is the slip rate.

_{out}is the output shaft torque, r is the radius of the driving wheel, T

_{ext}= r × W.

#### 2.2. Full Vehicle Model

## 3. Terminal Sliding Mode Controller

#### 3.1. Design of the Terminal Sliding Modulus

_{1}C

_{2}], Q(t) = CP(t)

_{1}C

_{2}] = [4 1].

#### 3.2. Terminal Sliding Mode Controller Design

## 4. Simulation and Experiment

#### 4.1. Simulation

_{t}= 25; C

_{t}= 6; K

_{T}= 1.4; I

_{v}= 0.006 kg·m

^{2}; I

_{e}= 0.005 kg·m

^{2}; I

_{s}= 0.004 kg·m

^{2}; η

_{e}= 0.95; B = 0.0008 N·m·s/rad; L = 8.5e − 3H; R = 2.875 Ω; and T

_{ext}= 3500 N·m.

- (1)
- Make the system’s position instruction relative rotation ${x}_{11d}=\mathrm{sin}(\pi t/2)$, drive wheel angular speed ${x}_{21d}=\mathrm{cos}\pi t$, and motor angular speed ${x}_{31d}=\mathrm{sin}\pi t$. Continuous functions are used to reduce chattering. ${\delta}_{0}=0.03$ and ${\delta}_{1}=5$. The simulation results are shown in Figure 4.

- (2)
- Make the system’s position instruction relative rotation ${x}_{11d}=1$, drive wheel angular speed ${x}_{21d}=0.5\mathrm{cos}\pi t$, and motor angular speed ${x}_{31d}=t$. Continuous functions are used to reduce chattering. ${\delta}_{0}=0.03$ and ${\delta}_{1}=5$. The simulation results are shown in Figure 5.

- (3)
- Simulate the actual situation in the field and compare the sliding mode variable algorithm with the PID algorithm. Set the brushless DC motor start as T
_{out}= 0 N·m and the motor speed = 1000 rad/min. When t = 0.6 s, sudden load torque T_{out}= 8 N·m. Figure 6 shows the motor torque simulation diagram, and Figure 7 shows the motor speed simulation diagram. The PID overshoot is large, the fluctuations are severe, and the terminal is accurately adjusted.

#### 4.2. Test Analysis

## 5. Conclusions

- (1)
- Based on the correlation parameters among modules, using the relative angle of the transmission output shaft, driving wheel velocity, mechanical angular velocity of motor as intermediate variables, we obtained the driving wheel velocity and mechanical angular velocity of motor for the output of three input and two output state equation;
- (2)
- Aiming at the vehicle speed, the sliding mode surface is designed using ”linear + nonlinear” features, and the adaptive terminal sliding mode variable control function is designed, so as to realize the control ability of adaptive online adjustment;
- (3)
- The simulation and test results show that, compared with the PID algorithm, the adaptive terminal sliding mode variable algorithm can quickly eliminate the voltage deviation, and achieve a fast response speed and short overshoot time. The tracking error on the sliding mode plane can converge to zero in a limited time. The control accuracy is better, and it has good robustness.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Diagram of an electric tractor. Note: 1—electronic commutation switch circuit, 2—sensor rotor, 3—main rotor, 4—main stator, and 5—sensor stator.

**Figure 5.**Output of the system state control function simulation. (

**a**) Drive wheel angular speed. (

**b**) ϖv controller output curve. (

**c**) Motor angular speed. (

**d**) ϖe controller output curve.

**Figure 9.**System sliding modulation algorithm under the control of an abrupt load curve. (

**a**) Motor speed and current. (

**b**) Drive wheel speed and torque.

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**MDPI and ACS Style**

Yin, S.; Mao, P.; Li, W.
A Method for Electric Tractor Molding Based on Terminal Sliding Mode Control Algorithm. *World Electr. Veh. J.* **2023**, *14*, 93.
https://doi.org/10.3390/wevj14040093

**AMA Style**

Yin S, Mao P, Li W.
A Method for Electric Tractor Molding Based on Terminal Sliding Mode Control Algorithm. *World Electric Vehicle Journal*. 2023; 14(4):93.
https://doi.org/10.3390/wevj14040093

**Chicago/Turabian Style**

Yin, Shanshan, Pengjun Mao, and Wenjun Li.
2023. "A Method for Electric Tractor Molding Based on Terminal Sliding Mode Control Algorithm" *World Electric Vehicle Journal* 14, no. 4: 93.
https://doi.org/10.3390/wevj14040093