In order to improve the electrical conversion efficiency of an electric tractor motor, a load torque based control strategy (LTCS) is designed in this paper by using a particle swarm optimization algorithm (PSO). By mathematically modeling electricmechanical performance and theoretical energy waste of the electric motor, as well as the transmission characteristics of the drivetrain, the objective function, control relationship, and analytical platform are established. Torque and rotation speed of the motor’s output shaft are defined as manipulated variables. LTCS searches the working points corresponding to the best energy conversion efficiency via PSO to control the running status of the electric motor and uses logic and fuzzy rules to fit the search initialization for load torque fluctuation. After using different plowing forces to imitate all the common tillage forces, the simulation of traction experiment is conducted, which proves that LTCS can make the tractor use electrical power efficiently and maintain agricultural applicability on farmland conditions. It provides a novel method of fabricating a more efficient electric motor used in the traction of an offroad vehicle.
A potential development trend of farming power is that sustainable energies, such as electricity and biodiesel, will gradually and eventually replace the nonrenewable fossil fuels. An electric tractor is one of the transformation directions. Carlini et al. presented a series hybrid electric powertrain for a small crawler tractor used for logging in forests. It reached a 30% increase in fuel economy and better ecological features in comparison with the traditional tractor [
Related studies have been performed for improving the energy conversion economy of electric vehicles. By analyzing five types of control strategies used in highpower vehicles, Garcia et al. proved that the equivalent fuel consumption minimization strategy had better applicability [
This paper begins with establishing the mathematical model that describes the electricmechanical performance and theoretical energy consumption of the electric motor, as well as the transmission characteristics of the electric tractor. Then, it introduces the design of LTCS and how it can control the electric motor to maintain high energy conversion efficiency. Finally, simulation of the traction experiment is conducted to verify the effect and agricultural applicability of LTCS.
Although the electric tractor shares many common structural features with the common electric vehicle, there are some significant differences between the two drivetrains. Particularly, the electric vehicle layout is organized as shown in Figure
Scheme of an electric tractor’s drivetrain.
According to the previous research, the EM is a brushless direct current motor (BLDC) [
After equivalent transformation, the electromechanical characteristics of BLDC can be described by the following equations [
The electromagnetic torque of BLDC,
Depending on (
When BLDC is working on traction, the electromagnetic torque of the motor can also be described by
Based on the Laplace transform of (
Consequently, the steady state characteristic can be established:
According to (
When the EM is running, electric power loss contains copper loss, icon loss, mechanical loss, and constant power used for driving the MC.
Copper loss,
According to (
The copper loss coefficient,
Icon loss power,
In the BLDC,
The mechanical loss
The mechanical power output and total power input of the electric motor can be described by the following equations:
According to (
According to (
When the electric tractor works in the farm, the torque output of the EM distributes to the driving wheel and PTO and overcomes the driving and working resistance, respectively. The torque coupling relationship between the electric motor shaft, driving wheel, and PTO can be obtained by applying the following equations:
When the tractor plows, the force balance of the drivetrain can be described by the following equations:
Driving speed and tractive force can be described as follows:
According to (
In comparison with classical optimization methods, PSO is an efficient rangesearching algorithm. By selecting the search threshold, the population behavior can be restricted to only running under working conditions and practical requirements. It is a helpful advantage to ensure that the control parameters produced by PSO conform to the speed and torque requirement of farming. Moreover, PSO can deal with nonsmooth, noncontinuous, and nondifferentiable functions simply with objective function information. Compared with other intelligence algorithms such as the Genetic Algorithm, there is one simple operator: velocity calculation in the PSO. Using the simpler algorithm means shorter computing time, less memory, and improved robustness [
By means of simulating bird flock preying behavior, particle swarm optimization used widely in the engineering field has the advantage of high robustness and low complexity [
The 1804 series hybrid electric tractor was selected as the study object of this paper in a project designed by taking the YTO1804 as a prototype [
Speedtraction force performance curve of the 1804 series hybrid electric tractor.
When an 1804 hybrid works under heavy load gear or moderate load gear, the relationship between the driving speed and the traction force could be described by
When the tractor works under the light load gear or transport gear, the relationship can be described by the following equation:
Since the 1804 hybrid always tills with a stable speed and main farm works are done by using heavy, moderate, and light load gear, meeting the requirement of the traction force is more important than meeting the requirement of the speed. Additionally, the control result can match the change of traction force well, and
Control function of the LTCS in the vehicle is shown in Figure
Schematic representation of the control function for the electric drivetrain.
When the position sensor measures the depth of AP, load torque can be calculated by
During every sampling time, the internal task actions of LTCS are built in Figure
Schematic description of internal task actions within the LTCS.
The best working point (
After every initialization signal, the search process runs only once. Via (
In every sampling step, the initialization signals sent by the time trigger and load torque controller are synchronous and mutually independent. When the initialization is triggered, the search process and following control process occurred immediately.
Using the sampling step as the period, the time trigger periodically sends the initialization signal. It is used to deal with the accumulation of smaller AP position changes, which cannot trigger the initialization signal of the load torque controller during every period.
In every period, the initialization can also be controlled by the torque controller, which judges the load torque changing status. If the load change that occurred during this period is large enough, the PSO searching is initialized immediately.
The load change degree is judged by the gearshift and footplate positions, which can be measured by the gear sensor and the AP position sensor.
Shifting gears is an operation greatly affected by the subjective intention of the driver. In other words, when the tractor meets visible topographic changes or the working type changes, where the load torque will likely experience a significant change, the driver usually shifts the gear. Logical algorithms are used to process the signal of the gearshift position. If the driver shifts the gear (which means the load torque condition change is large enough), the controller sends the initialization signal.
Under any gear, the driver can estimate the load force situation by viewing the tachometer reading. When the AP position is stable, changing the tachometer reading means that the force balance on the EM shaft has been broken. The driver should adjust the AP depth based on the change trend in the tachometer reading until the tractor speed is similar to what it was previously. A fuzzy controller is designed to deal with the AP signal, inferring the change degree of working condition and providing the initialization signal.
Wang et al. discussed the fuzzy rules that reflect the relationship between diver intention and AP operation [
Fuzzy rules to infer initialization.
Deeping rate  Footplate depth  

S  M  B  
−B  INIT  INIT  INIT 
−M  HOLD  INIT  INIT 
S  HOLD  HOLD  HOLD 
+M  HOLD  INIT  INIT 
+B  INIT  INIT  INIT 
The membership functions that belong to the footplate depth, the footplate deepening rate, and the collection mode are described by Figures
Membership functions of the footplate depth.
Membership functions of the footplate deepening rate.
Membership functions of the collection mode.
In the case of the footplate depth, it has three chosen membership functions: S, small depth; M, moderate depth; and B, big depth. They cover the full range of footplate depth. When the AP controls BLDC, its control function is equivalent to the voltage control process of the potentiometer. For the torque control of BLDC, the torque controlled by AP is normally proportional to the expected electric current, so the footplate depth membership functions are equally distributed. To transform the real domain into fuzzy domain scope
In the case of the footplate deepening rate, five membership functions are considered: S, small change rate; +M, moderate deepening rate; −M, moderate returning rate; +B, big deepening rate; and −B, big returning rate. When the tractor speed increases with an unchanged AP position, which means the load torque reduces, the driver may return the pedal until the speed changes back and vice versa. Thus, the formulation of footplate deepening rate membership functions should contain this case. The quantization factor of footplate deepening rate,
Depending on the test of McGehee et al. [
Regarding the output variables, the collection mode contains two membership functions: INIT, the initialization of LTCS, and HOLD, nothing else changing in the load torque control process. Because the opposition between initialization and hold operations is definite and complete, their fuzzy domains are complementary.
Surface of the fuzzy rules can be viewed in Figure
Fuzzy surface.
The simulation of the traction experiment is designed as a backward type. Working conditions, which act as the input of the simulation model, are required to contain all the common working resistances of the 1804 hybrid tractor. According to the common soil conditions of the Northeast China region, the rolling resistance coefficient,
Plowing parameters.
Number 




0  7  35  30 
1  6  35  30 
2  5  32  25 
3  4  35  25 
4  4  40  31 
5  3  30  20 
6  3  35  22 
7  1  50  20 
The working condition in the simulation can be described by Figure
Tractive force of the simulation. Note: numbering 0–7 corresponds to the numbers of plowing parameters in Table
According to our previous research [
Simulative parameters of the electric drivetrain.
Part  Parameter name  Value and unit 

Vehicle  Overall length  5.2 m 
Overall width  2.69 m  
Overall height  2.97 m  

2.85 m  

1.6 m  

112.64 kN  

0.9 m  

1.97 m  


GT  Heavy load gear ratio  5.38 
Moderate load gear ratio  3.88  
Light load gear ratio  2.63  
Transport gear ratio  1.65  

96.04%  


EM  Voltage rating  380 V 
Peak voltage  540 V  
Torque rating  4138 N·m  
Rotate speed rating  300 r/min  
Reduction ratio  23  

130 kW  

0.04 Ω  

0.0001 kg·m^{2}  

0.0368 N·m·min/r  

0.15 kW/N^{2}·m^{2}  

0.1 kW·min/r  

1.2 


0.0543 V·min/r  

0.5186 N·m/A  

0.21 kW  


MD 

3.2 

98%  


AP 

54° 

0.15 
Based on mass experimental data, Zhou et al. presented the theoretical models used to predict theoretical tractive performance of a wheeled tractor [
In (
Slip efficiency in the simulation.
In the simulation of plowing, the clutch between GT and PTO is separated. Therefore, the mechanical loss of the agricultural implement (AI) is irrelevant. The rest of the parameters of efficiency are calculated as
Accordingly, the transmission efficiency,
Based on (
In the simulation, the tractor working system is simplified as a longitudinal model, which tills in a straight line, and all the side forces can be disregarded. A driver response time to the peak force is set as 0.1 s. It is assumed that the driver can accurately adjust the AP depth in accordance with the load force change. The sampling step length is 5 s. The load force fluctuation owed to the AI and gear switching is ignored.
In the simulation, the PSO searching process runs on the platform developed by Birge [
The determination of maximum velocity
In this case, the searching space of PSO is 2dimensional and the objective function, (
As stated earlier, the PSO is searching for the best working point in constraint
In every control step, the value of
Shi and Eberhart advised that probably the most common population sizes of PSO are from 20 to 50 [
Figure
PSO searching on the heavy load situation.
Figure
PSO searching on the light load situation.
The control single of the load torque controller in the simulation is expressed by Figure
Output of load torque controller in the simulation.
Figure
The electrical characteristic controlled in the simulation.
The load torque followed control method (LTFC) is used popularly in the BLDC control of the electric tractor. According to the excepted torque, LTFC controls the mechanical output of the EM by adjusting the phase current [
Figure
Working points distribution of the high load gear.
By comparing the heavy load control performance of LTCS and LTFC in Figure
Figure
Working points distribution of moderate load gear.
Figure
Working points distribution of light load gear.
By contrast, the speeds of all of the working points controlled by LTFC are higher than the speed range of sowing, harrowing, and stubble chopping. This is because when the tractor is working with AI, the rotate speed of PTO is commonly changeless. In the 1804 series hybrid electric tractor, the rotate speed is 1000 r/min or 540 r/min. When the tractor speed exceeds the speed scope of its farming type, the farming quality may be decreased (e.g., for the sowing, a faster tractor speed means longer seed spacing, which will reduce the seeding rate and consequently decrease the crop production). Therefore, LTFC is not suitable for the light working conditions of electric tractor.
Figure
Working points distribution of transport gear.
In the design of LTCS, load torque is used as the independent variable of target function, and the enclosure space based on load torque is the only constraint of the PSO search. Consequently, the speed changes dependent on the status of the load force, and that is why the speed cannot be adjusted independently and intentionally.
Simulation results of energy conversion efficiency are depicted in Figure
The comparison of energy conversion efficiency under the control of LTCS and LTFC.
Figure
The comparison of ES power consumption under the control of LTCS and LTFC.
In summary, when LTCS is used for working the farm, the electric tractor possesses superior agricultural adaptation and an obvious energysaving effect. In offroad conditions, the electric tractor can also be engaged in some transport operations where speed performance is not required. In the future, when the LTCS is used in a realistic environment, the following is recommended:
The objective function should be further amended by considering the change of temperature or be built by experimental method.
The mechanical dynamic characteristics of the motor output shaft should be controlled by the PSO method presented by Elwer et al. [
The control parameters of PSO should be optimized by considering the hardware performance of the electric control unit selected; the principle is based on the premise of appropriate precision, so the convergence rate should be increased to the maximum speed.
In this paper, the load torque based control strategy used for maintaining high energy conversion efficiency of the traction motor in an electric tractor is presented and studied. The control process contains a PSO search that seeks the best working point with maximum energy conversion efficiency and initiation control and whose target is to adjust the searching results dynamically based on peak torque. First, by the mathematical modeling, the relation between the mechanical characteristic and energy conversion is established, and then the target function is performed. Second, by analyzing the speedtraction force performance of the 1804 hybrid, the load torque is selected as the constraint of the PSO search. By describing the schematic representation and the internal task action, the control method and flow are obtained. By making logic and fuzzy rules, the torque controller based on driver intention was designed. Finally, after the working condition collection, which covers most of the tillage force, simulation of traction experiment is conducted. The distribution of initialization signal output from the load torque controller fits the load force fluctuation, which means the initialization control can be selfadaptive to the working condition, and the search results can be timesensitive. Compared with LTFC, LTCS maintains the energy conversion efficiency of the EM near the maximum during the simulation time. Meanwhile, the working speed is sufficiently stable for the requirement of agriculture uniformity and suitable for the speed scope of tillage.
Maximum opening angle of AP (°)
Distance from barycenter to front axle (m)
Depth of AP (°)
Width of single ploughshare (cm)
Constant loss of EM (kW)
Acceleration factors ()
Per phase back EMF (V)
Back electromotive force (V)
Air resistance (kN)
Rolling resistance (kN)
Plowing resistance (kN)
Acceleration resistance (kN)
Slope resistance (kN)
Tractive force (kN)
Driving force (kN)
Rolling resistance coefficient ()
Tractor gravity (kN)
Plowing depth (cm)
Hitch point height (m)
Per phase current (A)
Winding current (A)
Gear ratio of AI ()
Gear ratio of GT ()
Gear ratio between EM and PTO ()
Gear ratio of MD ()
Rotational inertia of drivetrain (kg
Soil specific resistance (kN/cm^{2})
Back EMF constant (V
Torque constant (N
Copper loss coefficient (kW/N^{2}
Iron loss coefficient (kW
Air resistance coefficient (kW
Wheelbase (m)
Per phase selfinductance (H)
Mutual inductance (H)
Selfinductance (H)
Leakage inductance (H)
Free travel ratio of AP ()
Copper loss (kW)
Icon loss (kW)
Electric power input of EM (kW)
Mechanical loss (kW)
Mechanical power output of EM (kW)
Rating power of EM (kW)
Searching range of rotate speed (r/min)
Stator winding resistance (Ω)
Searching range of torque (N
Rolling radius of drive wheel (m)
Electromagnetic torque (N
Load torque of EM (N
Maximum torque of EM (N
Torque output of driving wheel (N
Torque output of AI (N
AP release time (s)
Per phase voltage (V)
Input voltage (V)
Viscous resistance coefficient (N
Tractor speed (km/h)
Number of ploughshares ()
Rotate speed of EM (r/min)
Rotate speed of driving wheel (r/min)
Rotate speed of AI (r/min)
Mechanical efficiency of AI (%)
Transmission efficiency (%)
Rolling efficiency (%)
Mechanical efficiency of GT (%)
Mechanical efficiency between EM and PTO (%)
Electric conversion energy efficiency of EM (%)
Tractive efficiency (%)
Slip efficiency (%)
Mechanical efficiency of MD (%)
Inertia weight ()
Quantization factor of footplate depth ()
Footplate deepening rate quantization factor ()
Number of iterations ()
Slip rate ().
Agricultural implement
Accelerator pedal
Brushless direct current motor
Electric motor
Electromotive force
Energy system
Gearbox transmission
Internal combustion engine
Load torque control strategy
Load torque followed control method
Motor controller
Main drive
Particle swarm optimization algorithm
Power takeoff shaft.
The authors declare that there are no competing interests regarding the publication of this paper.
The authors would like to thank the YTO Group Corporation for the study permission and technical support. The project is supported by National Natural Science Foundation of China (no. 51375145), Science and Technique Foundation of Henan Province (Grant no. 142102210424), and Research Program of Application Foundation and Advanced Technology of Henan Province (no. 152300410080). The authors thank Accdon for its linguistic assistance during the preparation of this paper.