An Artificial Neural Network Controller of a Permanent Magnet Brushless Motor for Electric Tractors Liyou XU 1,2, Shaomin ZHU 1, Zhifei XUE 2 and Jinzhong SHI 2 1 School of Vehicle and Traffic Engineering, Henan University of Science and Technology, Luoyang, Henan 471003, China 2 YTO Group Corporation, Luoyang, Henan 471004, China Abstract Aiming at the characteristics of facility agricultural electric tractor such as low working efficiency, high operation cost and complex working conditions, the common plowing operation condition of the tractor is selected as the testing condition. The force analysis of electric tractor is carried out, and the dynamic model of electric tractor is formulated. Based on the working principle of permanent magnet brushless motor, the mathematical model of the motor is established. Meanwhile, the whole vehicle simulation model of the electric tractor is built in Matlab/Simulink software platform. The PID controller and single neural network controller are designed according to the principle of PID and single neural network control. The PID controller and single neural network controller are embedded into the whole vehicle simulation model of the tractor. It is shown that: i) the fluctuation of simulation speed under single neural network controller is relatively small, which can quickly converge in the condition speed, ii) the continuous operation time of the tractor can reach up to 1.85h, an increase of 16.35% compared with PID controller, iii) this results in significant economic benefits, and iv) the electric tractor under the single neural network control can better adapt to the requirements of complex operating conditions. Keywords - Electric tractor, permanent magnet brushless motor, single neural network, testing conditions. I.INTRODUCTION The tractor is an essential tool in farm operation, and the facility agricultural electric tractor is mainly applied in the occasions with relatively high requirement for the environmental pollution such as greenhouse and orchard, which can carry out the operation such as plowing and rotary tillage. When operating in the closed environment, the discharged exhaust is easily to have significant impacts on human health and the safety of fruits and vegetables. Therefore, the research on electric tractor plays an important role in modernization construction of the agriculture [1-3]. In the electric tractor, to satisfy the complex operation condition of the tractor, high energy lightweight of the battery and high precision control of the motor torque are the key technology of the development [4-5]. At present, there are massive researches at home and abroad on motor torque. The tractor is a complex nonlinear time-varying system, and traditional PID control can hardly satisfy the nonlinear system requirement. The vector control method is largely dependent on motor parameters, which can hardly reach the ideal control effect when the motor is time-varying. The neural network control in the intelligent control has strong robustness, and can be able to approach the dynamic characteristics of arbitrary object with simple control structure, which can be used in the complex control system[6-11]. The facility agricultural electric tractor is taken as the research object, whole vehicle dynamic model and simulation model of the electric tractor are built based on the plowing operation condition, PWM method and single neural network are used to directly control the motor torque, to provide theoretical basis for the formulation of control strategy of permanent magnet brushless motor of electric tractor. II.DYNAMIC MODEL OF ELECTRIE TRACTOR A. Vehicle Dynamics Model of Electric Tractor The force of electric tractor during working process is relatively complex, and the driving force equilrium equation of electric tractor can be obtained considering the balance of each force of electric tractor, satisfying: F F F F F F (1) q F q --- the driving force, N; F T --- the traction resistance, N; F f --- the wheel rolling resistance, N; F i --- the climbing resistance, N; F w --- the air resistance, N; F j --- the acceleration resistance, N. B. Mathematical Model of The Motor T f i Assume that the motor works in a state of two-phase conduction, star connection, and three-phase symmetry, and the eddy current, slot effect and magnetic saturation are neglected, simplified model of permanent magnet brushless motor is shown in Fig. (1). W j DOI 10.5013/IJSSST.a.17.45.05 5.1 ISSN: 1473-804x online, 1473-8031 print
Fig. (1). Model of Permanent Magnet Brushless Motor In Fig. (1), every symbol is expressed as follows: u a, u b and u c --- the stator phase voltages, V; R --- the resistance of three-phase winding, Ω; i a, i b and i c --- the stator phase currents, A; L-M --- the difference between the phase self-inductance and mutual inductance, H; p --- the differential operator; e a, e b and e c --- the stator winding electromotive forces, V. By the Voltage Loop Balance in Fig.(1), the equation can be descred as: ua R 0 0ia L M M ia ea ub 0 R 0 M L M p eb u c 0 0 R ic M M L ic ec (2) Assuming there is no midline and three-phase winding Y connection, satisfying: i a ic 0 (3) Mi b Mic Mic 0 (4) By equations of (9), (10) and (11), it can be concluded that: ua R 0 0ia L M 0 0 ia ea ub 0 R 0 0 L M 0 p eb u c 0 0 R ic 0 0 L M ic ec (5) The electromagnetic torque equation is expressed as: 1 Te eaia eb ecic (6) T e --- the electromagnetic torque, N m; ω --- the angular velocity of the motor, rad/s. The rotor motion equation is expressed as: d T e T L J (7) dt T L --- the load torque, N m; J --- the moment of inertia of the motor, kg m 2 ; III. MONTOR CONTROL A. PWM Control of Motor Torque The voltage regulation and motor torque control of permanent magnet brushless motor is realized by using PWM chopper transform DC voltage to PWM signal, which can control the speed of chopper switch to change the width of pulse [12-14]. The permanent magnet brushless motor usually uses three-phase full-bridge topology for driving, each phase winding conducts 120 C electrical angle each time, and always keeping conduction of two-phase winding. During 120 C conduction period, PWM regulation is carried out to realize the adjustment of motor speed through the current on two conducted phases. If the ratio of high level time in a PWM period and the cycle of PWM wave is used for the characterization of the duty cycle, which is recorded as α, satisfying: t0 (8) t 0 --- the high level time in a PWM cycle, s; τ --- the cycle of PWM wave, s. B. Neural Network Control of Duty Cycle The neural network control is a kind of intelligent control method that simulates the brain behavior, and its control principle is shown in Fig. (2). In this paper, single neural network structure is used to adjust the duty cycle and control the motor torque. Considering the requirement for tractor operation, the difference between simulation speed and condition speed and the current acceleration are taken as the input parameter of neural network. Input, output and weight coefficient can be determined as the following equations: 2 O f x k (9) i i i1 kn 1 knk (10) k1 x1 x1 x2 k2n x2 x1 x2 1k 1n (11) k2 k 1 (12) x 1 --- the difference between simulation speed and condition speed, km/h; x 2 --- the simulate acceleration, m/s 2 ; k 1 --- the weight coefficient of x 1; k 2 --- the weight coefficient of x 2; θ --- the threshold; η --- the learning rate, 0.05 is adopted; O --- the output. d --- the angular acceleration of the rotor, rad/s2. dt DOI 10.5013/IJSSST.a.17.45.05 5.2 ISSN: 1473-804x online, 1473-8031 print
The traction resistance of the electric tractor is complex, which has great fluctuation. Under the condition of plowing operation, the traction resistance is set to 2500N, maximum fluctuation amplitude to 450N, and average time interval of the fluctuation to 60s. The relationship of traction resistance changing with time is shown in Fig. (4). Fig. (2). Elementary Diagram of Single Neural Network IV. TESTING CONDITIONS The facility agricultural tractor is mainly used in plowing, rotary tillage, and field management, and testing condition of plowing operation is built according to common operation of the tractor. Under the condition of plowing, the running distance is set to 0.549km, time to 400s, operation speed to 5.004km/h, and start-up time to 10s. The relationship of condition speed changing with time is shown in Fig. (3). Fig. (4). Relationship of Traction Resistance Changing With Time Fig. (3). Relationship of Speed Changing With Time V. RESULTS AND ANALYSIS A. Parameters Setting The whole vehicle simulation model of electric tractor is built in Matlab/Simulink platform based on the analysis of whole vehicle dynamic model of electric tractor and mathematical model of the motor. The whole vehicle simulation model under the single neural network control is shown in Fig. (5). When the Controller module changes to PID Controller, the model changes to the whole vehicle simulation model under the PID controller. The calculation of the initial values are shown in Table 1 and Table 2. Fig. (5). Simulation Model of Electric Tractor DOI 10.5013/IJSSST.a.17.45.05 5.3 ISSN: 1473-804x online, 1473-8031 print
TABLE 1. BASIC PARAMETERS OF THE ELECTRIC TRACTOR Parameters Value Size (m) 2.4 1.11 1.3 Structural quality (kg) 1000 Rated force (N) 3500 Rolling radius rq (m) 0.415 Adhesion coefficient of driving wheel φ 0.65 Rolling resistance coefficient f 0.08 Slip ratio δ 0.12 Gear ratio of Ⅰshift i1 2.29 Gear ratio of Ⅱshift i2 0.93 TABLE 2. BASIC PARAMETERS OF THE MOTOR Parameters Value DC power supply U (V) 220 Rated power P (kw) 7 Rated speed n (r/min) 2800 Initial duty ratio α0 0.5 Resistance of phase winding R (Ω) 0.5 Difference between the phase self-inductance and mutual inductance L-M (H) 0.00172 Moment of inertia J (kg m 2 ) 0.00292 B. Analysis of Results Under the plowing condition, the change relations of simulation speed, motor duty cycle and battery SOC with the simulation time when the traditional PID and single neural network control are used, illustrated in Fig. (6)~Fig. (8). Fig. (7). Relationship of Duty Cycle Changing With Time Fig. (6). Relationship of Speed Changing With Time Fig. (8). Relationship of SOC Changing With Time DOI 10.5013/IJSSST.a.17.45.05 5.4 ISSN: 1473-804x online, 1473-8031 print
From Fig. (6), it can be seen that the simulation speed diagram under the single neural network control can enter the stable state more quickly, with quick convergence rate and small speed fluctuation range. Therefore, the single neural network control has good adaptability during acceleration and shift process, which can better satisfy the requirement for complex operation conditions. From Fig. (6) and Fig. (7), it can be seen that the maximum duty cycle is 0.63. Since single neural network has memory and dynamic adjustment function, the duty cycle can be adjusted more quickly and reasonably when the traction resistance changes. The simulation speed under the single neural network control can better track the condition speed, with good dynamic characteristics. From Fig. (8), it can be seen that when the simulation time is 400s under the single neural network, the battery SOC decreases to 0.94, it can be estimated that the continuous operation time of the tractor is 1.85h. The battery SOC by the traditional PID control method decreases to 0.93, and the continuous operation time of the tractor is 1.59h, which shows that the single neural network control has better economic benefits. VI. CONCLUSIONS Under the circumstance of plowing, the simulation speed diagram of the single neural network control can enter the stable state more quickly, with quick convergence rate and small speed fluctuation range. The duty cycle can be adjusted more quickly and reasonably when the traction resistance changes. Under the plowing condition, when the simulation time of electric tractor is 400s, the battery SOC under the traditional PID control decreases to 0.93, and the battery SOC by the single neural network control method decreases to 0.94, and the increase amplitude of continuous operation time of the tractor is 16.35%, with relatively significant economic benefits. The speed control of permanent magnet brushless motor is realized by using PWM torque control and single neural network control, which can better adapt to the requirement of electric tractor for the complex operation conditions. ACKNOWLEDGEMENTS This work is supported by the National Key Research and Development Program of China during the 13th Five-Year Plan Period (no. 2016YFD0701002), the National Science & Technology Pillar Program during the 12th Five-year Plan Period (2014BAD08B04), the Base and Cutting-edge Technology Research Project of Henan Province (152300410080), and the China Postdoctoral Science Foundation Project (2015M582212). REFERENCES [1] Yi Lu, Fuzeng Yang and Yongcheng Liu, Research and design of miniature electric tractor, JOURNAL OF MACHINE DESIGN, vol. 30, no. 3, pp. 82-85, 2013. 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