Microsoft Word - ETASR_V13_N2_pp10357-10362 Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10357-10362 10357 www.etasr.com Ha: Torque Control of an In-Wheel Axial Flux Permanent Magnet Synchronous Motor using a Fuzzy … Torque Control of an In-Wheel Axial Flux Permanent Magnet Synchronous Motor using a Fuzzy Logic Controller for Electric Vehicles Vo Thanh Ha Faculty of Electrical and Electronics Engineering, University of Transport and Communications, Vietnam vothanhha.ktd@utc.edu.vn (corresponding author) Received: 17 January 2023 | Revised: 31 January 2023 | Accepted: 3 February 2023 ABSTRACT This paper presents the control design of an in-wheel axial-flux permanent magnet synchronous motor with one stator and one rotor, using a fuzzy logic controller for electric vehicles. In this controller, the surgeon ambiguous inference file is built by two input vectors, the stator current error and the derivative of the stator error. These input variables include five membership functions: Negative Big (NB), Negative Small (NS), Equal Zero (ZE), Positive Small (PS), and Positive Big (PB). The fuzzy logic controller was implemented using a 5×5 matrix to meet the required output stator voltage of the controller. The fuzzy logic torque controller was compared with the PI controller in stator current response, torque, and speed. The proposed controller was evaluated using simulation results from MATLAB/SIMULINK. Keywords-AFPMSM; fuzzy logic; PI; FOC; Electrical Vehicles (EVs) I. INTRODUCTION Electric cars are a revolutionary trend in today transportation. Electric cars have advantages compared to cars with internal combustion engines as they eliminate complicated gearboxes and emissions and are environmentally friendly [1- 2]. The powertrain structure of Electric Vehicles (EVs) tends to use an in-wheel distributed electric drive system consisting of multiple motors, which ensures traction at the front or rear of a car on two or four wheels, using a front, rear, or four-wheel drive system [3-4]. This electric powertrain improves driving performance by differentiating between wheels, makes full use of vehicle energy, improves transmission efficiency, increases range, eases braking, has good heat dissipation, and is more convenient for installation and maintenance [5-6]. The Axial Flux Permanent Magnet Synchronous Motor (AFPMSM) is widely used in in-wheel motor drive systems because it has short shaft length characteristics, is lightweight, has good vibration resistance, and has a long service life, thus improving reliability and safety [7]. Although AFPMSM motors enhance the performance of EVs, each vehicle should have installed multiple motors, resulting in a complex control system [8]. In- wheel motors increase the cost of a vehicle and have high requirements for control procedures, such as power balancing, electronic differential, and energy recovery. In addition, electric car in-wheel motors require small size, light weight, small torque, high efficiency, large overload capacity, and wide speed range [9]. Therefore, scientists have been interested in studying the control of traction and torque of in-wheel AFPMSMs and their response to wheels. Torque and speed controllers are controlled based on Direct Torque Control (DTC) and Field-Oriented Control (FOC). These controllers are designed using linear and nonlinear control methods such as PI, LQR, dead beat, sliding mode, flatness, fuzzy [10-14], or hybrid controllers such as fuzzy-neural, fuzzy-sliding, and PI- fuzzy [14-17]. However, the torque response has a slight pulsation, and the actual speed response quickly and accurately tracks the required speed [17-20]. Therefore, the study of intelligent control solutions to improve an integrated in-wheel AFPMSM torque in an EV should be combined with the required components and physical properties, such as brake and accelerator pedals, road inclination, and wind resistance. Consequently, these parameters are necessary to improve the performance and torque of EVs. This study presents the control design of an in-wheel AFPMSM, one stator, and one rotor, using a Fuzzy Logic Controller (FLC) for EV systems. In this controller, the surgeon ambiguous inference file is built by two input vectors, the stator current error and the derivative of the stator error. These input variables include five membership functions, Negative Big (NB), Negative Small (NS), Equal Zero (ZE), Positive Small (PS), and Positive Big (PB). The FLC was implemented with a 5×5 matrix so that the output stator voltage of the controller is met. The fuzzy logic torque controller was compared with the PI controller in stator current response, torque, and speed. Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10357-10362 10358 www.etasr.com Ha: Torque Control of an In-Wheel Axial Flux Permanent Magnet Synchronous Motor using a Fuzzy … II. MODEL AND CONTROL OF THE ELECTRIC CAR POWER SYSTEM A. Mathematical Model of an AFPMSM It is possible to utilize the standard PMSM model for an AFPMSM. Stator parameters, such as the inductor calculation, change between the two models. Furthermore, the Back-EMF produced by an excitation coil and a permanent magnet is the same. Therefore, the radial PMSM of a AFPMSM and the model are mathematically related. The stator voltage equation in the d-q frame of reference is given by: �� = �� + ��� �� + �� (1) �� = ���� + ��� �� − �� (2) The stator voltage equation is as follows: ̱�� = ��. �̱�� + ��̱���� (3) where Rs is the stator resistance and �̱�� is the stator flux. Then, converting (3) from the phase winding system of the stator to the coordinate system, quasi-rotor flux gives: ̱�� = ��. �̱�� + ��̱���� + � ��̱�� (4) The relationship between stator and rotor flux is described by: �̱�� = ���̱�� + �̱�� (5) where �̱�� is the polar flux vector. Since the d-axis of the coordinate system coincides with the axis of the polar flux, the perpendicular component (q-axis) of �̱��will be zero. Thus, the flux vector has only real components. ��̱��� = �� (6) The equation of flux components is given by: ���� = ������ + ����� = ������ (7) where isd, isq are the d and q coordinate stator currents, and Lsd, Lsq are the d and q coordinate inductance. Substituting (5) and (6) into (4) and passing through the d-q coordinate system gives the system of equations of the PMSM motor: � �� = ��� ������ + ����� − ������ �� = ��� ��� �� + ����� + ������ + �� (8) The torque of the motor is described by: !" = #$ %�&����� + '��� − ���(������) (9) The motor torque is comprised of two components: the primary component ����� and the reactive component. To create a control system, the stator current vector must be adjusted so that the vertical current vector is parallel to the polar flux. Therefore, there is a torque-generating current component, not a magnetizing current component, and motor torque is given by: !" = #$ %������ (10) B. Mathematical Model of the Electric Vehicle The gearbox model shows the angular speed and torque relationships according to the gear ratio *+ ,- ≺ 1, as shown in: � !"*+ ,- = !0ℎ 0ℎ = "*+ ,- (11) where !" is the motor torque, !0ℎ is the torque acting on the wheel, !� = !0ℎ is the load torque, and J is the inertia torque of the motor. Applying Newton's second law in the rotation of the motor gives: ! " − !01 = 2 �34�� (12) The drive wheel model can be expressed as: � 501 = 01�01!01 = !6 = 7��01 (13) The vehicle will act on the road surface with a force F while the wheel is resting on it with a force N and is being propelled by a torque Twh. In contrast, the road surface will act against the vehicle with a point of the same value in the opposite direction of Ft. In this scenario, the reasonable force that propels the car at speed is the frictional force Ft given by: 7� = 89.:.; (14) where μ is the grip coefficient. The following equation results from applying Newton's second law to the parts of the outside force operating on the vehicle's body: 89 �9<=�� = 7� − 7, -> − 7->?? − 89.:.@�A(C) (15) Air resistance is given by: 7, -> = EF�GH$ (5 9 + 5I�J�)$ (16) In some cases, the wind speed can be set to �I�J� = 0. The rolling resistance exists in the case of an underinflated tire and can be given by: 7->?? = L-7MN (17) 7MN = 89:OP@(C) (18) where 7MN is the vertical surface reaction and L- is the rolling resistance coefficient. III. FLC TORQUE CONTROLLER DESIGN The FLC controls the system by calculating the necessary voltages usd and usq so that the difference between the currents isd and isq is as tiny as possible. The exactly planned isd and isq stator currents are used to regulate the motor's torque control current. This paper outlines the modern controller design for the isd and the control strategy for an in-wheel AFPMSM, one stator, and one rotor, utilizing an FLC. This controller uses the stator current error and the derivative of the stator error as the two input vectors to build the ambiguous inference file. Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10357-10362 10359 www.etasr.com Ha: Torque Control of an In-Wheel Axial Flux Permanent Magnet Synchronous Motor using a Fuzzy … (a) (b) (c) Fig. 1. (a), (b) Inputs, (c) output, and fuzzy rules of the FLC controller. The input variables include five membership functions: Positive Big (PB), Positive Small (PS), Equal Zero (ZE), Negative Big (NB), and Negative Small (NS). Table I and Figure 1 show the FLC constructed using a 5×5 matrix. The FLC consists of 25 rules, which are implemented as follows:  If (input 1 is NB) and (input 2 is NB), then (output is NB)  If (input 1 is NB) and (input 2 is NS), then (output is NB)  If (input 1 is NB) and (input 2 is ZE), then (output is NB)  If (input 1 is PB) and (input 2 is PB), then (output is PB) TABLE I. MATRIX OF FLC CONTROLLER Input 1 (e) / Input 2 (Δe) NB NS ZE PS PB NB NB NB NB NS ZE NS NB NB NS ZE PS ZE NS NS ZE PS PB PS ZE ZE PS PB PB PB ZE PS PB PB PB IV. SIMULATION RESULTS A. Building Trajectories of Accelerator, Brake, and Operating Modes of Electric Vehicles The trajectories of accelerators and brakes of electric cars are built according to a function F(x1, x2, …xn). Figure 2 shows the trajectories of the accelerator and brakes. The F function can be obtained experimentally and the output is calculated by looking up or interpolating the defined table using the block parameters according to a method, such as linear (linear gradient), Lagrange (Linear Lagrange), closest point, block spline, and Akima spline interpolation. The Fcos function can range in size from 1 to 30. The first and second inputs define the row and column dimension breakpoints, respectively. Figure 3 shows the determination of the accelerator and brake trajectories. Fig. 2. The trajectories of the accelerator and brakes. Fig. 3. The parameters trajectories of accelerator and brakes. B. Simulation Results and Evaluation Figure 4 shows the control structure of the traction drive system for electric cars using the in-wheel AFPMSM, and Table II displays the simulation parameters. Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10357-10362 10360 www.etasr.com Ha: Torque Control of an In-Wheel Axial Flux Permanent Magnet Synchronous Motor using a Fuzzy … The proposed controller was simulated in MATLAB to evaluate its effectiveness for the traction transmission system in electric cars using an in-wheel AFPMSM, with the following simulation scenario:  Assume the speed of the wind is 0.  The car moves on a flat road, but at t = 3.5s to 4.3s, the car goes downhill.  At time t = 0s, the car starts to accelerate and the accelerator value increases from 0 to 1 after 0.45s. Torque reaches a maximum of 205Nm and remains there for 2s.  At t = 2s, the vehicle starts to decelerate, and the brake reaches a value from 0 to 1 at t = 3.5s. The torque gradually decreases to -205Nm and returns to 0 at t = 4.66s. C dq CQ dq uvw CQ AFPMSM CQ CQ sdu sq u s u  s u  si  si  sdi sqi  tv tu tw s  Torrque Controller s  * s di Voltage source inveter * sq i sd i sqi Inputs Incline Brake Accelerato *T Wind Vehicle Controller  dcU sdi sqi Fig. 4. The control structure for electric cars using an in-wheel AFPMSM motor, based on a FOC method. TABLE II. PARAMETERS FOR AFPMSM Motor parameters Value Symbol Value Power Pđm 35Kw Rated speed Nđm 1800rpm Rated voltage Uđm 275V Number of pole pairs Zp 8 Magnetic flux density R 0.0437 Maximum torque Pmax 205Nm Armature resistance Rs 0.0101Ω Shaft inductance d Ld 2.4368e-4H Shaft inductance q Lq 2.9758e-4H Fig. 5. The MATLAB/SIMULINK control structure for electric cars using an in-wheel AFPMSM. Table III shows the parameters of the simulated PI controller. Figures 6 and 7 show the stator current responses of the FLC and the PI controller. These figures show that the stator current response in the steady-state method is fast (0.4s) and accurate in the steady-state mode (the actual signal follows the set call). However, the proposed FLC gives better results than the PI controller in over-regulating (no over-throttling), while the PI controller with an over-regulating current at an over-regulating time is 10%. Table IV presents the evaluation criteria for the stator current responses of the PI and the FLC controllers. TABLE III. PARAMETERS FOR THE PI CONTROLLER Controller Ki Kp Current controller Id 7.103004e+2 0.8779 Current controller Iq 1.0615e+3 1.0744 TABLE IV. RESULTS OF EVALUATION RESPONSIBILITY Controller PI FLC Stator current isd Accelerated setting time (s) 0.4 0.4 Over-adjustment 10% 0% Stator current isq Set-up time (s) 0.4 0.4 Over-adjustment 10% 0% Torque Controller Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10357-10362 10361 www.etasr.com Ha: Torque Control of an In-Wheel Axial Flux Permanent Magnet Synchronous Motor using a Fuzzy … (a) (b) Fig. 6. Stator current responses (a) isd and (b) isq for the PI controller. (a) (b) Fig. 7. Stator current responses (a) isd and (b) isq for the FLC controller. Figures 8 and 9 show the comparison of the torque and speed responses of the FLC and the PI controller. These figures show that the torque of the two controllers has the same form as the isq current. The FLC has less pulse rate (3%) for the torque response than the PI controller (8%). Table V shows the torque and speed response criteria of the PI and the FLC controllers. TABLE V. RESULTS OF EVALUATION RESPONSIBILITY Controller PI FLC Torque responses Shape Same as isq current response Same as isq current response Torque ripple 8% 3% Speed responses Accelerated setting time 2.2 (s) 2.2 (s) Over-adjustment 0% 0% Fig. 8. Torque responses of the PI controller. Fig. 9. Torque responses of the FCL controller. Figure 10 shows the speed responses of an electric car transmission system using the PI controller and the FLC. The actual speed response of an electric car in both cases is in line Engineering, Technology & Applied Science Research Vol. 13, No. 2, 2023, 10357-10362 10362 www.etasr.com Ha: Torque Control of an In-Wheel Axial Flux Permanent Magnet Synchronous Motor using a Fuzzy … with the set requirements, and the speed response does not have too much speed adjustment at starting, accelerating, and decelerating. Fig. 10. Speed responses of the PI controller and the FLC. V. CONCLUSION This paper presented an in-wheel AFPMSM motor torque controller design for a traction drive system using a fuzzy logic control method. The proposed controller was compared with the PI controller and its efficiency was demonstrated through MATLAB simulations. The proposed controller provides better torque and speed response results than the PI controller in terms of steady-state time, over-adjustment, and torque pulsation. However, this controller has a complicated design, so it is necessary to study more simple but intelligent control solutions in the future. ACKNOWLEDGMENT This study was funded by the University of Transport and Communications (UTC) under grant number T2023-DT- 001TD. REFERENCES [1] X. Zhang, D. Göhlich, and J. 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