Improved Torque Control for In-Wheel AFPMSM Drives Using Fuzzy Logic and Neuro-Fuzzy Controller

1. Introduction

Electric cars are a revolutionary trend in transportation today. Electric cars have advantages compared to cars with internal combustion engines while eliminating complicated gearboxes and emissions and being environmentally friendly [1,2]. The powertrain structure of electric vehicles tends to use an in-wheel distributed electric drive system consisting of multiple motors, which ensures traction at the front or rear of the car on two or four wheels, making the car becomes a front-wheel drive, rear-wheel drive, or four-wheel drive system [3,4]. This electric powertrain improves the driving performance of electric cars by differentiating between the 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 for electric buses and tanks in the in-wheel motor drive system. Because this motor has short shaft length characteristics, the rotor is lightweight, has good vibration resistance, and has a long service life, thus improving the engine’s reliability and safety and reliability [7]. Although AFPMSM motors enhance the performance of electric vehicles, each vehicle needs to be installed with multiple motors, resulting in complex system control [8]. In addition, the in-wheel motor increases the vehicle’s cost and has high requirements for the vehicle’s control technology, such as power balancing, electronic differential, and energy recovery. In addition, motor in-wheel for electric cars require a small size, lightweight, 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 the AFPMSM motor in-wheel leading to having the motor’s response transmit traction from the motor to the wheels as required. Torque and speed controllers are controlled based on direct torque control (DTC) and based on field-oriented control (FOC). In addition, these controllers are designed by linear and nonlinear control methods such as PI, LQR, Dead beat, sliding control, flatness, fuzzy, [10,11,12,13] or hybrid controller such as fuzzy-neural, fuzzy-sliding mode control [14,15,16,17]. This research results only stop to evaluate the effectiveness of each solution for torque and speed control in the case of AFPMSM motors operating with unchanged load torque or motor parameters. However, the torque response has a slight pulsation, and the actual speed response quickly and accurately tracks the required speed [18,19,20]. Thereby, it is found that researching intelligent control solutions to improve an AFPMSM motor torque integrated with electric car in-wheel, combined with the required torque component by the physical properties of the vehicle car. For example, brake pedals, accelerator pedals, the impact of road inclination, and wind resistance. Therefore, these parameters are necessary to improve the performance and torque of electric vehicles.

This paper will present the control design of a in-wheel AFPMSM motor, one stator, and one rotor, using a fuzzy logic and neuro-fuzzy controller for electric vehicle. In this FLC 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 is implemented with a 5x5 matrix so that the output stator voltage of the controller is met as required [21,22,23]. Other hand, NFC controller for the neural network-based feature set and the fuzzy system. A forward-looking structured network characterizes the neural network, and the training algorithm is back-propagated. The data is trained based on the network error in the back-propagation training algorithm. The network error is the difference between the target and actual values. Therefore, an appropriate control model can be developed. The proposed fuzzy inference system model is based on the Sugeno model containing a set of rules. The vague concept consists of three steps: fuzzy, rule-based decision-making, and defuzzification. In this hybrid system, the neural network develops the dataset on the deviation between the natural is line with the set is (e) and its integral (∆e). Then, the generated dataset is fed to the fuzzy system, and the control rules are developed [24,25]. This NFC controller is caused by the training and testing phases. The FLC and NFC torque controllers are compared with the PI controller.

The present paper consists of six main parts. First, the state model of the electric car traction transmission system is shown in part 2. Then, based on mathematical equations, design torque controller by the FLC and NFC method in parts 3 &4. The theory’s correctness will be proved by the simulation results and evaluation of the current, speed, and torque responses between the proposed controller and compared with the PI controller in part 5. Finally, concluding the contributions. The research results and recommendations for future solutions to improve and enhance the torque response with simple controller design theory and experimental implementation

2. Thematical model and control of electric car power system

2.1. Mathematical model of the AFPMSM motor

It is possible to utilize the standard PMSM model for an AFPMSM. The stator parameters change between the two models, such as the inductor calculation. Furthermore, the Back-EMF produced by an excitation coil and a permanent magnet is same. Therefore, the radial PMSM of a permanent axial flux magnet synchronous motor and the model are mathematically related.

The stator voltage equation in the d-q frame of reference is given by Eq. (1).

(1)

(2)

The stator voltage math as follow:

(3)

Where:R_s: stator resistance; ${\underset{\_}{\psi }}_s^s$: stator flux

Then, covert Eq. (3) from the phase winding system of the stator to the coordinate system quasi-rotor flux:

(4)

The relationship between stator and rotor flux is described:

(5)

In Eq. (5), ${\underset{\_}{\psi }}_p^f$ 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 component) of ${\underset{\_}{\psi }}_p^f$will be zero. Thus, the flux vector has only real components.

(6)

Equation of flux components such as:

(7)

Substitute two Eq. (5) and Eq. (6) into Eq. (4) and pass through the dq coordinate system to have the system of equations of PMSM motor:

(8)

Where: i_sd ; i_sq are stator current in the d-q coordinate axis.

The equation for calculating the torque of the motor is described:

(9)

The motor’s torque comprises two components: the primary component ${\psi }_f{i}_{sq}$and the reactive component. In order 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. The following equation gives the motor torque.

(10)

2.2. Mathematical model of electric vehicle

The gearbox model shows the angular speed and torque relationships according to the gear ratio $k_{gear}\prec 1$ as shown in the Eq. (9):

(11)

Where: T_m is motor torque;$T_{\mathrm{W}h}$the torque acting on the wheel; with T_i = T_Whis the load moment J is the moment of inertia of the motor.

The equation of newton’s second law in the rotation of the motor, as shown in the Eq. (12):

(12)

Drive wheel model is expressed in the Eq. (13):

(13)

The vehicle will act on the road surface with a force of F while the wheel is resting on it with a force of N and is being propelled by a torque of T_wh. In contrast, the road surface will act against the vehicle with a point of the same value in the opposite direction of F_t. The reasonable force that propels the car at speed in this scenario is the frictional force or F_t.

The frictional force is calculated by Eq. (14):

(14)

Where: μ

Vehicle equation of motion with external force components the following equation results from applying Newton’s second law to the parts of the outside force operating on the vehicle's body

(15)

Air resistance as show in Eq. (16):

(16)

In some cases, in simulations, the wind speed can be set $V_{\mathrm{w}ind}=0$

Rolling resistance exists in the case of an underinflated tire are expressed in the Eqs. (17), (18).

(17)

(18)

where: F_zY is the vertical surface reaction, $f_r$ is the rolling resistance coefficient.

3. FLC torque controller design

By calculating the necessary voltage u_sd, u_sq, the fuzzy logic controller controls the system so that the difference between current i_sd and i_sq is as tiny as possible. The exactly planned isd and isq stator currents are used here to regulate the motor’s torque control current. This paper will outline the modern controller design for the i_sd. The control strategy for an AFPMSM motor, one stator, and one rotor utilizing a FLC controller for electric car in-wheels is presented in this work. The stator current error and the derivative of the stator error are used as the two input vectors in this controller to build the Surgeon ambiguous inference file. Five membership functions are included in these input variables: Positive big (PB), Positive small (PS), Equal zero (ZE), and Negative big (NB) (PB). As seen in Table 1 and Figure 1 the fuzzy logic controller is constructed using a 5x5 matrix.

The fuzzy logic control rule 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)

4. NFC torque controller design

The neuro-fuzzy controller (NFC) is a combination of neural network and fuzzy logic implemented according to the structure of Figure 2. This hybrid controller is proposed to satisfy the required voltage, considering the influence of noise. This hybrid controller reduces system complexity and improves torque response on demand.

The structure of the NFC controller consists of five layers: input layer, input member function layer, rule layer, output member function layer, and output layer. Decision tree fuzzy interference is to classify the data into one of the linear regression models to minimize the total squared error (SSE) is calculated by Eq. (19):

(19)

Where n is the number of input variables; P is the fuzzy division for each input variable, and er_i² is the error between the desired and actual output.

The two-input Sugeno fuzzy model is given in Figure 3.

The NFC controller for current i_sq consists of two inputs, the difference (e) between i_sq* anq i_sq, and error integral (∆e). The input signal is fuzzy into five triangular membership functions, negative big (NB), negative small (NS), equal zero (ZE), positive small (PS), and positive big (PB). The 5x5 = 25 fuzzy rules that combine with the output according to the two-input first-order Surgeon model:

• If x₁ is A₁ (NB) and x₂ is B1 (NB), then f₁ = p1e + q₁∆e + r₁
• If x₁ is A₁ (NB) and x₂ is B2 (NS), then f₂ = p2e + q₂∆e + r₂
• If x₁ is A₁ (NB) and x₂ is B3 (ZE), then f₃ = p3e + q₃∆e + r₃
• If x₁ is A₁ (NB) and x₂ is B4 (PS), then f₄ = p4e + q₄∆e + r₄
• If x₁ is A₁ (NB) and x₂ is B5 (PB), then f₅ = p5e + q₅∆e + r₅
• …
• If x₁ is A₂₅ (PB) and x₂ is B₂₅ (PB), then f₂₅ = p₂₅e + q₂₅∆e + r₂₅

Where: A_i and B_i are the premise fuzzy sets, and the parameters p_i, q_i and r_i are the fuzzy design parameters calculated during the training process (i=1, 2,…n). The two-input and one-output NFC structure is given as follows:

The first layer 1: The fuzzy process takes place the input signal is blurred into five triangular membership functions. For each output value of the first layer, we can quickly compute a membership function value denoted μ.

(20)

(21)

Where: i is the membership level of the dataset (A₁, A₂, B₁, B₂) and, ${\mathrm{O}}_{\mathrm{i}}^1$ is the output of the i node in layer 1.

The second layer is to check the weight of each function. This layer takes input values from the first layer and acts as optimization functions to represent data sets of corresponding input variables. The output of this node is described:

(22)

(23)

(24)

…………………..

(25)

3rd layer: This is a rule layer and takes input from the previous layer. Each node (each neuron) in this layer performs conditional matching of the rules. This layer calculates the activation level of each rule, and the number of layers is equivalent to the number of fuzzy rules. Each node of this class computes a weight that will be normalized. Layer 3 nodes calculate the ratio of the rule’s activation strength to the sum of all active rules:

(26)

4th layer: Defuzzification provides output values due to inference rules. The node output is calculated by multiplying the layer 3 output value and the corresponding f-rule:

(27)

5th layer: the output layer aggregates all inputs coming from the 4th layer and converts fuzzy classification results into the required value:

(28)

5. Simulation results

5.1. Building trajectories of accelerator, brake and operating modes of electric vehicles

The trajectories of accelerators and brakes of electric cars are built according to the function y = F (x1, x2, …xn). The trajectories of the accelerator and brakes of electric cars are created, as shown in Figure 5.

Where F is a function that can be obtained experimentally, the output value is calculated by looking up or interpolating the table of deals you define using the block parameters according to the method, such as linear (linear gradient), Lagrange (Linear Lagrange), point closest, block spline and Akima spline interpolation methods. The Fcos function can range in size from 1 to 30 values. Besides the first input defining the dimension breakpoints (rows), the second input defines the dimension breakpoints (columns). Trajectories of the accelerator and brake of electric vehicles are determined as shown in Figure 6.

5.2. Simulation results for PI, FLC and NFC torque controllers

The control structure of the traction drive system for electric cars using the in-wheel AFPMSM motor is shown in Figure 7. Simulation parameters are determined in Table 2.

Evaluating the effectiveness of the controller for the traction transmission system for electric cars using an in-wheel AFPMSM motor, the system is simulated on MATLAB 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 t = 0s, the car starts to accelerate the accelerator value increases from 0 to 1 after 0.45s. Torque reaches a maximum of 205 Nm and remains for 2s.

The torque gradually decreases to the value -205 Nm and returns to the value 0 at time t= 4.66s.

5.2.1. Subsubsection L_d, L_q parameters of the in-wheel AFPMSM motor remain unchanged

The PI controller is calculated with a set of integral and gains parameters, as shown in Table 3. The stator current responses of the FLC, and NFC torque controller are compared with the PI controller shown in Figure 8, Figure 9 and Figure 10. The evaluation table of criteria of stator current response of PI, FLC, and NFC controllers is presented in Table 4.

Figure 8, Figure 9 and Figure 10 show that the stator current response or three controllers is fast (0.4s) and accurate in the steady-state mode. However, the proposed FLC and NFC controllers perform better than the PI controller in over-regulating (no over-throttling). In contrast, the PI controller with an over-regulating current at an over-regulating time is 10%.

The torque and speed responses of the FLC, and NFC torque controllers are compared with the PI controller shown in Figure 11, Figure 12 and Figure 13. The evaluation table of the torque and speed response criteria of the controller PI, FLC and NFC controllers are shown in Table à6. The speed response of the electric car transmission system is shown in Figure 14.

Figure 11, Figure 12 and Figure 13 show that the torque of the three controllers has the same form as the i_sq stator current. The NFC controller has a torque ripper response that is the best of the two controllers (3%). Other hand, the FLC controllers for torque ripper response have less pulse rate (5%) than the PI controller (8%).

In addition, the actual speed response of the electric car of the two controllers is in line with the set requirements, and the speed response does not have too much speed adjustment at starting, accelerating, and decelerating (Figure 14).

5.2.2. L_d , L_q parameters of the in –wheel AFPMSM motor changed by 20%

The stator current responses of the FLC and NFC torque controllers are compared with PI shown in Figure 15, Figure 16 and Figure 17. The evaluation table of criteria of stator current response of PI, FLC, and NFC torque controllers is presented in Table 6.

The results of Figure 15, Figure 16 and Figure 17 show that the stator current response of all three methods is exact (0.5s) and is accurate in steady-state mode (the actual signal follows the set signal). However, the proposed NFC controller gives better results than the PI, and FLC controllers (no over-tuning), while the PI controller with i_sd over-regulating current is 10%, and i_sq is 20%, FLC controller with current regulation i_sd, i_sq is 5%.

The torque and speed responses of the NFC torque controller are compared with the FLC and PI controllers shown in Figure 18, Figure 19 and Figure 20. The evaluation table of the torque and speed response criteria of the PI, FLC, and NFC controllers is shown in Table 7.

Figure 18, Figure 19 and Figure 20 show that the torques of the three controllers have the same form as the isq current. The NFC controller for torque response has less pulse rate (5%) than the PI controller (30%) and FLC controller (16%).