the Speed of the Four In-Wheel

—This paper presents design and speed estimation for an Electric Vehicle (EV) with four in-wheel motors using Radial Basis Neural Network (RBNN). According to the steering angle and the speed of EV, the speeds of all wheels are calculated by equations derived from the Ackermann-Jeantand model using CoDeSys Software Package. The Electronic Differential System (EDS) is also simulated by Matlab/Simulink using the mathematical equations. RBNN is used for the estimation of the wheel speeds based on the steering angle and EV speed. Further, different levels of noise are added to the steering angle and the EV speed. The speeds of front wheels calculated by CoDeSys are sent to two Induction Motor (IM) drives via a Controller Area Network-Bus (CAN-Bus). These speed values are measured experimentally by a tachometer changing the steering angle and EV speed. RBNN results are verified by CoDeSys, Simulink, and experimental results. As a result, it is observed that RBNN is a good estimator for EDS of an EV with in-wheel motor due to its robustness to different levels of sensor noise.


INTRODUCTION
Electric Vehicles (EVs) are increasingly being used due to their reduced pollution emissions and fuel consumption [1,2].Further, recent efficient electric motors and developments in drive and battery technology have resulted to an increase in the popularity of EVs [3].EV motors having a differential gear are fitted into the wheels of the vehicle to reduce the mass caused from the batteries and drive-trains [4].In traditional vehicles, mechanical differentials are utilized in slippery and sloping roads to distribute power and torque equally to the traction wheels [1].On the contrary, the Electronic Differential System (EDS) is used in EVs to eliminate mechanical losses, maintenance, and repair costs of gears caused by the powertrains.According to the curve of the road, the outer wheel speed of the EV must be higher than the inner wheel speed for safe driving [5].
An EDS for EV is modelled by NN based on the vehicle speed and steering angle in [1].Using a fuzzy logic control method to estimate the slip rate of each wheel, a new Electronic Differential (ED) control for two in-wheel motors of EV is investigated in [4].The designed ED control is validated by Matlab/Simulink results.In [6], authors estimate the speeds of four wheels for EV by using the Ackermann-Jeantand model [6].The estimated speeds are also verified by Matlab/Simulink and experimental results.In [7], the speeds of the four wheels are calculated by NN PID ED based on the steering angle and speed of EV.An EDS for rear wheels of an EV used in Brushless DC motors is investigated by Fuzzy Logic Speed Controller using the Ackermann-Jeantand model [8].The proposed EDS is verified by Matlab/Simulink results.In [9], authors proposed an EDS for the rear wheels of EV driven by fault tolerant permanent magnet motors.The speeds of the wheels are calculated by Ackermann-Jeantand model.Authors in [10] design an EDS for the rear wheels of an EV using DC motors based on the steering angle and vehicle speed.The results of the designed EDS are verified by experimental results.NN control is used for estimating the rear wheels of an EV in [11].The simulation results are tested by two 37-kW IMs.In another paper [12], an EDS for two rear wheels of EV is presented and analyzed versus the speed and torque observed for the DC motor.
In this paper, an EDS for all four wheels of an EV is modeled and the speeds of all wheels are calculated by the CoDeSys Software Package using mathematical equations derived from the Ackermann-Jeantand model.Then, the EDS simulation is also conducted in Matlab/Simulink using these equations.The speeds of the wheels are estimated by an Radial Basis Neural Network (RBNN) based on the steering angle and the EV speed.Further, white noise at specified amplitudes is added to the EV speed and the steering angle in order to investigate the behavior under sensor noise.According to the

II. ELECTRONIC DIFFERENTIAL SYSTEM FOR EV
The Ackermann-Jeantand model is employed for EDS design which is generally preferred at low speeds due to the effect of centrifugal force and centripetal forces is utilized [4].
A position encoder is used for the steering angle (  ).Once  is zero, EV drives on a straight road.If  is different from zero, it means that EV drives on the curved road.According to the turning direction, the speed of the outer wheel has to be higher than that of the inner wheel [4,6,13].In this situation, the EDS is activated.The equations derived from this model are as follows: The inner and outer steering angles of the front wheel are respectively given by: where K is the distance between the left and right kingpin, L is the distance between the front and rear wheel.
To estimate the speeds, the turning radii of the front inner and outer wheels and rear inner and outer wheels can be respectively defined by: where d r is the distance between rear wheels.
The gravity centre radius of the EV is: where l r is the distance between the rear wheel and gravity centre.
The angular speeds of the front inner and outer wheels, and the rear inner and outer wheels can be respectively expressed by: where r is the radius of the wheel and V is speed of EV.
The equations derived from Ackermann-Jeantand geometry are given into CoDeSys Software Package.L, l r , d r , r, and K parameters taken from a vehicle model are shown in Table I.These parameters are used as the constant values in the CoDeSys programmer.The implementation of RBNN is similar to performing exact interpolation of various data points in a multidimensional space [14].The RBNNs are rather popular due to their simple structure, fast training, and implementation time.The network architecture of an RBNN is similar to that of a classical NN [15].The structure of RBNN includes the input layer, hidden layer and output layer [16,17].The input vector x is used as an input in all radial basis functions.µ j is the vector determining the center of basic function ϕ j and has elements µ ji .The weight parameter is represented by w kj and bias term is equal to w k0 .The hidden layer includes nonlinear radial basis activation function and the output layer is linear combination of hidden layer.Each node in the hidden layer uses an RBF as a nonlinear activation function.ϕ 0 (x)=1 corresponds to the bias in the output layer.The RBF network can give an optimal solution to the adjustable weights in the minimum Mean Squared Error (MSE) sense by linear optimization method [18].The smoothness level of interpolation function is controlled by the parameter of spread (σ).The relationship between input, output, and nonlinear transfer function is given by : RBNNs are generally utilized for classification and curve fitting.Our test system has two inputs: the steering angle and the speed of EV and the outputs are the speeds of front and rear wheels.The overall scheme is shown in Figure 1.The Signal-to-noise ratio is given by 10 log 20 (9) where A signal and A noise are RMS amplitudes of the signal and noise as decibel, respectively.
Gaussian White Noise (GWN) is added to NN systems for performance analysis.GWN in this case represents sensor interference in steering angle and EV speed [19].Different levels of GWN are used to obtain the optimal solution.MSE gives an idea about the behavior of the RBNN training process.Low MSE means a successful data fitting.Therefore, the number of epochs is selected at nearly fixed value of MSE.In this study, the number of epochs is taken as 400.The MSE versus number of epochs is shown in Figure 2.   The maximum speed of an EV having 21-inch wheel size is 50.806km/h.Therefore, this speed is used as maximum value in the simulation.Maximum manoeuvrability can be calculated by minimum circle radius of outer wheel trace at 10 km/h vehicle speed.Turning radius is given by Turning radius changes between 7 m and 9 m in passenger cars.Since the movement area where is placed in the wheels is another factor limited the steering of the wheel, the steering angle is taken as maximum value (15˚).The speeds of four wheels are calculated by Simulink changing the steering angle from 1° to 10° and EV speed from 0 to 40 km/h.Then, the relationship between input parameters (δ,V) and four wheel speeds are trained to NN model.The speeds are estimated by changing the steering angle from 10° to 15° and the EV speed from 40 to 50 km/h.The RBNN results are verified by Simulink results for all wheel speeds as shown in Table II, III, IV, and V.

V. EXPERIMENTAL RESULTS
The experimental setup is established to obtain the results of designed EDS as shown in Figure 5.The speeds of the front wheels calculated by CoDeSys are sent to three-phase IM drives (VFD C2000) via CAN-Bus.An encoder is used for the steering angle.Three-phase IM drives, HY-TTC 60 and encoder which are fed from 24 V power supply communicate with each other on CAN-Bus.HY-TTC 60 processor which is an advanced model of 16-bit controller family produced by TTControl Company and consists of power and control cards is a master unit on CAN-Bus line.Two drives connected to IM motors and encoder are slave units on the CAN-Bus line.Characteristic line impedances are used in beginning and end of the line.By changing the steering angle from 0° to 15° degree and taking the EV speed which is fixed as 50.806km/h, the speeds of front wheels calculated by CoDeSys using the Ackermann-Jeantand model are sent to IM drives.The speeds of front wheels are measured by a tachometer experimentally.CoDeSys results are verified by Simulink, experimental, and RBNN results as given in Table VI

VI. CONCLUSION
In this paper, EDS modelling and estimation parameters for front and rear wheels of an EV are realized.According to the steering angle and speed of the EV, the speeds of the four wheels are calculated by mathematical equations derived from the Ackermann-Jeantand model using the CoDeSys Software Package.Matlab/Simulink modeling of EDS is also realized by using the equations obtained from the Ackermann-Jeantand model.The speeds of the all wheels are calculated by Simulink changing the steering angle from 1˚ to 15˚ and the EV speed from 0 km/h to 50 km/h.Different levels of white noise are added to the steering angle and EV speed as sensor noise.RBNN is used to estimate the speeds changing the steering angle from 10˚ to 15˚ and the EV speed from 40 km/h to 50 km/h.The steering angle is taken by an encoder.The calculated front wheel speeds are sent to IM drives via CAN-Bus for taking experimental results by a tachometer.RBNN results are verified by comparing with Simulink, experimental and CoDeSys results.Furthermore, RBNN results are compared with Simulink results based on noise and function of spread at different levels.To conclude, RBNN is show to be appropriate for the estimation of EDS parameters due to its minor error and its robustness to different levels of sensor noise.

Fig. 5 .
Fig. 5.The experimental setup Estimation results of RBNN for the front and rear wheel speeds are compared with Simulink results.Differences between Simulink and RBNN results are illustrated for the front inner and outer wheel speeds based on the noise levels in Fig. 10-11, respectively.As shown in the figures, the errors of all wheel speeds increase with rising of steering angle and EV speed.

Fig. 11 .
Fig. 11.Difference between Simulink and RBNN results of front outer wheel.

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levels, the speeds estimated by the RBNN are compared with Simulink results.Furthermore, the speeds of the front wheels calculated by CoDeSys are sent to two IM drives and measured by a tachometer experimentally.RBNN results are also verified by CoDeSys, Simulink, and experimental results.

TABLE V .
. According to the difference of the comparison, MSE of all wheel speeds estimated by RBNN are shown in Table VII based on the noise level and function spread.Once examining the Table VII, the large number of the spread is preferred to estimate the speeds due to having less error based on different noise levels.Hence, the spread value and noise level are selected as 10 and 40 dB, respectively.RBNN results of the front inner and outer, rear inner and outer wheel speeds are illustrated based on the noise level in Figures 6-9, respectively.

TABLE VI .
COMPARISON OF CODESYS, SIMULINK, EXPERIMENTAL, AND RBNN RESULTS FOR FRONT WHEEL SPEEDS MEAN SQUARE ERRORS OF FOUR WHEEL SPEEDS