Microsoft Word - 15-889-ed.doc Engineering, Technology & Applied Science Research Vol. 6, No. 6, 2016, 1288-1293 1288 www.etasr.com Yildirim et al.: Computation of the Speed of the Four In-Wheel Motors of an Electric Vehicle Using… Computation of the Speed of Four In-Wheel Motors of an Electric Vehicle Using a Radial Basis Neural Network Merve Yildirim Department of Electrical and Electronics Engineering University of Firat, Elazig, Turkey merveyildirim@firat.edu.tr Mehmet Cem Catalbas Department of Electrical and Electronics Engineering University of Firat, Elazig, Turkey catalbas@firat.edu.tr Arif Gulten Department of Electrical and Electronics Engineering University of Firat, Elazig, Turkey agulten@firat.edu.tr Hasan Kurum Department of Electrical and Electronics Engineering University of Firat, Elazig, Turkey hkurum@firat.edu.tr Abstract—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. Keywords-electric vehicle; electronic differential system; in- wheel motor; radial basis neural network; speed estimation I. 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 This work is supported by TUBITAK (The Scientific and Technological Research Council of Turkey) with the project, 113M090. Engineering, Technology & Applied Science Research Vol. 6, No. 6, 2016, 1288-1293 1289 www.etasr.com Yildirim et al.: Computation of the Speed of the Four In-Wheel Motors of an Electric Vehicle Using… noise 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. 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:        ))tan()2/(( )tan( arctan2,1    KL L (1) 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: )sin( 2,1 2,1  L R  (2) 2)tan( 4,3 rdLR   (3) where dr is the distance between rear wheels. The gravity centre radius of the EV is: 2)(2))2/(( 3 rr ldR cg R  (4) where lr 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: rR RV w cg    )( 2,1 2,1 (5) rR RV w cg    )( 4,3 4,3 (6) 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, lr, dr, 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. TABLE I. EDS MODEL PARAMETERS Parameters L lr dr r K Values (m) 2.285 0.835 1.35 0.395 1.219 III. MODELLING OF EDS VIA RBNN 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. µj is the vector determining the center of basic function ϕj and has elements µji. The weight parameter is represented by wkj and bias term is equal to wk0. 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. ϕ0(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 :               22 exp)( j jx xj    (7)    M j k wx jkj wx k y 1 0 )()(  (8) 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. Fig. 1. Overall scheme Engineering, Technology & Applied Science Research Vol. 6, No. 6, 2016, 1288-1293 1290 www.etasr.com Yildirim et al.: Computation of the Speed of the Four In-Wheel Motors of an Electric Vehicle Using… The Signal-to-noise ratio is given by          noise A signal A dB SNR 10 log20 (9) where Asignal and Anoise 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. 0 50 100 150 200 250 300 350 400 10 -15 10 -10 10 -5 10 0 10 5 Number of Epochs M ea n S qu ar e E rr or Fig. 2. MSE versus number of epochs. IV. MATLAB/SIMULINK MODEL OF EDS EDS is simulated by Matlab/Simulink using the equations derived from the Ackermann Jeantand model. The simulation model and subsystem of the model are shown in Figures 3 and 4, respectively. Fig. 3. Matlab/Simulink model of EDS. Fig. 4. Subsystem of EDS model. The maximum speed of an EV having 21-inch wheel size is 50.806 km/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 ϛ )sin( 21    L (10) 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. TABLE II. COMPARISON OF SIMULINK AND RBNN RESULTS FOR FRONT INNER WHEEL. δ (°) 13 14 15 V (km/h) Simulink Results RBNN Results Simulink Results RBNN Results Simulink Results RBNN Results 45 43.334 43.300 43.300 43.253 43.282 43.210 46 44.297 44.226 44.263 44.171 44.244 44.117 47 45.260 45.119 45.225 45.052 45.205 44.985 48 46.223 45.961 46.187 45.879 46.167 45.792 49 47.186 46.729 47.149 46.626 47.129 46.514 50 48.149 47.393 48.112 47.264 48.091 47.122 TABLE III. COMPARISON OF SIMULINK AND RBNN RESULTS FOR FRONT OUTER WHEEL. δ (°) 13 14 15 V (km/h) Simulink Results RBNN Results Simulink Results RBNN Results Simulink Results RBNN Results 45 48.715 48.671 49.083 49.018 49.465 49.359 46 49.797 49.706 50.174 50.050 50.564 50.385 47 50.880 50.702 51.265 51.039 51.663 51.361 48 51.962 51.636 52.356 51.958 52.762 52.261 49 53.045 52.478 53.446 52.779 53.861 53.053 50 54.128 53.195 54.537 53.465 54.961 53.701 TABLE IV. COMPARISON OF SIMULINK AND RBNN RESULTS FOR REAR INNER WHEEL δ (°) 13 14 15 V (km/h) Simulink Results RBNN Results Simulink Results RBNN Results Simulink Results RBNN Results 45 41.783 41.752 41.514 41.474 41.241 41.184 46 42.711 42.645 42.436 42.355 42.157 42.052 47 43.640 43.507 43.359 43.203 43.074 42.883 48 44.568 44.320 44.281 43.997 43.990 43.657 49 45.497 45.059 45.204 44.715 44.907 44.350 50 46.425 45.697 46.126 45.327 45.823 44.933 Engineering, Technology & Applied Science Research Vol. 6, No. 6, 2016, 1288-1293 1291 www.etasr.com Yildirim et al.: Computation of the Speed of the Four In-Wheel Motors of an Electric Vehicle Using… TABLE V. COMPARISON OF SIMULINK AND RBNN RESULTS FOR REAR OUTER WHEEL. δ (°) 13 14 15 V (km/h) Simulink Results RBNN Results Simulink Results RBNN Results Simulink Results RBNN Results 45 47.899 47.856 48.115 48.053 48.331 48.233 46 48.963 48.874 49.184 49.066 49.405 49.237 47 50.028 49.853 50.254 50.035 50.479 50.192 48 51.092 50.769 51.323 50.935 51.553 51.071 49 52.156 51.595 52.392 51.738 52.627 51.845 50 53.221 52.294 53.461 52.405 53.701 52.475 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 50.806 km/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. 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 δ(°) Codesys Results (km/h) Simulink Results (km/h) Exp. Results (km/h) RBNN Results (km/h) n1 n2 n1 n2 n1 n2 n1 n2 0 50.807 50.807 50.803 50.803 50.803 50.803 50.805 50.805 1 50.577 51.050 50.582 51.054 50.562 51.054 50.575 51.048 2 50.360 51.306 50.361 51.305 50.351 51.285 50.359 51.305 3 50.158 51.576 50.160 51.577 50.139 51.536 50.157 51.575 4 49.969 51.859 49.969 51.858 49.959 51.848 49.968 51.858 5 49.794 52.155 49.798 52.160 49.778 52.149 49.793 52.154 6 49.633 52.465 49.637 52.461 49.607 52.431 49.632 52.463 7 49.487 52.787 49.486 52.783 49.496 52.742 49.486 52.786 8 49.355 53.123 49.356 53.124 49.346 53.084 49.354 53.122 9 49.239 53.471 49.235 53.476 49.225 53.446 49.238 53.470 10 49.137 53.834 49.134 53.838 49.134 53.828 49.136 53.832 11 49.051 54.209 49.054 54.210 49.044 54.159 49.049 54.207 12 48.980 54.598 48.984 54.602 48.954 54.572 48.978 54.596 13 48.926 55.001 48.923 55.004 48.903 54.963 48.922 54.997 14 48.888 55.417 48.883 55.416 48.873 55.386 48.882 55.412 15 48.867 55.847 48.863 55.848 48.843 55.808 48.858 55.839 TABLE VII. MEAN SQUARE ERRORS OF FOUR WHEEL SPEEDS Noise (dB) 30 dB Spread (σ) n1 n2 n3 n4 0.5 12.004 15.369 10.822 14.685 1 31.400 36.197 30.987 35.445 5 5.627 6.663 5.340 6.480 10 0.741 0.848 0.757 0.815 Spread (σ) 40 dB 0.5 11.987 15.346 10.807 14.662 1 30.909 35.763 30.484 35.006 5 5.397 6.369 5.094 6.205 10 0.323 0.368 0.320 0.364 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. Engineering, Technology & Applied Science Research Vol. 6, No. 6, 2016, 1288-1293 1292 www.etasr.com Yildirim et al.: Computation of the Speed of the Four In-Wheel Motors of an Electric Vehicle Using… Fig. 6. RBNN results of front inner wheel (40 dB). Fig. 7. RBNN results of front outer wheel (40 dB). Fig. 8. RBNN results of rear inner wheel (40 dB). Fig. 9. RBNN results of rear outer wheel (40 dB). Fig. 10. Difference between Simulink and RBNN results of front inner wheel. Fig. 11. Difference between Simulink and RBNN results of front outer wheel. 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. 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