Estimation and Control of Lateral Displacement of Electric Vehicle Using WPT Information

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1 Estimation and Contro of Latera Dispacement of Eectric Vehice Using WPT Information Pakorn Sukprasert Binh Minh Nguyen Hiroshi Fujimoto Department of Eectrica Engineering and Information Systems, The University of Tokyo Tokyo, Japan Emai: Department of Advanced Energy, The University of Tokyo Tokyo, Japan Emai: Department of Eectrica Engineering and Information Systems, The University of Tokyo Tokyo, Japan Emai: Abstract This work proposes a method to estimate atera dispacement of an eectric vehice from wireess power transfer information and vehices motion measurement through the Unscented Kaman fiter. By using the estimated atera dispacement as a feedback variabe, the trajectory of vehice is controed to the area of high performance transmission. The proposed method is vaidated by simuation and experiment. I. I NTRODUCTION Eectric vehices (EVs) provide the more preferabe environmenta benefits compared to combustion engine cars. Severa automobie manufacturers bring out the eectric vehices into a market. However, eectric vehices are not so attractive to ordinary consumers due to the probems of energy storage. Firsty, the eectric energy storage has ow energy density. An eectric vehice coud operate for a shorter distance with the weight of batteries same as the weight of gas in a combustion engine car. Secondy, batteries need a ong charging time. Thirdy, batteries have imited ifetime. They have to be changed in every 2-5 years. Finay, the battery price is expensive. As a resut, peope sti prefer purchasing combustion engine car. The above probems coud be soved if the wireess dynamic charging is appied for practica usage as the eectric vehices coud be empowered whie running on the road with embedded wireess power transmitter. The wireess power transfer (WPT) technoogy via couped magnetic resonance; which has high potentia to appy with EVs appication, was introduced in 2007[1]. The efficiency over 90 % is reached in stationary charging; however, the misaignment of transmitter coi and receiver coi causes ow couping coefficient. As a resut, ow transmission efficiency is obtained. Severa methods were proposed to improve transmission efficiency, for exampe, impedance matching[2] and oad optimization[5]. However, high couping coefficient is sti required for these methods. Therefore, the vehice trajectory shoud be controed to pass the high couping area. Severa sensors are used in vehice contro such as GPS, computer vision and aser. However, these sensors have some imitations and coud not directy detect the position of power transmitter. There are some papers proposing method for estimating position using WPT information. The paper [3] /15/$ IEEE Fig. 1. Schematic of eectric vehice with WPT receiver measured the refection coefficient vector from every transmitter in the system through vector network anayzer (VNA) and the position is estimated by mapping that vector in the database. However, this configuration is not suitabe for EV appication because of the price of VNA. Another paper[4] proposed a contro method to stop a vehice at the maximum power transfered point in one dimension according votage and votage derivative in secondary side. However, the exact position is not estimated and the position in two dimension shoud be considered in actua appication. This paper proposes method for estimating atera dispacement of the eectric vehice with respect to the aignment of transmitters by using information from WPT receiver side and onboard motion sensors. The estimated resut is appied for a feedback contro of atera dispacement to achieve high couping area. In this paper, the mode reated to this work is derived in Section II. The estimation appies Unscented Kaman fiter (UKF) and is vaidated by experiment in Section III. The feedback contro of atera dispacement empoys the estimated atera dispacement is described in Section IV. II. M ODEL OF V EHICLE WITH WPT R ECEIVER The schematic of an eectric vehice with WPT receiver is iustrated in Fig. 1. The parameters f and r is distance from the center of gravity to front whee axis and rear whee axis respectivey. The vehice motions considered in this paper is incuding ongitudina veocity vx, atera veocity vy and yaw 325

2 y = (vy + γan ) cos(ψ) vx sin(ψ) (3) Ψ = γ (4) C. Transfer Function From kinematic mode, yaw rate and side sip is expressed as: V γ = cos(β) tan(δ) (5) r β = tan 1 tan(δ) (6) Fig. 2. WPT equivaent circuit where δ is front steer ange. Assuming that the steering ange and side sip ange is sma, yaw rate and side sip ange coud be approximatey expressed as: vx δ (7) r β δ (8) Substituting these approximations to equation 3 and 4, the state space equation is expressed as: vx y 0 vx y (r + an ) = + δ (9) 0 0 Ψ vx Ψ γ The transfer function from front steering ange to atera dispacement is derived as: Fig. 3. Votage-dispacement characteristics rate γ. The motion in vertica gap from vibration, pitch and ro rotation is negect. The WPT receiver is mounted in front of a vehice with a ength an from the vehice s center of gravity. Two coordinate systems are considered in this work. The first system is reative position of a receiver with respect to singe transmitter. The measurement from WPT system is directy reated to this system. The second system is atera dispacement with respect to the aignment of transmitters. The goa of estimation and contro is concerned with this system. A. Differentia Equation of Reative Position This mode describes the reative position of one transmitter with respect to a receiver on vehice. Referring to Fig. 1, reative position is defined by dispacement from the receiver to the transmitter tr and orientation θ where the differentia equation is expressed as: tr = (vy + γan ) sin θ vx cos θ θ = (vy + γan ) cos θ + vx sin θ +γ tr (1) (2) B. Differentia Equation of Latera Dispacement This mode iustrates the atera dispacement y and heading ange Ψ of the receiver with respect to the aignment of transmitters. The motion in this system is expressed as: svx (an + r ) + vx2 Y (s) = δ(s) s2 (10) This transfer function wi be used in controer design. D. WPT Equivaent Circuit The WPT equivaent circuit is iustrated in Fig. 2. Under the assumption of perfect resonance, the votage across a constant oad on the receiver side Vr is expressed as [5] Vr = ω0 Lm RL Vs R1 RL + R1 R2 + (ω0 Lm )2 (11) where Vs votage source; RL resistive oad; R1 resistance in transmitter coi,; R2 resistance in receiver coi; Lm mutua inductance. As the WPT parameters Vs, RL, R1 and R2 are constant, the votage across oad in receiver side Vr reies ony on mutua inductance between a transmitter coi and a receiver coi. Additionay, the mutua inductance between spira circuar cois with definite dimension and vertica gap woud depend ony on dispacement between receiver coi and transmitter coi tr. The paper [6] proposes a method to cacuate mutua inductance between spira cois. In the experiment, the inner radius and outer radius of cois are 5.1 cm 15.0 cm respectivey. The vertica gap is 15 cm. 326

3 Fig. 4. Estimation process bock diagram Fig. 5. Vehice with wireess power transmitter aignment Fig. 6. Experiment setup The WPT system parameters are Vs = 3.54 V, R1 = 1.62 Ω, R2 = 0.74 Ω and R = 10.1 Ω. As a resut, the votage across oad Vr is a ony function of dispacement tr as shown in Fig. 3. The votage is drasticay dropped as the dispacement tr increases over 15 cm because the high couping between two cois coud be maintained up to this range. This votage-dispacement characteristic wi be directy used in measurement prediction in UKF on the next section. Euer method, the process equation, used in state prediction, is expressed as III. L ATERAL D ISPLACEMENT E STIMATION The bock diagram of atera dispacement estimation process is shown in Fig. 4. The reative position is estimated by utiizing vehice motion and measurement from receiver side through the Unscented Kaman fiter. Not ony the reative position to current transmitter is estimated, but the reative position to the previous transmitter is aso simutaneousy predicted. The atera dispacement is cacuated from these data. The Kaman fiter (KF) provides optima estimation according to process mode, measurement mode, input, measurement and initia state[7]. Because the motion equation of the vehice with receiver and the measurement in WPT receiver are noninear. Athough there are two we known agorithm for estimating in noninear system; Extended Kaman fiter (EKF) and Unscented Kaman fiter (UKF), the UKF coud provide more reiabe estimation especiay in case of the higher initia state error and higher speed. The UKF was proposed to estimate states in noninear system using accurate statistic approximation based on sigma points caed the unscented transformation (UT)[8] whie the EKF computes the statistics through first-order inearization. This is a fundamenta reason on why the UKF provides better estimation resut. A. Estimation of Reative Position to Singe Transmitter The estimation of reative position appies UKF agorithm. The state vector is reative position defined as x = [tr θ]t. The measurement is votage across constant oad in secondary side defined as y = Vr. The input is vehice motion defined as u = [vx vy γ]t. By discretizing Eq. (1) and (2) with forward tr,k+1 = tr,k + Ts ((vy,k + γan ) sin θk vx,k cos θk ) (12) (vy,k + γk an ) cos θk + vx,k sin θk θk+1 = θk + Ts + γk tr,k (13) The measurement equation, empoyed in measurement prediction, is directy appied a ookup tabe from votagedispacement characteristics in Fig. 3. The estimation woud be hed over unti the receiver votage higher than threshod votage Vth = 1.7 V is measured. Once the threshod votage is received, the estimator directy appies UKF agorithm. When the UKF is initiated, the initia state must be known. The initia dispacement tr,0 = 0.25 derived from votage-dispacement characteristics. Using ony one receiver, there is imited capabiity to detect the transmitter side. Therefore, it is necessary to make the assumption that the transmitter is on the right side of the vehice. In another word, the initia orientation θ0 is set to positive rea vaue. At this step, the estimated reative position woud converge to the actua vaue. Subsequenty, if the votage is under the threshod, the estimation woud rey ony on prediction according to Eq.(12) and (13). At this period, the receiver is eaving the current transmitter and going forward to the next transmitter. The UKF woud be appied again when the votage information of next transmitter is over the threshod. B. Cacuation of Latera Dispacement to Transmitter Aignment The atera dispacement is impossibe to be obtained from reative position of ony one transmitter. According to Fig. 5, if the reative positions of two transmitters are known, the atera dispacement can be computed by 327 y = tr,prev tr,cur sin (θprev θcur ) dtr (14)

4 (a) Longitudina veocity, vx Fig. 8. Contro system bock diagram C. Experiment Setup The WPT receiver is mounted in front of an eectric vehice COMS manufactured by Toyota Auto Body Co., Ltd. as shown in Fig. 6. The data from motion sensors and WPT receiver are coected and processed in rea time by an onboard RTinux computer. The interva between each transmitter is 2 m. The camera is aso mounted to record video which wi be processed for atera dispacement to compare with the estimation resut. (b) Latera veocity, vy D. Experiment The vehice moves aong the transmitters with the vehice motion in Fig. 7a, 7a and 7c. The measured votage in this experiment is shown in Fig. 7d. The votage over 1.7 V, shaded in red, is empoyed in update process in UKF. The estimation of atera dispacement is shown in the bue ine in Fig. 7e whie the back ine is the atera dispacement processed from computer vision. The estimation starts when the information from the second transmitter is received. The estimation resut is consistent with the atera dispacement computed by computer vision. There is error in estimation caused by the imperfect experiment setup. As mentioned at the beginning of this section, the correctness of estimation resut depends on the accuracy of measurement mode, input, process mode and measurement. The resistance of each transmitter coi is not exacty the same causing a sma difference in votage-dispacement characteristics. The vehice motion measurement is aso the cause of error. Aso, the atera dispacement is cacuated from the predicted reative position from the previous transmitter. The error coud aso occurs in this process. (c) Yaw rate, γ (d) Receiver votage, Vr (e) Latera dispacement, y Fig. 7. Estimation resuts IV. C ONTROL OF L ATERAL D ISPLACEMENT where (tr,prev, θprev ) reative position to previous transmitter; (tr,cur, θcur ) reative position to current transmitter; dtr interva between each transmitter. The estimator must continue predicting the reative position to the previous reference transmitter athough the measurement from next transmitter is avaiabe and the position to the next transmitter is estimated. By this way, the reative position to two transmitter is obtained by cacuating the actua atera dispacement according to (14). The feedback controer appies the estimated atera dispacement discussed in the previous section to cacuate a steering input to contro the vehice. The bock diagram of the contro system is shown in Fig. 8. A. Controer Design The PD controer is seected as a feedback controer in order that two poes of the cose oop coud be arbitrariy paced. The controer is designed based on the nomina mode in equation which is corresponding to these parameters: Vx = 0.8 m/s, = 1.2 m, r = 0.4 m. 328

5 (a) Trajectory (a) Longitudina veocity, vx (b) Receiver votage, Vr (b) Receiver votage, Vr (c) Steering ange, δ (c) Steering ange, δ (d) Latera dispacement, y (d) Latera dispacement, y Fig. 9. Contro simuation Fig. 10. Contro experiment Y (s) s = δ(s) s2 (15) The transfer function of the PD controer is CP D (s) = KP + KD s (16) If poes are paced at s = p1, p2, the gain is cacuated as (a + 1)p1 p2 (a + 1)(p1 + p2 + p1 p2 ) KP = and KD = b a vx (a n + r ) vx2 where a = and b =. The main criteria of contro design is sma maximum overshoot due to the imitation of the estimator whie the acceptabe setting time is around 4 seconds. B. Simuation In simuation, the vehice moves with a constant atera veocity at 0.8 m/s. The initia atera dispacement is 0.17 m whie the reference atera dispacement is 0.07 m. The gain Kp and Kd is 0.87 and 1.37 respectivey in order to pace the poes at s = 0.25, The controer woud start as soon as the estimated atera dispacement is avaiabe. The simuation resut is shown in Fig. 9. The vehice trajectory converges to the reference atera dispacement as show in Fig. 9a. The steering ange is shown in Fig. 9c. The controer is started when reaching the second transmitter. The actua atera dispacement and the estimated atera dispacement, used for feedback contro, is shown in Fig. 9d. The vehice coud achieve reference atera dispacement before reaching the third transmitter. C. Experiment The experiment resut is shown in Fig. 10. The controer starts when the atera dispacement estimator begins. The ongitudina veocity is shown in Fig. 10a which amost the same as speed used for controer design. The votage is shown in Fig. 10b. The steer command is shown in Fig. 10c making an effort to contro the vehice dispacement to the reference. The red ine is the designed steering ange whie the bue ine is the actua steering ange. The atera dispacement is 329

6 shown in Fig. 10d. The back ine is the reference atera dispacement which is 0.07 m. The bue ine is the atera dispacement processed from vision sensor whie the red ine is the estimated atera dispacement. The resut show that it coud amost achieved the reference atera dispacement before reaching the third transmitter. Athough there is error in the estimation with the same reason mentioned in the previous section, the controer is sti abe to contro the vehice. V. C ONCLUSION The atera dispacement estimation is proposed based on UKF and verified by experiment. The estimated resut is appied to contro the vehice. The error occurs mainy from the inaccurate measurement mode because of the imperfect in experiment setup. However, goa of controing the vehice to high couping area is achieved. Athough this experiment is performed at ow speed due to safety reason and imited experiment setup, it proves the concept of using WPT information for contro the vehice. R EFERENCES [1] A. Kurs, A. Karais, R. Moffatt, J. D. Joannopouos, P. Fisher, and M. Sojai, Wireess power transfer via strongy couped magnetic resonances, Science, vo. 317, no. 5834, pp , [2] T. C. Beh, M. Kato, T. Imura, S. Oh, and Y. Hori, Automated impedance matching system for robust wireess power transfer via magnetic resonance couping,ieee Transactions on Industria Eectronics, vo. 60, no. 9, pp , [3] S. Nakamura and H. Hashimoto, Basic study of magnetic resonance couping-based distance sensor with adjustabe sensing range using active quaity factor contro, 2013 IEEE/SICE Internationa Symposium on System Integration (SII), pages , Dec [4] P. Kotchapansompote, Y. Wang, T. Imura, H. Fujimoto, and Y. Hon. Eectric vehice automatic stop using wireess power transfer antennas. In IECON th Annua Conference on IEEE Industria Eectronics Society, pages , Nov [5] M. Kato, T. Imura, and Y. Hori, New characteristics anaysis considering transmission distance and oad variation in wireess power transfer via magnetic resonant couping, 2012 IEEE 34th Internationa in Teecommunications Energy Conference (INTELEC), pp. 1-5, [6] J. Acero, C. Carretero, I. Lope, R. Aonso, O. Lucia, and J. Burdio, Anaysis of the mutua inductance of panar-umped inductive power transfer systems, IEEE Transactions on Industria Eectronics, vo. 60, no. 1, pp , [7] R. E. Kaman, A new approach to inear fitering and prediction probems, Transactions of the ASME-Journa of Basic Engineering, vo. 82, no. Series D, pp , [8] S. Juier and J. Uhmann, Unscented fitering and noninear estimation, Proceedings of the IEEE, vo. 92, no. 3, pp , Powered by TCPDF (