IIC , MEC 電気自動車におけるロールおよびピッチモーメントオブザーバを 用いた規範モデル追従制御 落直哉 藤本博志 堀洋一 東京大学 Model Following Control with Roll and Pitch Moment Observer for El
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1 IIC 3, EC 3 電気自動車におけるロールおよびピッチモーメントオブザーバを 用いた規範モデル追従制御 落直哉 藤本博志 堀洋一 東京大学 odel Following Control with Roll and Pitch oment Observer for Electric Vehicle Naoya Ochi, Hiroshi Fujimoto, Yoichi Hori (The University of Tokyo Abstract In this paper, we propose a reference model following control with roll and pitch moment observer in electric vehicle with four in-wheel motors. The proposed method is built by roll and pitch control systems based on the observers, it is more robust against parameter variations of the plant and disturbance. In addition, the proposed method can follow the optimum angle command by using reference model regardless of the state of the vehicle. The effectiveness of the proposed method is verified by simulation and experimental results. キーワード 電気自動車 ロール制御 ピッチ制御 インホイールモータ アンチダイブ力 規範モデル追従制御 (electric vehicle, roll control, pitch control, in-wheel motors, anti-dive force, model following control. 序 論 電気自動車 (EV: Electric Vehicle は動力源がモータであ るため 車両運動制御の観点において 3 つの優位点を持つ 3 つの優位点とは モータのトルク応答が高速かつ正確で あること モータに流れる電流によりモータの発生トルク が正確に測定可能であること インホイールモータ (IW を用いることでモータを分散配置し独立駆動可能であるこ とである ( これらの利点を生かして 電気自動車の運動制御につい て数多くの研究が発表されている ( ( また 車体の姿 勢制御としてアクティブサスペンションを用いた姿勢制御 や荷重制御が研究されてきたが これらの手法ではアクチュ エータが増えてしまう ( ( その一方で 正負のアンチ ダイブ力を用いることにより駆動モータだけで姿勢制御や 荷重制御が可能である (3 ( ここで 正負のアンチダイ ブ力とはサスペンションの構造により車輪に駆動力が働い たときに車体の上下方向に働く力である IW 車は車載 モータ車に比べ正負のアンチダイブ力を大きく出すことが 可能である 車両の 3 軸周りの回転運動はヨーイング (ヨー角 ロー リング (ロール角 ピッチング (ピッチ角 がある ロール とは 自動車が旋回走行中に横加速度により旋回外側に車 体が傾くように発生し 同時に x 軸周りのモーメントが加 わることにより起きる車体のロール軸周りの運動である また ピッチとは自動車が直線走行中に駆動力または制動 力をかけると前後加速度が発生し 同時に y 軸周りのモー メントが加わることにより起きる車体の重心点周りの運動 である これらのロール角やピッチ角が大きく発生すると 乗り心地が悪くなるだけでなく 挙動が乱れやすくなりステ アレスポンスやブレーキ性能も悪化してしまうため ロー ル角やピッチ角を抑制する必要がある 特に これらが同 (a FPEV-Kanon Fig. (b In-wheel motor Experimental vehicle 時に発生する減速旋回時では挙動が非常に乱れやすく 事 故につながりやすい 著者等は四輪独立駆動の電気自動車 における 正負のアンチダイブ力を用いた定常円旋回中の ロール角制御 (7 減速旋回時を想定したロールとピッチの 同時制御 ( を提案した しかし これらの制御系では各指 令値として一定角度を入力するだけであった 文献 ( で は無理な角度指令値を入力することで駆動力が飽和し 実 験にて大きな有効性を示すことが出来ていない そこで 本稿では自動車の減速旋回時において 規範モ デルを用いて各角度指令値を生成し追従させる 規範モデ ル追従制御を提案する 指令値の生成に規範モデルを用い ることで より適切な指令値となり 無理の無い駆動力の 配分が可能になると考えられる また ロールモーメント オブザーバ (RO および ピッチモーメントオブザーバ (PO を構成することにより パラメータ変動等を外乱と して一括補償することでロバスト性の向上が期待できる 提案法の減速旋回時のロール角とピッチ角の抑制および指 令値への追従 パラメータ変動に対するロバスト性をシミュ レーションにて示す また 実験にて提案法の有効性を確 認する. 実験車両 本稿では 実験車両としてアウターロータ型インホイー /
2 Table Parameters of FPEV Kanon Vehicle weight( [kg] Wheelbase(l.7 [m] Distance between front axle and center of gravity(l f.999 [m] Distance between rear axle and center of gravity(l r.7 [m] Front wheel tread width(d f. [m] Rear wheel tread width(d r. [m] Front wheel inertia(j ωf. [kg/m ] Rear wheel inertia(j ωr. [kg/m ] Radius of the tire(r. [m] Î Î Æ Ü Æ ««Ð Ö Ý Ð Ý Ö Ð Æ Æ Ö Ö Ð Î «Ý «ÖÐ ÖÖ Ð Ö yall h g a x + y ( F x x xall y yall F xfl F xfr F xrl F xrr β γ h s h g a y a x d f d r u zfl u zfr u zrl u zrr F x Fig. 3 ÝÖÐ Fig. Ö ÝÖÖ Vehicle model u zfj F xfj tan ϕ f ( u zrj F xrj tan ϕ r (7 F zfj F zrj F zfj N f a x h ρ f a y h u zfj l f + l r d f ( Fig. 3 Anti dive force Fig. Half car model F zrj N r + a x h ρ r a y h u zrj l f + l r d r (9 FPEV Kanon Nm 3 Nm Fig. (a Fig. (b Table 3. 3 Fig. (9 F x F xfl + F xfr + F xrl + F xrr ( x d f ( u zfl + u zfr + d r (u zrl u zrr G fl F xfl + G fr F xfr + G rl F xrl + G rr F xrr ( xall h s a y + x (3 y l f u zfl l f u zfr + l ru zrl + l ru zrr H fl F xfl + H fr F xfr + H rl F xrl + H rr F xrr ( j l, r ϕ f ϕ r N f N r a x h l f l r ρ f ρ r 3 x xall ( I r s + C r s + K r θr ( I r C r K r xall θ r θ r I r s xall + C r s + K r (h I r s s a y + x ( + C r s + K r /
3 Fig. Refernce model Fig. Block diagram of proposed method Plant Table Refernce model Parameters of Reference model I C K Roll Pitch Roll Pitch Fig. 7 Block diagram of RO/PO 3 3 ( Fig. yall ( I p s + C p s + K p θp ( I p y C p K p xall θ p θ p I p s yall + C p s + K p (h I ps g a x + y (3 + C ps + K p Table Plant. Fig. Fig. Reference odel F x x y Fig. DFDL(Driving Force Distribution Law Fig. z ij θ r θ p ( ( ( θr I rns xall ( + C rns + K rn θp I pns yall ( + C pns + K pn Table Reference model V δ f ( ( yall h ga xn ( yall h s a yn (7 a yn (V δf ( l θ r θ p (RO (PO ( (3 ( Ir s + C r s + K r θr h s a y + x + xd (9 ( Ips + C ps + K p θp h ga x + y + yd ( 3/
4 Table 3 Parameter variations I C K Roll w/o variations Pitch w/ variations Roll.. 3. Pitch xd yd Fig. 7 xad h s a y C r θ r K r θ r + xd yad h g a x C p θ p K p θ p + yd Fig. 7 I n y I r θr xad + x ( I p θp yad + y ( F x Fig. 7 DFO(Driving Force Observer x y ( ( Fig. 7 Roll and Pitch oment Calculator 3 Driving Force Distribution Law : DFDL DFDL F x x y x y RO PO DFDL F xfl F x G fl G fr G rl G rr F xfr H fl H fr H rl H rr x d f d f dr dr F xrl F xrr y z (3 z T rf d. (Fig. C ( V s F x ( w v rad/s (3 PD (Fig. C C 3 ( (3 w roll rad/s w pitch rad/s w ro rad/s w po rad/s PID PID w roll rad/s w pitch rad/s Table 3 V km/h t s N t s.3 rad Fig. Fig. Fig. (a Fig. 9(a Fig. (b Fig. 9(b Fig. (c Fig. 9(c Fig. (d Fig. 9(d Fig. (a (d Fig. 9(a (d. V m/s /
5 x 3 x 3 (a Velocity (b Roll angle (c Pitch angle (d Driving force Fig. Simulation results of conventional method(w/o parameter variations x 3 x 3 (a Velocity (b Roll angle (c Pitch angle (d Driving force Fig. 9 Simulation results of proposed method(w/o parameter variations x 3 x 3 (a Velocity (b Roll angle (c Pitch angle (d Driving force Fig. Simulation results of conventional method(w/ parameter variations x 3 x 3 (a Velocity (b Roll angle (c Pitch angle (d Driving force Fig. Simulation results of proposed method(w/ parameter variations N.9 rad w roll rad/s w pitch rad/s w ro rad/s w po rad/s Fig. Fig. 3 Fig. (a Fig. 3(a Fig. (b Fig. 3(b Fig. (c Fig. 3(c Fig. 3(b Fig. 3(c Fig. (d Fig. 3(d 7 s /
6 .... x 3.. (avelocity (broll angle (cpitch angle (ddriving force Fig. Experimental results w/o control.... x 3.. (avelocity (broll angle (cpitch angle (ddriving force Fig. 3 Experimental results w/ control 7. NEDO ( ID:A7d 7 Y. Hori: Future vehicle driven by electricity and control research on four-wheel-motored UOTElectric arch II, IEEE Trans. on Industrial Electronics, Vol., No., pp. 9 9, K. Kawashima, T. Uchida,. Tomizuka, Y. Hori: Rolling stability control of in-wheel electric vehicle based on two-degree-of-freedom control, The th IEEE International Workshop on Advanced otion Control, pp. 7 7, 3 S. Sato H. fujimoto: Proposal of pitching Control for Electric Vehicle with In-Wheel otor, IEE of Japan Technical eeting Recoard, IIC 7, pp. 7, 7 E. Katsuyama: Decoupled 3D oment Control by In- Wheel otor, JSAE Annual Congress(Spring, No.3, pp., Y. Hanamura, K. Fujita, Y. Araki,. Oya, H. Harada: Control of Vehicle aneuverability and Stability of Wheeled Vehicle by Active Suspension Control with Additional Vertical Load Control, The Japan Society of echanical Engineers. C No. 9 9, pp. 3 3, 99 S. Buma H. Satou T.Yonekawa T. Ohnuma K. Hattori. Sugihara: Synthesis and Development of the Avtive Control Suspension, Transactions of the Japan Society of echanical Engineers. C Vol.7 No. 3 pp. 7 3,99 7 N. Ochi H. Fujimoto, Y. Hori: Roll Angle Control using Positive and Negative Anti-dive Force for Electric Vehicle with Four In-wheel otors, IEE of Japan Industry Applications Society Conference, pp. 33 3, N. Ochi H. Fujimoto, Y. Hori: Roll and Pitch Control using Positive and Negative Anti-dive Force for Electric Vehicle with Four In-wheel otors, Transportation and Logistics Conference, pp. 9 9, 9, (3 /
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