This thesis presents the algorithmic solutions of the nonlinear vehicle lateral dynamic control problem based on state observer, which has been validated both in a simulation environment and real-time. Different vehicle body slip angle (β) estimation methodologies are proposed and checked in the study, by combining the model-based estimation with adaptive mechanisms to form the adaptive nonlinear observers.

It has been commonly recognized that electric vehicles (EVs) are inherently more suitable to realize active safety stability control over conventional Internal Combustion engine Vehicles (ICVs). In EVs, the motor torque can be measured and controlled accurately; and in-wheel motors can be installed in each EVs' rear and front tires. Based on these structural merits, vehicle motion can be stabilized by additional yaw moment generated as a result of the difference in tire driving or braking forces between the right and left side of the vehicle, which is so called 'Direct Yaw-moment Control' (DYC). By applying Model Matching Control, the yaw moment optimal decision can be derived from the deviations of the state feedback compensator of body slip angle β and yaw rate γ from their desired values. Since sensors for the direct measurement of β are very expensive, the construction of an observer for its estimation is desirable.

Generally, such observer is based on the state equations derived from the vehicle dynamics. However, the implementation of these techniques is still difficult since the vehicle dynamics are highly nonlinear, especially forβ. The main nonlinearity of vehicle dynamics comes from the tire force saturation imposed by the limits of tire adherence, which makesβ response change considerably if the vehicle is cornering much more than usual. In other words, the model structure or model parameters should vary according to the different operating regimes for a more practical controller design. In addition, the nonlinear nature of vehicle dynamics is further complicated by the influence of the characteristics of whole chassis elements (tires, suspensions and steering system). It is hard to determine the physical model parameters theoretically.

In chapter 1 of the thesis, the basic principles and research situations of state observer-based stability control systems are described. Then the development and motion control studies of in-wheel-motored vehicles are introduced. In chapter 2, the vehicle lateral dynamics are represented by introducing tire and vehicle models with different complexity. The discussion of vehicle lateral dynamics is initiated by explaining fundamental concepts and introducing linear tire and vehicle models, which provide a basic idea of what states and parameters of a vehicle are important for vehicle dynamics control. The identification methods for the key parameters for the observer purpose are described. The analysis is also extended to the nonlinear handling characteristics according to the vehicle dynamic models. In chapter 3, the basic ideas of state observer theories are introduced, including the linear, nonlinear and fuzzy observers. The algorithms of recursive Kalman Filter equations and the algorithms of recursive least-squares (RLS) for parameter identifications and adaptive observer design are also explained. In chapter 4, different methodologies are applied for body slip angle observation, including the observer with nonlinear tire model, the hybrid observer based on fuzzy logic modeling and the adaptive observer by combining the kinematic estimations. The performance of the different methodologies and sensitivity on the modeling error are checked under the qualitative analysis and evaluated by simulations quantitatively. In chapter 5, the experiments of proposed observers are conducted in the In-Wheel-Motor electric vehicle "UOT Electric March II". The configuration of experimental systems in the test EV is introduced and the experimental results are shown. In chapter 6, the estimated vehicle states are used in the DYC system to modify a vehicle's handling characteristics through a full state feedback controller, which implies applicability of the proposed observers to a practical vehicle controller.

Based on the studies, the algorithmic solutions of vehicle state observer considering the nonlinear vehicle lateral dynamics are presented and evaluated.

The conventional linear observer (based on linear 2-DOF vehicle model) for body slip angle estimation can not eliminate the estimated β error as expectation especially when vehicle in limit condition, in which the observation of β is vital for vehicle stability control. So the author has been trying to improve it by combining with the kinematic estimation (integration estimation) and on-line cornering stiffness identification (Figure 1). Kalman Filter theory is adopted for the fusion of the information from model-based estimation and the kinematic estimation, by determining the Kalman Filter feedback matrix L related to the tuning of covariance matrices of process (vehicle model) noise and measurement noise. The influence of sensor bias on the integration results can be minimized, by resetting the integration value when getting to the steady states by the model-based observer. On the other hand, the body slip angle estimated through the kinematic approach during transient maneuvers is used to correct tire cornering stiffness in order to take into account changes in tires' properties. Some improvement has been shown in the experimental results, but still with some error for the delay of tire cornering stiffness identification algorithm. Further work will be on the improvement of on line RLS algorithm to make higher responsibility of cornering stiffness identification.

The robustness over tire cornering stiffness error is the main advantage of the proposed nonlinear observer over the linear ones, although a relative simplified form of function is adopted to describe the nonlinear tire characteristics. The simulation results also show the estimate β values are more sensitive to the road surface friction coefficient μ errors, which confirm the importance of μ identification to ensure the observer's accuracy. However, compared with linear observer, the nonlinear functions in the nonlinear observer are realized in the ECU as long mathematical sums. This over-complication is unnecessary, especially in the region where the tire characteristic is linear. Another problem in such observer is the fixed form of functions applied in the nonlinear tire model, which weakens the ability of modeling adaptation and makes the modeling of vehicle dynamics can not consider the real conditions including the characteristics of whole vehicle chassis.

The study on hybrid observer pays the main attention to an algorithmic solution of the nonlinear vehicle dynamic control problem, as well as the real-time control aspect. In the first step of the hybrid observer design, to deal with the difficulties associated with nonlinearity modeling, as well as to make use of the linear observer advantages such as simplicity in the design and implementation, the nonlinear vehicle dynamics are represented by Takagi-Sugeno (T-S) fuzzy models. These modeling techniques are considered appropriate for on-line control system design (linear 2-DOF vehicle model). In the next step, a fuzzy-based modeling approach is used to get a hybrid-like vehicle model which is calculated as a weighted sum of the outputs of two local linear models. For practical applications, parameter identification is conducted experimentally. An adaptation mechanism of the fuzzy membership functions has been included to make the model fit different running conditions and road friction changes. The membership functions of the weighting factors are chosen to be dependent on lateral acceleration and road friction coefficient. The two local observers are based on local linear tire models, which inherently leads to a relatively simple design, have been combined into a single overall observer by means of fuzzy rules (Figure 2). Furthermore, the nonlinear global system results show high β estimation capabilities and good adaptation to changing road friction.

A series of simulations are performed to evaluate the effectiveness of the proposed β observer when incorporated into a DYC-based control scheme. The estimated vehicle states are applied as feedback signals to a stability controller, which virtually modifies a vehicle's handling characteristics. We have shown that the designed controller rely critically on the estimated value ofβ and further research and effort will be devoted into the implementation of a full dynamic stability control of the electric vehicle "UOT MARCH II".

The future work will also focus on the theoretical analysis of the stability and convergence of proposed observers. In addition, based on the analysis, the adaptive laws will also be improved and verified.

本論文は,Body Slip Angle Estimation for Stability Control of Electric Vehicle(電気自動車の安定性制御のための車体すべり角推定に関する研究)と題し,車体運動制御における重要な状態変数である車体すべり角βの推定に基づく二次元車両制御の提案を行い,車両を操縦限界範囲内に制御することによって,車両運動の安定性を向上する技術を研究した結果をまとめたもので,英文で記述された全7章からなる。

今後電気自動車がさらに普及,進展していくためには電気自動車の駆動源である電気モータに注目する必要がある。電気モータは内燃機関式自動車に対して次のような優位点を持つ。すなわち,速い応答速度を利用した高度な制御が可能になること,出力トルクの大きさが正確にわかるので,タイヤと路面の間に生じる駆動力や制動力の推定がリアルタイムで可能になることなどであり,路面状態を考慮した全く新しい制御が実現できることを意味している。また,モータの小型化にともなって分散配置が可能になり,駆動輪の完全独立制御が実現できる。例えば左右輪の間に制駆動力を生じさせて車両運動を制御することができる。

本論文で提案する制御は車両状態を望みのモデルに追従させることを目指したもので,ヨーレートγと車体すべり角βの状態フィードバック制御により実現する。βは重要なパラメータであるがその測定には,路面を画像処理する高価格のオプティカルセンサが必要であるため現実的ではなく,簡単なヨーレートセンサや加速度センサから推定する必要がある。しかし,従来の手法はリアルタイム性,モデルエラー,非線形領域での推定などに問題があり,本論文では,これらの問題を解決する新しい推定方法を提案している。

第1章は序論であり研究の背景などを述べている。

第2章「Vehicle Lateral Dynamics(車体縦方向の運動学)」では,車両運動のメカニズムと発生する力を用いた車両二次元運動の方程式を説明している。

第3章「State Observer Theories(状態オブザーバの理論)」では,状態変数の推定器や制御器に利用するために,近似を行った線形状態方程式を導き,各種パラメータの推定と制御の必要性について述べている。

第4章「Methodologies of Vehicle Body Slip Angle Observation(車体すべり角の推定手法)」では,新しい車体すべり角βの推定方法を提案している。具体的には,タイヤの非線形飽和特性を表すモデルに基づく非線形オブザーバ,ファジー(Fuzzy)推論を用いたハイブリッドオブザーバを提案している。

第5章「Experimental Studies of Vehicle State Observers(車体の状態オブザーバの実験的検討)」では,モータのトルク値から路面状態とコーナリングパワーを推定する適応オブザーバを提案し,非線形領域でも正確にβが推定できることを示している。

第6章「Stability Control Based on State Observer(状態オブザーバにもとづく安定化制御)」では,ヨーレートと車体すべり角の推定状態をもとにした制御系を構成し,シミュレーションおよび実験用に製作した電気自動車(東大三月号II)を用いた実験を行い,本手法が車両の横方向運動の安定化に大きく貢献することを検証している。

第7章は結論である。

付録として,本論文で重要な役割を果たした「Modeling of Tire Characteristics(タイヤダイナミクスのモデリング)」を付けている。

以上これを要するに,本論文は,電気自動車の車体運動制御における重要な状態変数である車体すべり角βの推定を行ういくつかのオブザーバを提案し,詳細な数値計算と,実際に製作した実験用電気自動車を用いた走行実験によって,車両運動の安定性向上に大きく寄与できることを示したもので,電気工学,自動車工学,制御工学上,貢献するところが少なくない。

よって本論文は博士(工学)の学位請求論文として合格と認められる。