基於Brush輪胎模型對個別輪胎之縱向剛度與摩擦係數之疊代估測法則

Abstract

隨著車輛的普及，汽車已成為人類生活的一部份，如何提高車輛的安全性與操控性一直是國內外汽車大廠致力研發的重點。而輪胎與路面間摩擦係數的資訊對於實現車輛主動安全系統來說十分重要，若能即時得到該資訊，進而用於車輛動態系統控制，就能提高行車安全，故本研究提出一套估測系統已有效且即時地獲得車輛各別輪胎與路面間的摩擦係數資訊。 本研究在離散時間系統下，利用未知參數較少的Brush tire model設計兩套能夠即時個別估測車輛四個輪胎與路面間摩擦係數之方法。且在輪胎縱向剛度未知的情況下，利用縱向力估測誤差逐步收斂至零的條件，分別設計摩擦係數與縱向剛度兩個估測器，並將兩估測器對接組成循環估測系統。最後，再以較為貼近真實輪胎之Magic formula輪胎模型進行模擬，並且探討不同方法間之估測效果。本研究刻意在設計估測器與模擬驗證時使用不同的輪胎模型，以測試所提出之估測演算法對輪胎模型不確定性的穩健性。 本研究提出兩套估測方法，皆以縱向力估測誤差作為設計之依據，而方法一為單點估測，顧名思義就是在每個取樣時間點取當時的資料加以計算之；方法二為多點估測，則取多個時間點的資料進行分析。由於設計上所利用的資料量與假設條件不同，故兩種方法適用的行車狀況也不盡相同。由模擬結果可知，在直線行駛的模擬中，定加/減速度時，單點估測方法能有效估測摩擦係數於相同路面之情況，但在split-μ路面上的估測仍有待加強；在變加速度且路面相同的狀況下，單點估測方法也有不錯的估測效果，但此方法需要較長的計算時間；而多點估測方法雖然有參數估測誤差，但在split-μ路面上其估測效果仍相對可靠。然而，在同時轉向與加速的情況下，兩方法的估測效果都仍有待加強。

Real-time estimate of the tire-road friction coefficient is an important information for vehicular active safety systems to achieve better performance such that safe driving is guaranteed. In this thesis, we propose two iterative estimation schemes for each driving wheel based on the modified brush tire model which is suitable for the combined longitudinal and lateral motion and consists of only two parameters, i.e. the longitudinal stiffness and the tire-road friction coefficient. Two separate discrete-time estimators are designed to estimate one parameter at a time, assuming the other is known. Then these two estimators are connected together to perform iterative estimation for both parameters. For each estimator, two design strategies are considered. One is called the one-point estimation which is designed based on the information of one sampling time, and the other is called the three-point estimation which is based on the information of the three most recent samples. The performance is verified by simulations of a 14-DOF complex nonlinear vehicle model and magic formula. We use different tire models to verify the robustness of tire model uncertainty for our algorithms. Simulations for various driving scenarios are carried out, including forwarding acceleration, simultaneous acceleration and turning, and split-μ tests. The results show that the proposed algorithms are able to correctly estimate the tire-road friction coefficient of each driving wheel when the vehicle is accelerating/decelerating along a straight line. However, the performance deteriorates whenever the vehicle is under a combined motion of turning and accelerating/decelerating.