車輛系統之轉向分析與控制設計

Abstract

本論文主要在探討車輛系統之穩定化設計及狀態跟隨設計。近幾年來，智慧型車輛系統的研究吸引了許多學者的興趣，尤其是在定速巡航駕駛方面的研究，更是有許多相關的論文成果發表。本論文即在探討定速巡航駕駛時，車輛系統所會遇到的穩定性問題。假設車輛行駛在固定的速度下，則可獲得車輛轉向系統之二階非線性動態方程式。在已發表的文獻中，鞍點分叉(saddle-node bifurcation)現象已在車輛系統中被觀察到。此一分叉現象不僅會造成系統操作上的不穩定，且可能會讓車輛失控打滑甚至翻車。因此，本論文提出利用線性與非線性控制法則來設計車輛轉向系統之穩定化控制器，以增強車輛系統之操控性。 在穩定化控制器設計方面，我們所提出之車輛模式分叉點的可控性為第一次在已知發表文獻中被探討。接著，我們利用狀態迴授控制法則(state feedback control law)設計轉向系統之穩定化控制器，此法則使用Jacobian矩陣來線性化非線性系統。為了增強系統的效能，我們進一步提出非線性控制器設計。首先，系統動態方程式被分為affine-type nominal系統和其餘項等兩部分，如此，已知之標準迴授線性化(feedback linearization)法則即可直接應用在此nominal系統之控制器設計，而系統餘項則應用Lyapunov再設計方法來作補償驗證。此外，我們也採用平滑模式控制(sliding mode control)法則設計車輛系統的適應性控制器，並利用Lyapunov穩定性判斷準則推導驗證，以確保整體系統在分叉點附近之操作穩定性。同時，藉由平衡點之參數化分析，本論文也探討控制器之增益值大小對車輛轉向系統特性之影響。在狀態跟隨設計方面，我們採用平滑模式控制法則使車輛系統狀態能夠跟隨預先設計好的軌跡，並透過數值模擬的結果驗證所提出控制器設計之實用可行性。

In this dissertation, issues of stabilization designs and path-following design for vehicle's lateral dynamics are presented. In the recent years, the study of intelligent transportation systems has attracted considerable attention, especially the steering control of vehicle under cruise control mode. Based on the assumption of constant driving speed, a second-order nonlinear lateral dynamical model is obtained. It is observed that saddle-node bifurcation will appear in vehicle dynamics with respect to the variation of the front wheel steering angle, which might result in spin and/or system instability. In order to possibly prevent the occurrence of such an instability, we propose linear and nonlinear stabilization designs for vehicle system. The controllability of this vehicle dynamics at the saddle-node bifurcation point is first discussed. This leads to the design of a state feedback control law for system stabilization. To enhance the performance of linear control design, nonlinear control schemes for vehicle's lateral dynamics are discussed. The vehicle dynamics at the saddle-node bifurcation point is decomposed as an affine nominal model plus the remaining term of the overall system dynamics. Feedback linearization scheme is then employed to construct the stabilizing control law for the nominal model. To cover the remaining term of system dynamics, Lyapunov redesign is adopted and added to feedback linearization scheme. After that, sliding mode control method is applied to design the robust control law for vehicle dynamics. The stability of the overall vehicle dynamics at the saddle-node bifurcation point is guaranteed by applying Lyapunov stability criteria. Parametric analysis of system equilibrium for an example vehicle model with proposed control designs is also obtained to classify the regime of control gains for potential behavior of vehicle's dynamical behavior. In addition to stabilization designs for vehicle's lateral dynamics, we also design the path-following control law for vehicle system by applying sliding mode control method. Numerical simulations for an example model demonstrate the effectiveness of analytical results.