臺灣博碩士論文加值系統

本論文以H∞控制方法來設計撓性車體及輪軸之1/2車主動式懸吊系統(Active suspension)，其中包含兩個主要部分：即系統動態建模與控制。首先，以漢米頓原理(Hamilton’s principle)得到撓性車體及輪軸之動態方程式及邊界條件，再利用模態加總法(Mode summation)求得撓性梁上任一點之位移，最後以拉格朗日方程式(Lagrange’s equation)求得1/2車主動式懸吊系統之二階常微分方程式並以狀態方程式(State equation)表示。在控制器設計上，先分析系統頻域及時域特性，以H∞控制理論根據頻域特性設計達到時域要求之控制器。模擬結果顯示，H∞控制方法比傳統被動式懸吊系統更有效降低車身之振動，亦可增進車輛行駛的安全性和舒適性。
撓性車輛為一連續性分部參數系統(Distributed parameter system)，在控制系統設計中將連續系統化為無限多之單自由度系統組合表示之，如此一來便不會有因模態截斷法設計造成的控制或觀測超溢(Control and observation spill over)的問題發生，且只需一組感測器及致動器即可有效抑制系統振動，較一般文獻所提的分佈致動器法更能在實際運用上實現。在本論文中各懸吊系統採用一組感測器與致動器分離之控制器做設計，經由模擬結果顯示，此方法確實有效消除系統無限多個模態之振動以及穩態誤差，並且減少干擾對撓性1/2車懸吊系統的影響。

The development and implementation of controlled suspension systems to provide higher levels of ride isolation and road holding has spurred a great deal of interests among control researchers. This thesis is concerned with some control issues for a flexible one-half car suspension system. It includes system mathematical modeling, dynamic analysis, and controller design. A realizable actuator and a sensor are applied to design the control system. First, Hamilton principle is used to derive the equations of motion and boundary conditions of the suspension system. Then, the displacement at any point along the vehicle body and wheel axle can be derived from Mode summation method. Next, the Lagrange's equation is used to formulate the second order equation of the active suspension system and represented in state space form. It is well known that, we can obtain low oscillation and passengers can feel not only the comfortable ride quality but also the safety of the vehicle. The H∞ performance is used to measure the ride comfort such that more general road disturbance can be considered.
Many control system design methods for a flexible manipulator are either based on reduced order model or require distributed actuators, which are not available in reality. Because the control design and the computer simulation are based on the concept of the infinite dimensional system, there will not “control and observation spillover problems” happen and computational error concern which are encountered in most of the control of flexible structures. In this thesis, by using a discrete set of actuator and sensor without involving truncation of the higher frequency modes, it can be seen from computer simulation, the designed control system for a flexible one-half car suspension system can not only stabilize all the vibration modes but also can eliminate the steady state errors.

目錄
摘要I
AbstractII
誌謝III
目錄IV
圖表索引VI
第1章緒論 1
1.1前言1
1.2懸吊系統的種類2
1.3研究動機與目的6
1.4文獻回顧7
1.5研究流程10
第2章車輛系統之數學模式推導11
2.1撓性1/2車模型之建立11
2.2撓性車體及輪軸動態方程式推導13
2.2.1偏微分方程式堆導15
2.2.2特徵值及特徵函數16
2.2.3動態方程式23
2.31/2車懸吊系統之運動方程式25
第3章H∞控制理論29
3.1範數29
3.2一般化控制問題32
3.3廣義的控制問題35
3.4求解H∞控制問題37
3.5H∞控制的強健穩定與性能41
3.5.1小增益定理42
3.5.2乘積不確定性42
3.5.3加法不確定性44
3.5.4靈敏度函數、互補靈敏度函數及控制能量函數45
第4章控制器設計與電腦模擬50
4.1車輛行駛乘舒性50
4.2混合靈敏度問題51
4.3H∞控制器設計52
4.3.1權重函數選取53
4.3.2懸吊系統模擬56
4.4模擬結果與討論70
第5章結論與未來研究方向73
5.1結論73
5.2未來研究方向74
附錄一80
附錄二83

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