臺灣博碩士論文加值系統

在此研究中，使用Lagrange 方程式推導運動方程和其限制條件，在滾動不滑動的條件下，每一個腳踏車輪都有兩個完整和非完整限制條件。使得方程式具有DAE型式。此運動模型已藉由對照基準模型和實驗結果而被驗證其成效。
為了解運動方程式中的DAE並確保腳踏車模擬系統中數學的準確性，需要討論其限制條件處理的計算方法。基本上有兩種方法，第一為座標簡化法(coordinate reduction)，第二為內嵌法(embedding method)。另外三種數值法，Baumgarte，後穩定法(post-stabilization)和SMC後穩定法，在此用來修正並提升解題效率。上述方法的成效將被應用，並完成比較其計算時間和數值精確度之結果。
當腳踏車改變方向時，騎乘者總是必須去控制腳踏車的側傾角。換言之，控制側傾角為產生轉向或路徑跟隨的首要步驟。在本研究中，使用兩步驟做路徑跟隨控制。第一步驟，在側傾角跟隨控制器中，藉由控制轉向角轉矩，訓練其跟隨參考輸入，確保側傾角在不同情形下的穩定性。
第二步驟，發展路徑跟隨控制器以產生適當的參考側傾角，並讓側傾角利用模糊控制器可以跟隨預定義路徑。此控制法則之效果已藉由數學模型所推導的模擬結果證明。此控制法則之成效可用來評估不同之條件，包含：誤差資訊、預路徑設定、固定車速、變動車速和外部干擾因素。

In this dissertation, the equations of motion with nine generalized coordinates of a bicycle are developed. For constraints, rolling-without-slipping contact condition between wheels and ground is considered. For each wheel, two holonomic and two non-holonomic constraints are introduced in a set of differential-algebraic equations (DAEs). The dynamics model is validated by verifying the constraints, by comparison with a benchmark model, as well as with experiment results.
The mathematic equations are then used to implement a simulation routine. To solve the DAEs of motion and ensure numerical accuracy in simulation of the bicycle system, computational methods for constraint handling are discussed and compared, including two methods to establish the underlying ODEs from the DAEs (coordinate reduction and embedding methods), and three numerical stabilization methods (Baumgarte, post-stabilization and sliding-mode-control post-stabilization).
The path-following control is decoupled in two steps. First, the roll-angle-tracking controller is studied to control the bicycle following a reference command by applying steering torque while ensuring the roll stability with consideration of several approaches, including PID, fuzzy logic, pole placement and sliding mode.
In the second step, the path-tracking controller is developed to generate appropriate roll-angle reference for the roll-angle-tracking controller in order to control the bicycle following a pre-defined path, by using fuzzy logic controllers. The effectiveness of the control schemes is proven by simulations with the developed mathematic model. Performance of the control schemes are evaluated in different conditions, including error information, path preview, constant speed, varying speed, and external disturbance.

博碩士論文暨電子檔案上網授權書..............iii
中文摘要............iv
ABSTRACT............v
ACKNOWLEDGEMENTS............vi
TABLE OF CONTENTS............vii
LIST OF FIGURES............x
LIST OF TABLES............xv

Chapter I: INTRODUCTION............1
1.1 Motivation............1
1.2 Literature Review............2
1.2.1 Bicycle Dynamics, Steering and Models............2
1.2.1.1 Bicycle Dynamics............2
1.2.1.2 Bicycle Steering............4
1.2.1.3 Bicycle Models............6
1.2.2 Bicycle Control............9
1.2.3 Numerical Stabilization............10
1.2.4 Fuzzy-Logic Control............11
1.2.5 Sliding-Mode Control............13
1.2.6 Genetic Algorithms............14
1.3 Research Objective and Process............15
Chapter II: BICYCLE DYNAMICS MODEL............19
2.1 Unconstrained Equations of Motion............19
2.2 Constraint Equations............23
2.3 Simulation Parameter Sets............27
2.4 Model Validation............29
2.4.1 By Comparison with a Benchmark Bicycle Model............29
2.4.1.1 Benchmark Bicycle Model............30
2.4.1.2 System-Identification Approach............32
2.4.1.3 Identified Pole Location............34
2.4.2 By Experiment............38
2.4.2.1 Comparison Method............38
2.4.2.2 Measuring Equipments............40
2.4.2.3 Equipment Installation............43
2.4.2.4 Results and Discussion............47
2.5 Dynamic Behaviors............54
2.5.1 Dynamic Modes............54
2.5.2 Limit Cycles............58
2.5.3 Non-minimum Phase Steering............61
Chapter III: BICYCLE DYNAMICS SIMULATION............64
3.1 ODE-Formulation Methods............64
3.1.1 Coordinate Reduction............64
3.1.2 Embedding Method............66
3.2 Numerical-Stabilization Methods............68
3.2.1 Baumgarte’s Method............69
3.2.2 Post-Stabilization Method............70
3.2.3 Sliding-Mode-Control (SMC) Post-Stabilization Method and Modifications............71
3.3 Comparison and Discussion............73
Chapter IV: ROLL-ANGLE-TRACKING CONTROL............82
4.1 PID Controller............82
4.2 Fuzzy-Logic Controller (FLC)............86
4.2.1 Constant-Speed Controller............86
4.2.2 Optimization of FLC Using Genetic Algorithms............90
4.2.3 Variable-Speed Controller............93
4.3 Pole-Placement Controller (PPC)............101
4.3.1 Controller Design............101
4.3.2 Simulation Results............102
4.4 Sliding-Mode Controller (SMC)............105
4.4.1 Controller Design............105
4.4.2 Simulation Results............109
4.5 Discussion............116
Chapter V: PATH-TRACKING CONTROL............117
5.1 Control without Path Preview............117
5.1.1 General Discussion............118
5.1.2 Controller with Only Distance Error............120
5.1.3 Controller with Both Distance and Direction Errors............122
5.1.4 Simulation Results and Comparison............125
5.2 Control with Path Preview............127
5.3 Variable-Speed Controller............132
5.4 Disturbance Rejection............140
Chapter VI: CONCLUSIONS AND PERSPECTIVES............143
REFERENCES............145
Appendix: CONSTRAINT JACOBIAN MATRIX............152
AUTOBIOGRAPHY............154
LIST OF PUBLICATIONS............155
Journal Submissions............155
Conference Submissions............155

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