||Sliding Mode Control-Based Robust Tracker Design
||Department of Electrical Engineering
Sliding mode control
input-output direct feed-through term
本論文旨在發展連續/離散之新型強健滑模控制器設計演算法。本論文研究主題包括: 一、提出針對一類非線性系統並具有未知輸入非線性與擾動的強健自適應滑模控制器/追蹤器之設計方法。為了避免控制輸入在傳統的滑模控制下會產生高頻的抖動現象，本論文詳細地討論利用連續函數取代傳統符號( )函數來實現控制器設計，藉此抖動的缺點可以被克服。此外，所提出的自適應法則為低階且不具有高估的現象。二、針對資料採樣系統方面，提出一新穎離散滑模控制方法，並且保證在採樣時間下滑模面存在。本論文詳細地討論當所提出的滑模軌跡抵達滑模面後，干擾對於控制系統的影響。在具有匹配的干擾下，其對於控制系統的影響得以完全地被抑制；在具有非匹配的干擾下，雖然其對於控制系統的影響依然存在，但控制系統的響應會被抑制在一定的範圍之內，其範圍透過本論文所提之演算方法是可以被估測的。三、針對滑模控制的數位再設計方面，本論文提出一新穎的分析與設計方法。透過尤拉(Euler)近似法可以將已設計好的連續滑模控制器進行數位再設計，在採樣點保證離散滑模面的存在。因此，所提出的滑模控制之數位再設計方法，可以保留原本已設計好的連續滑模控制之性能，且具有良好的擾動抑制能力。最後，透過數值的模擬證明所提方法的有效性與強健性。
This dissertation presents new robust continuous/discrete sliding mode controller design algorithms. This includes the following research topics. First, the novel robust SMC-based adaptive chattering-free controller/tracker design algorithms for a class of continuous-time nonlinear systems with unknown input nonlinearity and perturbations are developed. To avoid the unexpected chattering phenomenon in the traditional SMC, the smooth/continuous function is introduced to replace the discontinuous function with a detailed discussion on the proposed SMC-based controller design directly. Furthermore, the proposed adaptive laws are in low order and without overestimation. Second, for the discrete-time SMC, a new control strategy is developed for the stability of generalized continuous-time controlled systems. Since the controlled system states are operated in the pre-specified sliding manifold, the bounds of responses of controlled systems with external matched and mismatched disturbances are discussed. Third, a new digital-redesign-based discrete-time SMC approach using Euler’s approximation method is developed to obtain a discrete-time SMC-based tracker such that the performance can also be satisfied as the continuous-time SMC-based tracker as possible. Finally, the corresponding numerical results show the effectiveness and robustness of the proposed control methods.
摘 要 i
List of Figures vii
Symbols and Abbreviations xii
Capter 1 Introduction 1
1.1 Literature review 2
1.1.1 Continuous-time robust SMC-based adaptive controller/tracker 2
1.1.2 Discrete-time SMC-based controller/tracker 8
1.2 Motivation of dissertation 11
1.3 Contributions of dissertation 12
1.4 Organization of dissertation 13
Chapter 2 A Robust SMC-Based Adaptive Chattering-Free Controller Design for Continuous-Time Chaotic Systems with Unknown Input Nonlinearity 14
2.1 System description and problem formulation 15
2.2 Control design algorithm 18
2.3 Numerical simulations 23
2.4 Summary 35
Chapter 3 A Robust SMC-Based Adaptive Chattering-Free RBFNN Tracker Design for a Class of Continuous-Time Nonlinear Systems with Unknown Input Nonlinearity and Uncertainties 36
3.1 System description and problem formulation 37
3.2 Robust tracker design 38
3.3 Numerical simulations 47
3.4 Summary 60
Chapter 4 A Robust SMC-Based Adaptive Chattering-Free H-Infinity Model Reference Tracking Controller Design for a Class of Continuous-Time Nonlinear Systems with Unknown Input Nonlinearity, Uncertainties and Mismatched Disturbances 61
4.1 System description and problem formulation 62
4.2 Robust tracker design 64
4.3 Numerical simulations 73
4.4 Summary 82
Chapter 5 A New Discrete-Time SMC-Based Regulator Design for Sampled-Data Systems 83
5.1 System description and problem formulation 84
5.2 Discrete-time SMC-based regulator 86
5.3 Numerical simulations 92
5.4 Summary 102
Chapter 6 A Novel SMC-Based Digital-Redesign LQDT Design for Sampled-Data Systems with Uncertainties and Direct Feed-Through Term 103
6.1 Tracker design based on the final-value theorem 104
6.2 Derivation of continuous-time robust SMC-based tracker 107
6.3 Novel SMC-based digital-redesign LQDT 110
6.4 Numerical simulations 116
6.5 Summary 120
Chapter 7 Conclusions and Future Researches 121
7.1 Conclusions 121
7.2 Future works 125
Appendix A The Final-Value-Theorem-Based LQAT and the Digital-Redesign Approach for Linear Continuous-Time Systems with/without Direct Feed-Through Term 140
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