本篇論文旨在應用強健之二階順滑模態理論，於非線性機械系統的追蹤控制律設計。首先，從傳統順滑模態控制理論出發，探討了順滑模態理論對於匹配式擾動 (matched perturbation) 之強健性，與其在有限時間 (finite time) 內達到之降階 (reduced-order) 特性；但其代價乃是由切換控制 (switching control) 所誘發之高頻控制訊號切換，意即顫振 (chattering) 現象。為了得到一連續的控制訊號，又不失去其對於匹配式擾動的強健性，引入了於二階順滑模態控制理論當中的超扭演算法 (super-twisting sliding mode algorithm)，相較於其他二階順滑模態控制演算法，其僅需要滑動變數 (sliding variable) 的回授資訊，而不需要其微分資訊，這使其常被應用於相對階數 (relative degree) 為1的系統。於本研究，講述了數個數值模擬範例，來說明超扭演算法的強健性，有限時間穩定性，以及在頻率域中的穩定性詮釋。就實際工程問題的觀點而言，首先考慮了常見的伺服馬達定位控制問題，引入了具有非對稱 Coulomb 摩擦的非線性馬達模型，接著進行系統參數的鑑別，最後根據超扭演算法設計定位控制器。多個比較的數值模擬與實驗驗證，亦顯示了超扭控制器對於擾動的強健特性以及快速的收斂性，並且其實現簡單，對於存在複雜擾動的環境下，超扭控制器可以驅動系統追蹤到期望的參考軌跡。作為冗餘反應輪姿態控制的前期研究，本研究首先討論了由單軸反應輪驅動之定位模組，模擬與實驗結果亦顯示了超扭控制器的有效性。對於冗餘反應輪姿態控制之課題，為了實現全方向的姿態控制，引入了四元數 (quaternion) 作為姿態的描述方法，並據此進行控制 (quaternion-based control)。對於其冗餘反應輪構型下之致動器分析，基於最佳化理論，提出了最小能量花費之力量分布矩陣 (force distribution matrix)。值得一提的是，基於四元數表示法的非線性降階動態，本論文提出了解析解來說明其穩定性與收斂特性。針對於太空任務當中可能遭遇到的任務需求，提出了切線-法線-雙法線 (tangent-normal-binormal) 座標系的姿態命令產生方式。模擬的結果顯示了超扭控制器的有效性及其優異特性。

The purpose of this study is to apply the robust second-order sliding mode theory in the trajectory tracking control law design for nonlinear mechanical systems. The first of the thesis begins from the conventional sliding mode control (CSMC) theory, the robustness to the matched perturbations, finite-time stability, and reduced-order property are observed. However, the price of robust properties is that the designed switching control will induce the high-frequency switching of the control signal, which is the chattering phenomenon. One of the second-order sliding mode control approaches, namely the super-twisting sliding mode algorithm (STSMA), is introduced to obtain a continuous control signal and preserve the robust property to the matched perturbations. Comparing the STSMA to the other second-order sliding mode control algorithms only needs to feedback the sliding variable but its derivatives one does not. This characteristic so that the STSMA is often applied in the systems with the relative degree equal to one. Multiple numerical examples are provided about the super-twisting algorithm to illustrate its robustness, finite-time property, and stability interpretations in the frequency-domain. From the realistic engineering problem point of view, firstly consider the well-known positioning control of the servo motor. The nonlinear, unsymmetrical Coulomb friction model is introduced. The corresponding system parameter identification techniques are also conducted. Based on the identified dynamic model, the robust super-twisting positioning controller is designed. Comparative numerical simulations and experiment validations are carried on. The results reveal the robustness and the high-precise tracking performance of the super-twisting controller concerning the traditional linear controller. Remarkably, the implementation of a super-twisting controller is not difficult. For the environment with the unknown complex disturbance, the super-twisting controller still can derive the linear/nonlinear system to the desired trajectory. As the preliminary research of the redundant reaction wheel driven attitude control system, the single-axis reaction wheel driven positioning module is firstly discussed. The simulations/experiments results show that the effectiveness of the proposed control scheme. To realize the fully orientational attitude control of the spacecraft, the quaternion-based attitude representation is introduced, and the associating quaternion-based control is conducted. Based on the optimal control theory, the optimal force distribution matrix (FDM) to minimize the control energy for the redundant reaction wheels configuration is presented. It should be noted that the stability and the convergent behavior of the nonlinear reduced-order dynamics are addressed utilizing an analytic solution. From the space mission scenario point of view, the tangent-normal-binormal (TNB) frame attitude command follow strategy is proposed. The simulation results illustrate that the superior tracking performance and effectiveness of the super-twisting controller.

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