順滑模式控制理論在剛性機械系統之應用

Abstract

本論文是針對剛性機械系統之內在特性及追蹤控制間題加以探討，諸如剛 性太空飛行器和機器手臂。這剛性機械系統之數學模式包含有運動及動態 方程式。首先，我們研究使用Euler參數和Rodrigues參數表示法之運動方 程式的內在特性，而且對運動方程式的被動性質也加以討論。基於運動方 程式的這些內在特性，一些能達到追蹤控制目的之線性順滑平面將被介紹 應用於順滑模式控制架構。此外，為了改善順滑模式控制法在未進入順滑 模式前之不可預知和不期望的響應，平順參考模組之順滑模式控制架構被 提出使用。此新控制架構的靈感是來自線性控制系統。最後，我們找出簡 型順滑模式控制法中的簡型向量組之通用表示式，並建立一個有系統選取 簡型向量組的程序。另外，一種特殊的簡型向量組的特性將被探究。利用 慣量矩陣的正交特徵向量，另一種相對於定數簡型向量組的系統狀態相關 簡型向量組被發表。這種使用系統狀態相關簡型向量組的簡型順滑模式控 制法被成功地應用在具有參數不確定性和外在擾動的剛性機械系統的追蹤 控制問題上。 This dissertation is concerned with the intrinsic properties and tracking control problems of rigid mechanical systems such as rigid spacecrafts and robots. The mathematical models of rigid mechanical systems contain the kinematic and dynamic equations. First, we investigate the intrinsic properties of the kinematic equations with the representations of Euler parameters and Rodrigues parameters. The passive feature of the kinematic equations is also discussed. Based on these intrinsic properties of the kinematic equations, some linear sliding manifolds are introduced to achieve the objective of tracking control problems with the sliding-mode control (SMC) scheme. In addition, in order to improve the unpredictable and undesired performance of the SMC scheme in reaching phase, the smoothing model-reference sliding-mode control (SMRSMC) scheme is presented, which is motivated from the linear control systems. Finally, the general form of a simplex needed in the simplex sliding-mode control (SSMC) method is shown. A systematic procedure for selecting a simplex are established and the properties of a special simplex is studied. With the orthonormal eigenvectors of a inertia matrix, a state-dependent simplex is proposed contrary to a constant simplex. The simplex sliding-mode control with the state-dependent simplex is successfully applied to the tracking control problem of rigid mechanical systems, which possess parameter uncertainties and are disturbed by external signals.