均分型單體順滑模態控制

Abstract

本論文提出一種新的控制理論，稱作均分型單體順滑模態控制，它主要針對受匹配式干擾影響的多輸入系統。此均分型單體順滑模態控制設計基礎主要是基於均分型單體集合，此種單體集合具有單位長度與能夠平均切割控制空間的特性。另外，在本文中亦提出兩種方法來獲得適當的均分型單體集合。藉著利用此均分型單體集合，在此將發展出一種簡潔的方法來快速的決定系統軌跡並且提出一種特殊的平滑化策略用來解決單體順滑模態控制所引起的切跳問題。最重要的是在本文中能夠理論性地證明單體順滑模態控制能夠抑制具上界受限的匹配式干擾。在另一方面，灰預測理論被利用來預測匹配式干擾。藉著利用灰預測理論，均分型單體順滑模態控制能夠在不需要預先知道匹配式干擾的上界資訊情況下，便能夠消除匹配式干擾。最後，為了擴展均分型單體順滑模態控制的實用性，將它應用於處理機械手臂的追蹤控制的問題。

This dissertation presents a novel control technology for multi-input systems, called uniformly distributed simplex sliding-mode control (UDSSMC), to deal with matched disturbances. The UDSSMC is mainly designed based on the uniformly distributed simplex set, which contains vectors of unit magnitude and distributed uniformly in the control space. Two approaches are proposed to obtain the uniformly distributed simplex set easily and directly. By employing the uniformly distributed simplex set, a new concise scheme is introduced to quickly determine the sub-region where the system trajectory currently stays and a specific smoothing strategy is presented to ameliorate the chattering problem caused by switching functions. Most importantly, it is theoretically shown that the upper-bounded matched disturbances can be eliminated by UDSSMC. Furthermore, a grey prediction is adopted to forecast the matched disturbances and thus no prior information concerning their upper bounds are required. Finally, the success of UDSSMC is demonstrated by the tracking control of robotic manipulators.