網路控制系統的穩定性分析

Abstract

當控制系統由網路互相溝通聯繫形成一個迴路，此系統稱為網路控制系統。考慮網路控制系統中，狀態迴授需由網路傳送，所以有不能隨時更新的問題。因此，探討控制系統僅在某些時間點更新控制訊號對系統穩定性的影響是一門重要的課題。 本篇論文利用Lyapunov Theorem，針對網路控制系統未及時更新迴授的控制推導一些數學不等式，這些式子包含用於取得使系統穩定的控制器其更新區間之最大容許時間範圍，以及有雜訊項的系統其在不即時更新迴授控制器，但仍然要使系統穩定其可接受之狀態誤差的最大值，最後亦導出網路控制系統的Hinf控制器。利用這些推導結果可以得到在網路控制器中，系統狀態由網路傳送，其對於系統穩定度的影響以及所需的最小傳輸時間範圍。

Feedback control systems where the control loops are closed through a real-time network are called Networked Control Systems (NCSs). In the NCSs, state feedback must be transmitted by the network, but it may be jammed in the channel. So it is a matter in updated delay. Therefore, discussion and analysis of the stability of control systems with control signals being updated at some moment is an important topic. In this thesis, we derive several conditions to guarantee stability of NCSs with control signals being updated in retard according to the Lyapunov Theorem. The maximum range of time interval to update the control signal to ensure the stability of NCSs is derived. The transmission error upper bound between two successive transmissions in NCSs with disturbances is also obtained. Moreover, the Hinf control of NCSs is considered.