時變時滯網路系統之回授控制與穩定性分析

由於數據通信網絡技術得且快速發展，網絡即時控制應用受到極大的關注。然而，網絡控制系統（NCS）也導致時間延遲，嚴重降低控制性能和穩定性，這些是難以避免的問題。網絡引起的延遲的特性可以是根據不同的網絡協議，節點，軟體和硬體恆定，有界的，隨機的，或不可預測性質。此外，時間延遲的存在常常是不穩定的，在實際系統的來源。因此，時間延遲非線性系統帶死區的穩定性分析的問題一直是最重要的議題在控制設計工程之一。我們提出改進的穩定性標準使用了一種新的分區技術的線性系統的間隔時間變延遲。在這裡，我們選擇一個合適的李亞普諾夫函數，其中自由權矩陣，配方法和零等式完成應用來獲得穩定的標準。特別是，新的技術是整合分割成許多區間能夠得到鬆弛條件。在另一方面，我們提出了一個線性矩陣不等式（LMI）為基礎的方法來穩定網絡轉換器在非線性動態。在網絡引起時變時滯，該系統包括一個共用控制器遠端調節變換器的輸出。考慮實際應用的網絡轉換器，這項研究的問題是推導理論時間延遲的邊界。首先，我們描繪網絡轉換器轉到Takagi-Sugeno(T-S)模糊系統。然後用謹慎地選擇李亞普諾夫函數方法，我們推導出TS模糊系統穩定的充分條件。我們將充分條件轉換成線性矩陣不等式。通過求解線性矩陣不等式數值，我們得到的控制器增益和時間延遲的最大允許上限（MAUB）。相比採用典型的李雅普諾夫泛函方法保守的結果，該MAUB在這裡獲得的是相當實用的網絡轉換器。然後，我們進行數值模擬和實際實驗中令人滿意的結果進一步驗證了理論推導。

關鍵字

轉換器；穩定性；線性矩陣不等式；網路引起延遲；李亞普諾夫函數；網路控制系統； T-S模糊系統

並列摘要

Real-time network control applications have gained great attentions owing to the rapid development of data communication network technologies. However, networked control system (NCS) also result in unavoidable problems in time delays that seriously degrade control performance and stability. The characteristics of network-induced delays may be in constant, bounded, random, or unpredictable natures depending on the network protocols, nodes, software, and hardware. Moreover, the existence of time-delay is frequently a source of instability in the real systems. Therefore, the problem of stability analysis of time delay nonlinear systems with a dead zone has been one of the most important topics for the control design engineer. We propose improved stability criteria for linear systems with interval time-varying delay using a novel partitioning technique. Here, we choose an appropriate Lyapunov-Krasovskii functional, where free weighting matrices, completion of squares method and zero equalities are applied to obtain the stability criteria. Especially, the new technique is to partition the integration into as many intervals as possible to obtain the relaxed criteria. On the other hand, we present an linear matrix inequality (LMI)-based approach to stabilize networked converters with nonlinear dynamics. The system consists of a common controller remotely regulating converter outputs where the network induces time-varying delay. The research problem is to derive the theoretical bound of time delay which is a practical consideration for networked converter applications. We first represent the networked converter into a Takagi-Sugeno (T-S) fuzzy system. Then using a carefully chosen Lyapunov-Krasovskii functional approach, we derive the sufficient conditions of stabilization of the T-S fuzzy system. We transform the sufficient conditions into LMIs. By solving the LMIs numerically, we obtain the controller gains and the maximum allowable upper bound (MAUB) of time delay. Compared to conservative results using typical Lyapunov-Krasovskii functional approaches, the MAUB obtained here is quite practical for the networked converters. We then carry out numerical simulations and practical experiments where satisfactory results further verify the theoretical derivation.

並列關鍵字

Lyapunov-Krasovskii functional ； Network-induced delay ； Linear matrix inequality ； Stability ； Converters ； T-S fuzzy system ； Networked control system (NCS)

參考文獻

[1] W. Zhang, M. S. Branicky, and S. M. Phillips, Stability of networked control systems,"

IEEE Trans. Contr. Syst. Mag., vol. 21, no. 1, pp. 84{99, Feb 2001.

[2] G. C. Walsh, O. Beldiman, and L. G. Bushnell, Asymptotic behavior of nonlinear

[3] G. C. Walsh, Y. Hong, and L. G. Bushnell, Stability analysis of networked control

[4] L. Montestruque and P. Antsaklis, Stability of model-based networked control systems

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時變時滯網路系統之回授控制與穩定性分析

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