The State-Space Discrete-Time Model with a State Delay

含有狀態延遲之狀態空間離散模式

陳春明(Chuen-Ming Chen)；鄭永業(Yong-Ya Zheng)

state space ； delay time ； discrete-time model ； 狀態空間 ； 延遲時間 ； 離散模式

萬能學報

41期（2019 / 07 / 01）

139 - 151

英文

A new approach for model conversion of a state-delay system is proposed in this paper. The derivation and the main results are all in the state-space formation such that the further application and design of a signal system can be more convenient. To proceed this work in continuous-to-discrete model conversion, the digitally sampling period is larger than the delay time is considered, and the discrete-time model is especially derived from the continuous-time system so that it has a wider range for sampling period in real system implementation. Moreover, a reasonably larger sampling period in the digital model can decrease the computation time in the processor system. In the discrete-to-continuous model conversion, a simple method is also proposed to determine the unknown state-delay time from the available discrete-time model, and thus the generated continuous-time model is established through some existing relationship, and the delay time also can be evaluated for the originally continuous model of physical systems.

本文針對狀態延遲系統提出一個新的模式轉換方法。文中的推導與主要的結果都以狀態空間的架構呈現，使得在信號系統的進一步運用與設計能更加方便。在進行連續至數位的模式轉換工作中，考慮了數位取樣週期比延遲時間大的情形，以特殊的推導方式．由連續時間系統中求得離散時間模式，使得在真實的系統執行時，可具有較寬廣的取樣週期。此外，在數位模式中，一個合理較大的取樣週期可以減少處理器系統的計算時間。在數位至連續模式轉換中，提出一種簡易的方法，由所獲取的離散時間模式存在的一些關係中，計算求得未知的狀態延遲時間，進而回復其原始連續時間的物理系統模式。

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