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頻率響應及其描述

發布日期:2022-04-17 點擊率:199

  利用系統對正弦輸入信號的穩態響應來描述系統特性,是一種廣泛應用的頻域分析方法。

 基本概念

    設線性定常系統的輸入、輸出信號分別為,其拉氏變換為,則系統的傳遞函數為



,其中為正弦信號的角頻率。系統的穩態響應為為穩態響應為正弦輸出的相移。


頻率響應:線性控制系統對正弦輸入的穩態響應。也就是說對于這種系統所給的參考輸入信號,只限于正弦函數,而其輸出是考慮穩定狀態,即當時間 

幅頻特性:正弦輸出對正弦輸入的幅值比


                              


 是系統的傳遞函數  換成純虛數  以 


當輸入信號為正弦信號,即為正弦信號的振幅;,其中的振幅;相對正弦輸入時的情況。頻率特性記為  



                               



相頻特性:正弦輸出對正弦輸入的相移



                               系統的頻率特性  的一種特殊形式,即將傳遞函數中的  ,就是該系統的頻率特性。也就是說,任何線性系統的頻率特性都可由傳遞函數中的  代替而求得,這種通過傳遞函數求取頻率響應的方法稱為解析法。


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