In systems theory, closed-loop poles are the positions of the poles (or eigenvalues) of a closed-loop transfer function in the s-plane. The open-loop transfer function is equal to the product of all transfer function blocks in the in the block diagram. The closed-loop transfer function is obtained by dividing the open-loop transfer function by the sum of one and the product of all transfer function blocks throughout the negative feedback loop. The closed-loop transfer function may also be obtained by algebraic or block diagram manipulation. Once the closed-loop transfer function is obtained for the system, the closed-loop poles are obtained by solving the characteristic equation. The characteristic equation is nothing more than setting the denominator of the closed-loop transfer function
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| - Closed-loop pole (en)
- 閉迴路極點 (zh)
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| - 閉迴路極點是S平面上閉迴路傳遞函數極點（或是特徵值）的位置。開迴路傳遞函數等於方塊圖上前向路徑（forward path）所有傳遞函數方塊的積。閉迴路傳遞函數的計算方式是將開迴路傳遞函數除以（反馈迴路中所有傳遞函數方塊的積加1）。閉迴路傳遞函數也可以用方塊圖的處理或是代數的處理來計算。只要找到了系統的閉迴路傳遞函數，可以求解其特徵方程式來找閉迴路極點。特徵方程式就是讓閉迴路傳遞函數分母為零所得的方程式。 在控制理论中主要有兩種分析回授系統的方式：传递函数法（頻域法）及状态空间法（時域法）。若使用传递函数法，主要會關注传递函数的極點及零點在S平面的位罝。設計者會關注兩種不同的轉移函數。若不讓反馈迴路運作時，所探討的是開迴路傳遞函數，若考慮反馈迴路運作時，所探討的是閉迴路傳遞函數。有關這二個的關係，請參考根軌跡圖。 (zh)
- In systems theory, closed-loop poles are the positions of the poles (or eigenvalues) of a closed-loop transfer function in the s-plane. The open-loop transfer function is equal to the product of all transfer function blocks in the in the block diagram. The closed-loop transfer function is obtained by dividing the open-loop transfer function by the sum of one and the product of all transfer function blocks throughout the negative feedback loop. The closed-loop transfer function may also be obtained by algebraic or block diagram manipulation. Once the closed-loop transfer function is obtained for the system, the closed-loop poles are obtained by solving the characteristic equation. The characteristic equation is nothing more than setting the denominator of the closed-loop transfer function (en)
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| - In systems theory, closed-loop poles are the positions of the poles (or eigenvalues) of a closed-loop transfer function in the s-plane. The open-loop transfer function is equal to the product of all transfer function blocks in the in the block diagram. The closed-loop transfer function is obtained by dividing the open-loop transfer function by the sum of one and the product of all transfer function blocks throughout the negative feedback loop. The closed-loop transfer function may also be obtained by algebraic or block diagram manipulation. Once the closed-loop transfer function is obtained for the system, the closed-loop poles are obtained by solving the characteristic equation. The characteristic equation is nothing more than setting the denominator of the closed-loop transfer function to zero. In control theory there are two main methods of analyzing feedback systems: the transfer function (or frequency domain) method and the state space method. When the transfer function method is used, attention is focused on the locations in the s-plane where the transfer function is undefined (the poles) or zero (the zeroes; see Zeroes and poles). Two different transfer functions are of interest to the designer. If the feedback loops in the system are opened (that is prevented from operating) one speaks of the open-loop transfer function, while if the feedback loops are operating normally one speaks of the closed-loop transfer function. For more on the relationship between the two see root-locus. (en)
- 閉迴路極點是S平面上閉迴路傳遞函數極點（或是特徵值）的位置。開迴路傳遞函數等於方塊圖上前向路徑（forward path）所有傳遞函數方塊的積。閉迴路傳遞函數的計算方式是將開迴路傳遞函數除以（反馈迴路中所有傳遞函數方塊的積加1）。閉迴路傳遞函數也可以用方塊圖的處理或是代數的處理來計算。只要找到了系統的閉迴路傳遞函數，可以求解其特徵方程式來找閉迴路極點。特徵方程式就是讓閉迴路傳遞函數分母為零所得的方程式。 在控制理论中主要有兩種分析回授系統的方式：传递函数法（頻域法）及状态空间法（時域法）。若使用传递函数法，主要會關注传递函数的極點及零點在S平面的位罝。設計者會關注兩種不同的轉移函數。若不讓反馈迴路運作時，所探討的是開迴路傳遞函數，若考慮反馈迴路運作時，所探討的是閉迴路傳遞函數。有關這二個的關係，請參考根軌跡圖。 (zh)
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