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Линеаризация обратной связью Feedback linearization Methode der globalen Linearisierung Controllo in feedback linearization 回授線性化
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Il controllo in feedback linearization è una tecnica di base utilizzata nel controllo di sistemi non lineari. Quest'approccio consiste nella trasformazione di un sistema non lineare in un equivalente sistema lineare, grazie a un cambio di variabili e a un ingresso appositamente scelto. La feedback linearization può essere applicata a quei sistemi non lineari che possono essere riscritti nella seguente forma dove è il vettore di stato, è il vettore di ingresso e è il vettore di uscita. L'obiettivo è sviluppare un vettore di ingresso Feedback linearization is a common strategy employed in nonlinear control to control nonlinear systems. Feedback linearization techniques may be applied to nonlinear control systems of the form where is the state, are the inputs. The approach involves transforming a nonlinear control system into an equivalent linear control system through a change of variables and a suitable control input. In particular, one seeks a change of coordinates and control input so that the dynamics of in the coordinates take the form of a linear, controllable control system, Die Idee beim Regelungsentwurf durch globale Linearisierung besteht darin, eine geeignete Rückführung zu finden, die ein nichtlineares System linearisiert und damit eine Regelung vereinfacht. Zumeist wird dazu der Ausgang zurückgeführt, weshalb die Methode auch als Linearisierung durch Ausgangsrückführung bekannt ist. Die globale Linearisierung wird vor allem in der Regelungstechnik eingesetzt, weshalb wir nun ein solches Beispiel betrachten. 回授線性化（Feedback linearization）是在控制理论中控制非線性系統的常見作法，其作法是透過適當的控制輸入及狀態變數轉換，將非線性系統轉換為等效的線性系統。非線性系統的回授線性化可以用以下的形式表示 其中為狀態向量，為輸入的向量，而是輸出向量。其目標是要找到以下的控制輸入 可以得到新的輸入和輸出之間的線性關係。之後就可以用線性系統的控制策略來控制線性化後的系統。 控制輸入中有包括系統的狀態變數，因此需要狀態變數的回授或是狀態觀測器來計算狀態變數。 Линеариза́ция обра́тной свя́зью - способ приведения системы, абстрактно описываемой в виде к виду где - некоторое внешнее управляющее воздействие. При этом нелинейная система становится линейной, а внешнее управление предусмотрено для стабилизации и управления оставшейся линейной частью системы. В качестве закона управления обычно применяют этот закон управления часто приводит к цели управления, если функция вычислима.
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回授線性化（Feedback linearization）是在控制理论中控制非線性系統的常見作法，其作法是透過適當的控制輸入及狀態變數轉換，將非線性系統轉換為等效的線性系統。非線性系統的回授線性化可以用以下的形式表示 其中為狀態向量，為輸入的向量，而是輸出向量。其目標是要找到以下的控制輸入 可以得到新的輸入和輸出之間的線性關係。之後就可以用線性系統的控制策略來控制線性化後的系統。 控制輸入中有包括系統的狀態變數，因此需要狀態變數的回授或是狀態觀測器來計算狀態變數。 Линеариза́ция обра́тной свя́зью - способ приведения системы, абстрактно описываемой в виде к виду где - некоторое внешнее управляющее воздействие. При этом нелинейная система становится линейной, а внешнее управление предусмотрено для стабилизации и управления оставшейся линейной частью системы. В качестве закона управления обычно применяют этот закон управления часто приводит к цели управления, если функция вычислима. Feedback linearization is a common strategy employed in nonlinear control to control nonlinear systems. Feedback linearization techniques may be applied to nonlinear control systems of the form where is the state, are the inputs. The approach involves transforming a nonlinear control system into an equivalent linear control system through a change of variables and a suitable control input. In particular, one seeks a change of coordinates and control input so that the dynamics of in the coordinates take the form of a linear, controllable control system, An outer-loop control strategy for the resulting linear control system can then be applied to achieve the control objective. Il controllo in feedback linearization è una tecnica di base utilizzata nel controllo di sistemi non lineari. Quest'approccio consiste nella trasformazione di un sistema non lineare in un equivalente sistema lineare, grazie a un cambio di variabili e a un ingresso appositamente scelto. La feedback linearization può essere applicata a quei sistemi non lineari che possono essere riscritti nella seguente forma dove è il vettore di stato, è il vettore di ingresso e è il vettore di uscita. L'obiettivo è sviluppare un vettore di ingresso che renda lineare la funzione ingresso-uscita tra il nuovo ingresso e l'uscita . A questo punto può essere applicata una classica strategia di controllo per sistemi lineari. Si noti che a differenza di tecniche di linearizzazione classiche come l'espansione di Taylor, che approssimano una funzione non lineare ad una lineare in un certo intorno, la feedback linearization trasforma esattamente il sistema a ciclo chiuso in un sistema lineare. Die Idee beim Regelungsentwurf durch globale Linearisierung besteht darin, eine geeignete Rückführung zu finden, die ein nichtlineares System linearisiert und damit eine Regelung vereinfacht. Zumeist wird dazu der Ausgang zurückgeführt, weshalb die Methode auch als Linearisierung durch Ausgangsrückführung bekannt ist. Die globale Linearisierung wird vor allem in der Regelungstechnik eingesetzt, weshalb wir nun ein solches Beispiel betrachten.
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