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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク state observer ： ウィキペディア英語版 state observer In control theory, a state observer is a system that provides an estimate of the internal state of a given real system, from measurements of the input and output of the real system. It is typically computer-implemented, and provides the basis of many practical applications. Knowing the system state is necessary to solve many control theory problems; for example, stabilizing a system using state feedback. In most practical cases, the physical state of the system cannot be determined by direct observation. Instead, indirect effects of the internal state are observed by way of the system outputs. A simple example is that of vehicles in a tunnel: the rates and velocities at which vehicles enter and leave the tunnel can be observed directly, but the exact state inside the tunnel can only be estimated. If a system is observable, it is possible to fully reconstruct the system state from its output measurements using the state observer. == Typical observer model == The state of a linear, time-invariant physical discrete-time system is assumed to satisfy : $x(k+1)\; =\; A\; x(k)\; +\; B\; u(k)$ : $y(k)\; =\; C\; x(k)\; +\; D\; u(k)$ where, at time $k$, $x(k)$ is the plant's state; $u(k)$ is its inputs; and $y(k)$ is its outputs. These equations simply say that the plant's current outputs and its future state are both determined solely by its current states and the current inputs. (Although these equations are expressed in terms of discrete time steps, very similar equations hold for continuous systems). If this system is observable then the output of the plant, $y(k)$, can be used to steer the state of the state observer. The observer model of the physical system is then typically derived from the above equations. Additional terms may be included in order to ensure that, on receiving successive measured values of the plant's inputs and outputs, the model's state converges to that of the plant. In particular, the output of the observer may be subtracted from the output of the plant and then multiplied by a matrix $L$; this is then added to the equations for the state of the observer to produce a so-called ''Luenberger observer'', defined by the equations below. Note that the variables of a state observer are commonly denoted by a "hat": $\backslash hat(k)$ and $\backslash hat(k)$ to distinguish them from the variables of the equations satisfied by the physical system. : $\backslash hat(k+1)\; =\; A\; \backslash hat(k)\; +\; L\; \backslash left(-\; \backslash hat(k)\backslash right)\; +\; B\; u(k)$ : $\backslash hat(k)\; =\; C\; \backslash hat(k)\; +\; D\; u(k)$ The observer is called asymptotically stable if the observer error $e(k)\; =\; \backslash hat(k)\; -\; x(k)$ converges to zero when $k\; \backslash rightarrow\; \backslash infty$. For a Luenberger observer, the observer error satisfies $e(k+1)\; =\; (A\; -\; LC)\; e(k)$. The Luenberger observer for this discrete-time system is therefore asymptotically stable when the matrix $A\; -\; LC$ has all the eigenvalues inside the unit circle. For control purposes the output of the observer system is fed back to the input of both the observer and the plant through the gains matrix $K$. : $u(k)=\; -K\; \backslash hat(k)$ The observer equations then become: : $\backslash hat(k+1)\; =\; A\; \backslash hat(k)\; +\; L\; \backslash left(y(k)\; -\; \backslash hat(k)\backslash right)\; -\; B\; K\; \backslash hat(k)$ : $\backslash hat(k)\; =\; C\; \backslash hat(k)\; -\; D\; K\; \backslash hat(k)$ or, more simply, : $\backslash hat(k+1)\; =\; \backslash left(A\; -\; B\; K\; \backslash right)\; \backslash hat(k)\; +\; L\; \backslash left(y(k)\; -\; \backslash hat(k)\backslash right)$ : $\backslash hat(k)\; =\; \backslash left(C\; -\; D\; K\backslash right)\; \backslash hat(k)$ Due to the separation principle we know that we can choose $K$ and $L$ independently without harm to the overall stability of the systems. As a rule of thumb, the poles of the observer $A-LC$ are usually chosen to converge 10 times faster than the poles of the system $A-BK$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「state observer」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.