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Transfer function matrix Macierz transmitancji 傳遞函數矩陣
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傳遞函數矩陣(transfer function matrix)或傳遞矩陣(transfer matrix)是控制系統以及許多工程領域的名詞,是將SISO系統中的传递函数擴展到MIMO系統。矩阵表示系統輸出跟輸入之間的關係。在線性非時變系統中是格外有用的工具,因為其傳遞函數矩陣可以用S平面來表示。 在一些只由被動元件組成的系統中,可以清楚的區分哪些變數是輸入,哪些是輸出。在電子系統中的作法,將所有電壓變數組合成一組,視為是傳遞函數矩陣的輸出,再將電流變數組合成另外一組起來,視為是輸入。這樣形成的傳遞函數矩陣中,每個元素都是阻抗。這種阻抗(及阻抗矩陣)的概念也用到其他能量的學科中,特別是力學及聲學。 許多控制系統包括不同的能量形式,其傳遞函數矩陣也會有不同的單位,一方面需要描述其中在各能量形式之間轉換的换能器,另一方面也要描述整體的系統。若系統中有適當能量流動的模型,需要選擇對應的變數,以方便模型的建立。 Macierz transmitancji (operatorowych), macierz transmitancyjna – termin stosowany w teorii sterowania na określenie macierzy, która wiąże wejście z wyjściem w przypadku układów o wielu wejściach i wyjściach. Macierz transmitancji stanowi zatem rozszerzenie koncepcji transmitancji operatorowej na układy o wielu wejściach i wyjściach. Jeśli jest wektorem wyjść, a wektorem wejść układu o wielu wejściach i wyjściach, to wielkości te wiąże macierz transmitancji co można zapisać: W przypadku układu z jednym wejściem i wyjściem otrzymuje się związek transmitancji z równaniami stanu: In control system theory, and various branches of engineering, a transfer function matrix, or just transfer matrix is a generalisation of the transfer functions of single-input single-output (SISO) systems to (MIMO) systems. The matrix relates the outputs of the system to its inputs. It is a particularly useful construction for linear time-invariant (LTI) systems because it can be expressed in terms of the s-plane.
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Macierz transmitancji (operatorowych), macierz transmitancyjna – termin stosowany w teorii sterowania na określenie macierzy, która wiąże wejście z wyjściem w przypadku układów o wielu wejściach i wyjściach. Macierz transmitancji stanowi zatem rozszerzenie koncepcji transmitancji operatorowej na układy o wielu wejściach i wyjściach. Jeśli jest wektorem wyjść, a wektorem wejść układu o wielu wejściach i wyjściach, to wielkości te wiąże macierz transmitancji co można zapisać: Jeśli wektor wejść jest wektorem o wymiarze a wektor wyjść jest wektorem o wymiarze wówczas macierz transmitancji ma wymiar x co można zapisać: W przypadku układu z jednym wejściem i wyjściem otrzymuje się związek transmitancji z równaniami stanu: Podobnie w przypadku układu o wielu wejściach i wyjściach można wyprowadzić związek macierzy transmitancji z równaniami stanu: Wytłuszczenia symboli we wzorach wskazują, że chodzi o wektory (macierze), a nie o wartości skalarne. 傳遞函數矩陣(transfer function matrix)或傳遞矩陣(transfer matrix)是控制系統以及許多工程領域的名詞,是將SISO系統中的传递函数擴展到MIMO系統。矩阵表示系統輸出跟輸入之間的關係。在線性非時變系統中是格外有用的工具,因為其傳遞函數矩陣可以用S平面來表示。 在一些只由被動元件組成的系統中,可以清楚的區分哪些變數是輸入,哪些是輸出。在電子系統中的作法,將所有電壓變數組合成一組,視為是傳遞函數矩陣的輸出,再將電流變數組合成另外一組起來,視為是輸入。這樣形成的傳遞函數矩陣中,每個元素都是阻抗。這種阻抗(及阻抗矩陣)的概念也用到其他能量的學科中,特別是力學及聲學。 許多控制系統包括不同的能量形式,其傳遞函數矩陣也會有不同的單位,一方面需要描述其中在各能量形式之間轉換的换能器,另一方面也要描述整體的系統。若系統中有適當能量流動的模型,需要選擇對應的變數,以方便模型的建立。 In control system theory, and various branches of engineering, a transfer function matrix, or just transfer matrix is a generalisation of the transfer functions of single-input single-output (SISO) systems to (MIMO) systems. The matrix relates the outputs of the system to its inputs. It is a particularly useful construction for linear time-invariant (LTI) systems because it can be expressed in terms of the s-plane. In some systems, especially ones consisting entirely of passive components, it can be ambiguous which variables are inputs and which are outputs. In electrical engineering, a common scheme is to gather all the voltage variables on one side and all the current variables on the other regardless of which are inputs or outputs. This results in all the elements of the transfer matrix being in units of impedance. The concept of impedance (and hence impedance matrices) has been borrowed into other energy domains by analogy, especially mechanics and acoustics. Many control systems span several different energy domains. This requires transfer matrices with elements in mixed units. This is needed both to describe transducers that make connections between domains and to describe the system as a whole. If the matrix is to properly model energy flows in the system, compatible variables must be chosen to allow this.
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