机械工程测试与控制技术课件-(2.10.3)--信号流图.pptVIP

Chapter 2: Mathematical Models of Systems Ui(s) I1(s)–I2(s) UA(s) -1 1 I2(s) -1 1 -1 Uo(s) 1 Three loops: L1 L2 L3 Chapter 2: Mathematical Models of Systems Therefore Chapter 2: Mathematical Models of Systems Example 2: Find the transfer function Three forward paths: P1=G1G2G3G4G5G6, P2=G1G2G7G6, P3=G1G2G3G4G8 Chapter 2: Mathematical Models of Systems The gain of the above three feedback loops are L1=-G2G3G4G5H2, L2=-G5G6H1, L3=-G8H1 * * * ?2004~2011 School of Mechanical Engineering, Southeast University, 025 Chapter 2: Mathematical Models of Systems 2.7 Signal-Flow graph models Signal-flow graph A signal-flow graph is a diagram consisting of nodes that are connected by several directed branches and is a graphical representation of a set of linear relations. An example： x1 x2 x3 x4 x5 x5 1 e a f b d c 1 g Chapter 2: Mathematical Models of Systems Nodes The input and output points or junctions are called nodes. A node is marked as “○” and denotes a signal in the system. The output value of a node is the summation of all signals entering the node. Branches A branch is a unidirectional path segment between two nodes, which relates the dependency of an input and an output variable in a manner equivalent to a block of a block diagram. The relation between two nodes is written next to the branch and is named as branch gain (i.e. the transfer function). Chapter 2: Mathematical Models of Systems Input (Origin) node A node without other input variables, is used to denote the input signal of a system. Output (Confluent or trapped) node A node without output, is used to denote the output signal of a system. Origin Confluent x1 x2 x3 x4 x5 x5 1 e a f b d c 1 g Chapter 2: Mathematical Models of Systems Mixed nodes A node with inputs and outputs. x1 x2 x3 x4 x5 x5 1 e a f b d c 1 g Path A path is a branch or a continuous sequence of branches that can be traversed from one signal (node) to another signal (node). Chapter 2: Mathematical Models of