北京理工大学810自动控制原理考研课件3.ppt

Terms: Source is a node with only outgoing branches. Sink is a node with only incoming branches. Path is a group of connected branches having the same sense of direction. Forward path is a path originating from a source and no node is encountered more than once. Path gain is the product of the coefficient associated with the branches along the path. Feedback loop is a path originating from a node and terminating at the same node. In addition, a node cannot be encountered more than once. Loop gain is the product of coefficients associated with the branching forming a feedback loop. Nontouching loops: loops are nontouching if they do not possess any common nodes or branches. Loops: be, cf Hath: abcd a b c d e f The Mason Gain Formula: The overall transmittance (gain) can be obtained from the Mason gain formula: 　 　Y(s) is output, and R(s) is input. N——count of forward path -- the gain of all different loops; -- the product of the gains of two non-touching loops; -- the product of the gains of three non-touching loops. Pk-- the gain of the kth forward path; Dk-- the cofactor of the path Pk, is the remainder of D with the loops touching the kth path removed. Example 2.4 Example 2.5 　 R(s) G1 G2 G3 G4 G5 Y(s) L1 L2 L3 L4 L5 Solution： 1、 Home Work E2.4, E2.8, E2.14, E2.28, E2.29 P2.2 * 2.6 Block Diagram Models Introduction The Block Diagram Model – which consists of block, arrow, summing junction and branch point. A block diagram represents the flow of information and the function performed by each component in the system. Arrows are used to show the direction of the flow of information. Block diagram representation The block represents the function or dynamic characteristics of the component and is represented by a transfer function. The complete block diagram shows how the functional components are connected and the mathematic equations that determine the response of each component. a c=a-b b d=c=a-b G(s) U(s) Y(s)