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To build a typical element by using OA To build initial element To build a typical 2nd order system What if? An example of signal flow graph Summary of Basic rules of Signal Flow Graph （1） A signal flow graph applies only to linear systems. The equations based on which a signal flow graph is drawn must be algebraic equations in the form of effects as functions of causes. Nodes are used to represent variables. Normally, the nodes are arranged from left to right, following a succession of causes and effects through the system. Summary of Basic rules of Signal Flow Graph （2） Signal travel along branches only in the direction described by the arrows of branches. The branch directing from node yk to yj, represents the dependence of the variable yj, upon yk, but not the reverse. A signal yk traveling along a branch between nodes yk and yj is multiplied by the gain of the branch, akj, so that a signal akj yk is delivered at node yj. Definition for Signal Flow Graphs(1) Definition for Signal Flow Graphs(2) Definition for Signal Flow Graphs(2) Definition for Signal Flow Graphs(2) Definition for Signal Flow Graphs(3) Definition for Signal Flow Graphs(3) Definition for Signal Flow Graphs(3) Definition for Signal Flow Graphs(5) Signal Flow Graph Algebra （1） Signal Flow Graph Algebra （2） Signal Flow Graph Algebra （3） Signal Flow Graph Algebra （4） Mason Gain Formula(1) Mason Gain Formula(2) Mason Gain Formula(3) Mason Gain Formula(4) Mason Gain Formula(5) Δn is the cofactor of Pn. It is the determinant of the remaining sub- graph when forward path that produces Pn is removed. Δn is equal to unity when the forward path touches all the loops in the signal flow graph or when the graph contains no loops. Two parts of a signal flow graph are said to be non touching if they do not share a common node. 孙供杭馋绽宗阎类笨铝定梳人署腐隔苟阐缎队葬裂蜗非篱杰痰荣墩骂鹊穗Feedback Control-5Feedback Control-5 Please draw a signal flow graph for the system and find the overall gain between the R(s) and C(s). ― e w