ME369 Modeling,Analysis and System Control-A --Lecture 141015 Week 5# Ch2.1~ Oct.13(M) Transfer function,block diagram HW2 due 2.3 Signal Flow Graphs Ch3.9, Oct.15(W) Linearization 3.10(4h) HW3 Week 6# Oct.20(M) Quiz 1 Ch5.1, Transient,first order systems 5.2 Oct.22(W) Transient,second order systems Ch5.3
ME369 Modeling, Analysis and System Control-A --Lecture_141015 Week 5# Oct.13(M) Transfer function, block diagram Ch2.1 ~ 2.3 HW2 due Oct.15(W) Signal Flow Graphs Linearization Ch3.9, 3.10 (4th ) HW3 Week 6# Oct.20(M) Quiz 1 Transient, first order systems Ch5.1, 5.2 Oct.22(W) Transient, second order systems Ch5.3
Problems of HW3 ·Refer to the ftp site. ftp://public.sjtu.edu.cn ·User:yuanjj ·Password:public DUE:Oct.25(F)
Problems of HW3 • Refer to the ftp site. • ftp://public.sjtu.edu.cn • User: yuanjj • Password: public DUE: Oct. 25 (F)
Signal Flow Graph A Visual tool to represent the causal relationships between the components of the system. Characterizing the system by a network of directed branches and associated gains (transfer function) connected at nodes. .Signal flow graph is equivalent to Block diagram. .Effective in complex system reduction
Signal Flow Graph • A Visual tool to represent the causal relationships between the components of the system. • Characterizing the system by a network of directed branches and associated gains (transfer function) connected at nodes. •Signal flow graph is equivalent to Block diagram. •Effective in complex system reduction
Signal Flow Graph Definition: .Node:A node is a point representing a variable or signal. Transmittance:The Transmittance is a real gain or complex gain can be expressed in terms of the transfer function between two nodes. .Branch:A Branch is a directed line segment joining two nodes. G3 G G2 GA GA 日96
Signal Flow Graph Definition: •Node : A node is a point representing a variable or signal. •Branch: A Branch is a directed line segment joining two nodes. •Transmittance : The Transmittance is a real gain or complex gain can be expressed in terms of the transfer function between two nodes
Signal Flow Graph .Input Node or source:A node that has only outgoing branches.This corresponds to an independent variable. .Output node or sink:A node that has only incoming branches.This corresponds to an dependent variable. .Mixed node:A node that has both incoming and outgoing branches. G3 G GA GA 日96
Signal Flow Graph •Input Node or source : A node that has only outgoing branches. This corresponds to an independent variable. •Output node or sink: A node that has only incoming branches. This corresponds to an dependent variable. •Mixed node: A node that has both incoming and outgoing branches
Signal Flow Graph .Path:A path is a transversal of connected branches in the direction of the branch arrows. Loop:If a path ends at the same node from 20 which it began and does not cross any other node R(s) Y(s) 10 more than once,it is 30 closed or it's a loop
Signal Flow Graph •Path : A path is a transversal of connected branches in the direction of the branch arrows. •Loop: If a path ends at the same node from which it began and does not cross any other node more than once, it is closed or it’s a loop
Signal Flow Graph .Nontouching Loops:Loops are nontouching if they do not possess any common nodes. .Forward path:is a path from an input node to an 20 output node that does not cross any nodes R(s) Y(s) more than once. 30 .Gain (Forward path or Loop):is the production of branch transmittance of a forward path or Loop
Signal Flow Graph •Nontouching Loops: Loops are nontouching if they do not possess any common nodes. •Forward path: is a path from an input node to an output node that does not cross any nodes more than once. •Gain (Forward path or Loop): is the production of branch transmittance of a forward path or Loop
Signal Flow Graph:basic rules Q X2=10 a+6 XE x10-26 0x3=x10 ab 0Y月 ab ab x3 1-bc 0 1 X3 be ￥10 b 0X4 X20 ￥2gbc 日6
Signal Flow Graph: basic rules
Signal flow graph VS Block diagram Ex3-13.Obtain the closed-loop transfer function C(s)/R(s) He G2 G H GG2Gs 1-GG2 H1+G2G3 H2 +GG2Gs Convert to the Signal flow graph
Signal flow graph VS Block diagram Ex3-13. Obtain the closed-loop transfer function C(s)/R(s) Convert to the Signal flow graph ?
Signal Block H G H -H2 transmittance G2 G R(s) C(s) C(s) node H -1
node Signal transmittance Block