Lecture 3Mathematics model (II)North China Electric Power UniversitySun HairongTopics of this class Block diagram reduction (cont.)Mason formula Reading: Module 1. 1. Block diagram reduction Examples Example 1:Solution:Example 2:Solution:Example 3Solution:2. Mason formula ：characteristic equation ：gain summation of all loops ：product summation of all the two untouchable loops ：product summation of all the three untouchable loops n ：the number of forward path ：gain of the kth forward path ：cofactor of the kth forward path2.1 The formula Cofactor of the kth forward path: The number of forward path and the gain of the forward path: The loops and their gain:Example 1Solution:L1=-G1G2G3H2, L2=-G1G2G3H1, L2=-G2G3G4 Untouchable loops: L1&L2, L1&L3 The transfer function between input and output: The loops and their gain: The number of forward path and the gain of the forward path:Example 2:Solution: Cofactor of the kth forward path: L1=-G1G2H1, L2=-G2H1, L2=-G2G3H2 Untouchable loops: The transfer function between input and output: The number of forward path and the gain of the forward path:Example 3:Solution: The loops and their gain: Cofactor of the kth forward path: L1=-G1G2G3, L2=-G1G2H1, L3=-G2G3H2, L4=G1G4. L5=G4H2 Untouchable loops: The transfer function between input and output: