Improvement of Mason Rule for Solving the Complicated Block Diagram

Background: This study first efficiently applies the previous result Chen Electrical Unifying Approach (CEUA) utilized in the basic circuit theory to construct the control system matrix equation of the complicated block diagram. Methods: Based on the simple matrix operations proposed in this study, we can easily derive the transfer function without using the traditional Mason rule and the reduced techniques of the block diagram. We have successfully proposed a unifying approach to improve the disadvantages of the Mason rule, in which all loops must be found out and only the transfer function between the input node and the output node is evaluated, and the shortcoming of the reduced techniques for the block diagram is that the calculating process is too complex to be accepted. Results: The salient features of the proposed method are that the transfer function of the complicated block diagram can be easily obtained without using traditional Mason rule and the transfer function of any two nodes is immediately derived within only one calculation. Conclusion: We compared some demonstrated examples with some traditional approaches. Moreover, to demonstrate the practical applicability, the study has investigated one practical example.