An Algorithm for Automatic Reduction of Complex Signal Flow Graphs

1976 ◽  
Vol 98 (4) ◽  
pp. 367-374
Author(s):  
K. R. Young ◽  
L. L. Hoberock ◽  
J. G. Thompson
Keyword(s):  
Control Systems ◽  
Block Diagram ◽  
Directed Graphs ◽  
Complex Signal ◽  
Interactive Graphics ◽  
Signal Flow Graph ◽  
Signal Flow ◽  
Signal Flow Graphs ◽  
Computer Analyses ◽  
Flow Graphs

A computer algorithm is developed that provides efficient means to compute transmittances directly from a signal flow graph or a block diagram. Signal flow graphs are cast as directed graphs described by adjacency matrices. Nonsearch computation, designed for compilers without symbolic capability, is used to identify all arcs that are members of simple cycles for use with Mason’s gain formula. The routine does not require the visual acumen of an interpreter to reduce the topology of the graph, and it is particularly useful for analyzing control systems described for computer analyses by means of interactive graphics.

scholarly journals Metabolic control analysis. An application of signal flow graphs

1990 ◽  
Vol 269 (1) ◽  
pp. 141-147 ◽  
Author(s):  
A K Sen
Keyword(s):  
Feedback Inhibition ◽  
Metabolic Control Analysis ◽  
Control Analysis ◽  
Signal Flow Graph ◽  
Flow Graph ◽  
Signal Flow ◽  
Signal Flow Graphs ◽  
The Individual ◽  
Flow Graphs ◽  
Control Coefficients

In this paper the method of signal-flow graphs is used for calculating the Control Coefficients of metabolic pathways in terms of enzyme elasticities. The method is applied to an unbranched pathway (a) without feedback or feedforward regulation and (b) with feedback inhibition of the first enzyme by the last variable metabolite. It is shown that, by using a signal-flow graph, the control structure of a metabolic pathway can be represented in a graphical manner directly from the configuration of the pathway, without the necessity of writing the governing equations in a matrix form. From a signal-flow graph the various Control Coefficients can be evaluated in an easy and straightforward fashion without recourse to matrix inversion or other algebraic techniques. A signal-flow graph also provides a visual framework for analysing the cause-effect relationships of the individual enzymes.

Direct Application of the Loop Rule to Bond Graphs

1972 ◽  
Vol 94 (3) ◽  
pp. 253-261 ◽  
Author(s):  
F. T. Brown
Keyword(s):  
Transfer Function ◽  
Direct Reduction ◽  
Direct Application ◽  
Constant Parameter ◽  
Signal Flow Graph ◽  
Bond Graphs ◽  
Flow Graph ◽  
Signal Flow ◽  
Signal Flow Graphs ◽  
Flow Graphs

The Shannon-Mason loop rule permits direct reduction of a linear constant-parameter signal flow graph to a transfer function. Signal flow graphs can be constructed from bond graphs or sets of equations. Application of the loop rule to the parent bond graphs, however, with the aid of certain rules, is shown to be quicker and less prone to error. Also, four invariant classes of bond graph meshes are distinguished, with implications in physical analogies and in computation.

A CRITERION OF A MULTI-LOOP OSCILLATOR CIRCUIT

2007 ◽  
Vol 16 (01) ◽  
pp. 105-111 ◽  
Author(s):  
CHUN-LI HOU ◽  
CHEN-CHUAN HUANG ◽  
JIUN-WEI HORNG
Keyword(s):  
Feedback Control ◽  
Graph Representation ◽  
Signal Flow Graph ◽  
Flow Graph ◽  
Oscillator Circuit ◽  
Signal Flow ◽  
Signal Flow Graphs ◽  
Analysis Methods ◽  
Loop Feedback ◽  
Flow Graphs

Multi-loop feedback control has attracted considerable attention due to its simplicity and ease of implementation.1 In order to simplify the cumbersome analysis of a multi-loop circuit, the signal flow graph representation should be used rather than our familiar nodal analysis methods. This paper presents a criterion from the well-established Mason's formula for multi-loop oscillator in terms of signal flow graphs. The multi-loop oscillator circuit based on two operational transresistance amplifiers (OTRAs) is used as an example.

Compact Form of Mason's Gain Formula for Signal Flow Graphs

2010 ◽  
Vol 47 (4) ◽  
pp. 393-403 ◽  
Author(s):  
V. C. Prasad
Keyword(s):  
Signal Processing ◽  
Graph Theory ◽  
Digital Signal Processing ◽  
Control Systems ◽  
Digital Signal ◽  
Tree Structure ◽  
New Techniques ◽  
Signal Flow ◽  
Signal Flow Graphs ◽  
Flow Graphs

Mason's gain formula requires combining all paths and all loops judiciously. New techniques are presented in this paper to do this. All possible non-touching loop combinations can be generated systematically and represented compactly using a tree structure and/or factoring technique. Both numerator and denominator of the formula can be treated identically. The approach is simple enough to be used in teaching students Mason's gain formula as part of courses in control systems, digital signal processing, graph theory and applications, among others.

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