A block diagram is an interconnection of symbols reprenting certain basic mathematical operations in such a way that the overall diagram obeys the system’s mathematical model. Inspecting a block diagram of asystem may provide new insight into the system’s structure an behavior beyond that available from the differential equation themselves.
Simplifying Block Diagrams
When a system is modeled in a block diagram form the overall transfer function can be obtained by using block diagram simplification, which is often easier and more informative than algebraic manipulation, even though the methods are in every way equivalent. The central motivation behind simplifying a block diagram is the reduction of the complexity of the block diagram and obtaining the overall transfer function, while maintaining the same relationship among remaining variables. There are two main techniques that can be used.
– Direct Block Diagram Reduction
A complication block diagram involving many feedback loops can be simplified by a step-by-step rearrangement, using rules of block diagram algebra.
– The Signal Flow Graph
It introduced by S. J. Mason as a cause-and-effect representation of linear systems. In addition to the difference in physical appearances between the signal flow graph and the block diagram, the signal flow graph is constrained by more rigid mathematical rules. The signal flow graph is defined as agraphical means of portraying the input-output relationships between the variables of a set of linear algebratic equations. Consider a linier system described by a set of n algebratic aquations such that,
These n-equation are written in the form of cause-and relationships:
This is the most important axiom in forming the set of algebratic equations for signal flow graphs. In the case where the system is represented by a set of differential equations, the equations must be first transformed into Laplace transform equations. To be continued…