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1. Control Systems
Paper code : EC602
Dr. Anilesh Dey
Associate Professor and HOD
Department of ECE, Narula Institute of Technology
Lecture 5

2. Last Lecture
• Block Diagram Algebra numerical problems
Today’s Topic
• Signal Flow Graph
• MASON’S Gain Formula

3. Background:
Block diagram reduction is the excellent method for
determining the transfer function of the control
system.
However, in a complicated system, it is very
difficult and time-consuming process that is why an
alternate method, i.e., SFG was developed by S.J
Mason which relates the input and output system
variables graphically.
In the signal flow graph, the transfer function is
referred to as transmittance.

4. Characteristics of SFG:
SFG is a graphical representation of the relationship
between the variables of a set of linear algebraic equations.
It doesn't require any reduction technique or process.
It represents a network in which nodes are used for the
representation of system variable which is connected by
direct branches.
SFG is a diagram which represents a set of equations. It
consists of nodes and branches such that each branch of
SFG having an arrow which represents the flow of the signal.
It is only applicable to the linear system.

5. Mason Gain Formula

6. For the given signal flow graph find the ratio C/R.

12. Obtain signal flow graph representation for a system whose block
diagram given below and using Mason’s gain formula determine the
ratio C/R.

14. • References:
1. Automatic Control Systems 8th edition– by B. C. Kuo 2003– John Wiley and son’s,
2. Control Systems Engineering – by I. J. Nagrath and M. Gopal, New Age International (P)
Limited, Publishers, 2nd edition.
3. Control Systems –by Ramesh Babu
4. Modern Control Engineering – by Katsuhiko Ogata – Prentice Hall of India Pvt. Ltd., 3rd
edition, 1998.
5. NPTEL video lecture--by Dr. Ramkrishna Pasumarthy

15. Feel free to contact me
Dr.Anilesh Dey
anileshdey@ieee.org
anilesh.dey@nit.ac.in
head_ece.nit@jisgroup.org
End of Lecture 5. Meet u @lecture 6