**Signal Flow Graph in Control Systems:**

**Signal flow graph** is used to represent the control system graphically and it was developed by S.J.Mason.Signal flow graph is a diagram that represents a set of simultaneous linear algebraic equations.By differential equations governing a **control system** can be algebraic equations in s-domain.The **signal flow graph** of the system can be constructed using these equations.

#### It should be noted that the **signal flow graph approach** and the block diagram approach yield the same information.The advantage in signal flow graph method is that, using **Mason’s gain formula** the overall gain of the system can be computed easily.This method is simpler than the tedious block diagram reduction techniques.

#### The **signal flow graph** depicts the flow of signals from one point of a system to another and give, relationships among the signals. A signal flow graph consists of a network in which nodes are connected by directed branches.Each node represents a system variable and each branch connected between two nodes acts as a signal multiplier.Each branch has a gain or transmittance.When the signal pass through, a branch, it gets multiplied by the gain of the branch.

#### In a **signal flow graph**, the signal flows in only one direction.The direction of signal flow indicated by an arrow placed on the branch and the gain (multiplication factor) is indicated along the branch.

**Explanation of terms used in Signal Flow Graph:**

**Node** : A node is a point representing a variable or signal.

**Branch**: A branch is directed line segment joining two nodes. The arrow on the branch indicates the direction of signal flow an the gain of a branch. is the transmittance.

**Transmittance**: The gain acquired by the signal when it travels from one node to another is called transmittance.The transmittance can he real or complex.

**Input node ( Source)**: It is a node that has only outgoing branches.

**Output node ( Sink )**: It is a node that has only incoming branches.

#### Mixed node : It is a node that has both incoming and outgoing branches.

#### (vii) The signals travel along branches only in the marked direction and then it gets multiplied by the gain or transmittance of the branch.

#### (viii) The **signal flow graph** of system is not unique.By rearranging the system equations different types of signal flow graphs can be drawn for a given system.

**Signal Flow Graph Algebra:**

#### Signal flow graph for a system can be reduced to obtain the transfer function on of the system using the following rules.The guideline in developing the rules for **signal flow graph** algebra is that the signal at a anode is given by sum of all incoming signals.

**Rule 1** : Incoming signal to a node through a branch is given by the product of a signal at previous node and the gain of the branch.Check below **solved examples**.