Lecture 6 - Notes

January 19th, 2016

Block Diagrams

• A block diagram is a diagram of a system in which the system is represented as a a series of connected systems.

Basic Structures

Series (Cascade)

• Defined by

$$Y(s) = G(s)X_{1}(s) + G_{2}(s)X_{2}(s)$$

Open Loop

• No feedback loop therefore any disturbance or change in conditions may reduce the ability to complete the desired task

Parallel

• Defined by $$Y(S) = G_{1}(s)G_{2}(s)X(s)$$

Closed Loop (Feedback Loop)

• The output of a system is routed back as an input to the system (the system feeds back into itself)

• Open-loop transfer function

$$\frac{Outputs}{Inputs} = \frac{C(s)}{R(s)} = \frac{G(s)}{1 + G(s)H(s)}$$

Signal Flow Graph Rules

Signal-Flow Graph (Mason Graph)

• Specialized simplification of a block diagram
• Summing symbols and takeoff points are eliminated and are replaced with nodes
• The components or subsystems are