Block Diagram Simplification in Control Systems, Lecture notes of Automatic Controls

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Chapter (2)

BLOCK DIAGRAM

SIMPLIFICATION

Learning Outcomes

1) Identify the different element of Block Diagrams.

2) Simplify the complicated Block diagram to the simplest form.

Block Diagram

➢ Block Diagram is a pictorial representation of the functions performed by each

component and of the flow signals.

➢ Block Diagram depicts the interrelation that exist among the various components.

Transfer Function g(t) Input r(t) Output c(t) Fig. Elements of Block Diagram Transfer Function G(s) Input R(s) Output C(s)

Basic Elements of Block Diagram G(s) is a function of the system parameters only

1. Blocks in series (Cascaded)

➢ Note: The order of multiplication does not affect the overall transfer function

1. Blocks in series (Example)

By multiplication the overall transfer function is

3. Feedback Closed Loop

3. Feedback Closed Loop ❑ When the feedback signal is subtracted from the reference input signal, the loop is called negative feedback loop. ❑ The transfer function of a negative feedback loop is given by: ❑ G(s) is called the forward gain ❑ H(s) is called the feedback gain ❑ The product G(s)H(s) is called the loop gain.

3. Feedback Closed Loop with disturbance

5. Moving a summing junction after a block

7. Moving a pickoff point after a block

❑ Both configurations produce the same output for the same input

8. Moving a pickoff point ahead of a block

The algebraic rules for block diagrams

Example (2)

Simplify the block diagram and obtain the overall transfer function C(s)/R(s)