SECTION 5: BLOCK DIAGRAMS - College of Engineering

SECTION 5: BLOCK DIAGRAMS

ESE 499 ? Feedback Control Systems

2 Block Diagram Manipulation

K. Webb

ESE 499

Block Diagrams

3

In the introductory section we saw examples of block diagrams to represent systems, e.g.:

Block diagrams consist of

Blocks ? these represent subsystems ? typically modeled by, and labeled with, a transfer function

Signals ? inputs and outputs of blocks ? signal direction indicated by arrows ? could be voltage, velocity, force, etc.

Summing junctions ? points were signals are algebraically summed ? subtraction indicated by a negative sign near where the signal joins the summing junction

K. Webb

ESE 499

Standard Block Diagram Forms

4

The basic input/output relationship for a single block is:

=

Block diagram blocks can be connected in three basic forms:

Cascade Parallel Feedback

We'll next look at each of these forms and derive a singleblock equivalent for each

K. Webb

ESE 499

Cascade Form

5

Blocks connected in cascade:

1 = 1 , 2 = 1 2 = 2 3 = 1 2 3 = 1 2 3 = = 1 2 3

The equivalent transfer function of cascaded blocks is the product of the individual transfer functions

K. Webb

ESE 499

Parallel Form

6

Blocks connected in parallel:

1 = 1 2 = 2 3 = 3 = 1 ? 2 ? 3

= 1 ? 2 ? 3 = 1 ? 2 ? 3 = = 1 ? 2 ? 3

The equivalent transfer function is the sum of the individual transfer functions:

K. Webb

ESE 499

Feedback Form

7

Of obvious interest to us, is the feedback form:

= = - = -

1 + =

= 1 +

The closed-loop transfer function, , is

= = 1 +

K. Webb

ESE 499

Feedback Form

8

= 1 +

Note that this is negative feedback, for positive feedback:

= 1 -

The factor in the denominator is the loop gain or open-loop transfer function

The gain from input to output with the feedback path broken is the forward path gain ? here,

In general:

forward path gain = 1 - loop gain

K. Webb

ESE 499

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