Control Engineering (BDA 30703)Lecture #05

By :

Dr Salihatun Md Salleh

Department of Mechanical Engineering,

Faculty of Mechanical Engineering & Manufacturing,

Universiti Teknologi Tun Hussein Onn

2012

Block Diagram

• Normally relation between input signal X(s), Output

signal Y(s), and transfer function, G(s), are visualize in

block diagram.

• To describe the relationship between the output and the

input a block diagram is used as shown in Fig. 1.

TRANSFER

FUNCTION

Input Output

X(s) Y(s)

G(s)

X(s) Y(s)

• One advantage of using s-domain is that the output

signal Y(s) is the result of the multiplication between the

input signal X(s) and the transfer function G(s). This

cannot be done in t-domain.

Figure 2

The space shuttle

consists of multiple

subsystems. Can

you identify those

that are control

systems, or parts of

control systems?

Figure 3

Components of a

block diagram for

a linear,

time-invariant

system

Forms of Block Diagram

1. Cascade Form

2. Parallel Form

3. Feedback Form

Figure 4

a. Cascaded

subsystems;

b. equivalent transfer

function

Figure 5

a. Parallel

subsystems;

b. equivalent

transfer

function

Figure 6

a. Feedback control

system;

b. simplified model;

c. equivalent transfer

function

Block Diagram Algebra

Figure 7

Block diagram

algebra for summing

junctions—

equivalent forms for moving

a block

a. to the left past a

summing junction;

b. to the right past a

summing junction

( )

)()(*)()(*)(

)()(*)()(

sCsGsXsGsR

sCsGsXsR

=+

=+

)()(*)(

1)(*)(

)()()(*)(

sCsXsG

sRsG

sCsXsGsR

=

+

=+

Figure 8

Block diagram algebra

for pickoff points—

equivalent forms for

moving a block

a. to the left past a

pickoff point;

b. to the right past a

pickoff point

Figure 9

Block diagram

for Example1

Example 1:

Reduction of Block Diagram

Figure 10

Steps in solving

Example 1:

a. collapse summing

junctions;

b. form equivalent

cascaded system

in the forward path

and equivalent

parallel system in the

feedback path;

c. form equivalent

feedback system and

multiply by cascaded

G1(s)

Figure 11

Block diagram for

Example 2

Example 2 :

Figure 12

Steps in the

block diagram

reduction for

Example 2

Tutorial 1

Q1:

Reduce the block diagram shown in figure below to a single transfer

function, T(s)=C(s)/R(s)

Q2 :

Find the equivalent transfer function, T(s)=C(s)/R(s), for the system shown

in figure below

Q3 :

Find the equivalent transfer function, T(s)=C(s)/R(s), for the system shown

in figure below

Figure 13

Signal-flow graph components:

a. system;

b. signal;

c. interconnection of systems and signals

Figure 14

Building signal-flow

graphs:

a. cascaded system

nodes (from Figure 4(a));

b. cascaded system

signal-flow graph;

c. parallel system

nodes (from Figure 5(a));

d. parallel system

signal-flow graph;

e. feedback system

nodes (from Figure

5.6(b));

f. feedback system

signal-flow graph

Figure 15

Signal-flow graph

development:

a. signal nodes;

b. signal-flow graph;

c. simplified signal-flow

graph