Introduction to Industrial Automation

Figure 4.11  State diagram of a machine operation with three speeds.

---

Logical Design of Automation Circuits 

◾

 

127

Thus, the state diagram shown in Figure 4.11 requires coding with two auxiliary variables A 

and B, while their binary assignment coding for each state is also indicated in the same figure. 

Subsequently, the procedure for extracting the logical functions remains similar to the one pre-

sented before. In the beginning, we apply the logical expression (1) for every one of the auxiliary 

variables of the selected coding, after defining the logical expressions of the Turn ON and Turn 

OFF transitions carefully. Moreover, we implement the logic for every state of the diagram, based 

on the corresponding assigned code of the auxiliary variables. Thus, for this specific example we 

have that:

 

Turn OFF of A S S b

S S b

B

B

=

+

=

=

2 1

0

1

3 0

0

0

 

 

( )

( )

==

+

=

b B b B b

0

0

0

where 

Turn OFF of A XY Z

w

=

 

( )

 means generally that the Turn OFF change from 1 to 0 of the 

variable A is caused by the signal Z and through the transition from the X state to the Y state, under 

the W condition (AND logic). In the same approach, we have that:

 

Turn ON of A S S b

b B

B

=

=

=

1 2

2

1

2

 

( )

 

Turn OFF of B S S

S S b

b

A

A

=

+

=

=

=

1 0

0

2 3

3

1

0

 

 

( )

( )

bb A b A

0

3

+

 

Turn ON of B S S b

b A

A

=

=

=

0 1

1

0

1

 

( )

The application of the formula (1) for the A and B variables will result in:

 

A b b B A

=

+

0

2

(

)

 

B b A b A b A B

b

A b

A b A B

=

+

+ =

+

+

+

0

3

1

0

3

1

(

) (

)(

)(

)

Moreover, for the three power relays C

1

, C

2

, and C

3

 (corresponding to three speeds and hence to 

three states S

1

, S

2

, and S

3

) we will have, according to the states’ coding, that:

 

C

AB, C

AB, C

AB

1

2

3

=

=

=

The implementation of the previous logical expressions will result in the automation circuit depicted 

in Figure 4.12.

---

128

 

◾

  Introduction to Industrial Automation