Logical Design of Automation Circuits
◾
147
For each of the auxiliary variables, we have:
Turn ON A S S
x
Turn OFF A S
x
B
C
=
=
=
=
=
1 2
0
1
2
( )
,
,
BC
SS
yB
Turn ON B S S
y
z
B
C
A
1
0
1
1 3
0
( )
( )
,
,
=
=
=
=
=
C
C
A
C
zAC
Turn OFF B S S
wAC
Turn
w
=
=
=
=
=
=
1
3 1
0
1
( )
,
ON C S S
Turn OFF C S S
b
A
B
=
=
=
=
0 1
0
0
1 0
1
( )
(
,
bb
x
S S
b AB xAB
S S
A
B
A
B
0
0
0
4 3
0
1
1
3 4
)
( )
,
,
=
=
=
=
+
=
+
+
( )
,
y
b AB yAB
A
B
=
=
=
+
0
1
0
Applying the logical Equation (1) to three auxiliary variables, we obtain,
A yBC xBC A
y B C xBC A
=
+
= + +
+
(
) (
)(
)
B wAC zAC B
w A C zAC B
=
+
=
+ +
+
(
) (
)(
)
C
b AB yAB b AB xAB C
b
A B y A B b AB x
=
+
(
)
+
+
=
+ +
+ +
+
0
1
0
1
(
) (
)(
)(
AAB C
+
),
and also
R
ABC, R
ABC, L
ABC, L
ABC
LS
HS
LS
HS
=
=
=
=
S
0
S
1
R
LS
b
1
b
0
S
3
L
LS
z
w
S
4
L
HS
y
x
S
2
R
HS
x
y
ABC
000
001
011
010
101
R = motion to the right, L = motion to the left, LS = low speed, HS = high speed
Figure 4.35 State diagram for application in Section 4.3.1, shown in Figure 4.34.
148
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Introduction to Industrial Automation
The implementation of these logical expressions results in the automation circuit shown in
Figure 4.36, where it can also be checked that its operation satisfies the desired described
automation.
4.4.2 Palindromic Movement of a Worktable with Memory
In Figure 4.37, a simplified form of the carrier (lead screw worktable) of a machine tool is depicted,
which is called a “lathe”. The worktable of the lathe is desired to be moved in between two limit
positions to the left and to the right, according to the following specifications:
1. Initially, we define the movement of the table to the right with “S
R
” and the movement to
the left with “S
L
”. In both states, and with the press of a button “s” (STOP), the table stops
in its current position.
N
A
R
x
R
LS
Α
b
1
b
0
C
Α
Β
B
C
y
Β
A
B
z
C
A
C
w
A
B
C
A
B
A
C
A
y
B
x
B
A
C
Β
R
HS
C
Β
C
Α
Β
Α
C
L
HS
L
LS
Β
Figure 4.36 Automation circuit for application in Section 4.3.1 based on the state diagram of
Figure 4.35.
Logical Design of Automation Circuits
◾
149
2. With a press of the button “m” (memory button), the table continues moving in the same
manner before it was stopped, due to the press of the button “s”.
3. If the table is moving to the right (S
R
), then either by the press of a button “a” or when it
reaches the end of its movement where the limit switch “z” is energized, the direction of the
motion will be inverted, which means that the table should move to the left (S
L
).
4. With the same approach, when the table is moving to the left (S
L
), either with a press of
a button “d”, or when it reaches in the end of its movement where the limit switch “w” is
energized, the direction of the motion will be inverted, which means that the table should
move to the right (S
R
).
5. If, during the movement of the table to the left (S
L
), the limit switch “w” is ener-
gized, while the limit switch “z” remains energized, due to a fault (e.g., the limit switch
has been blocked), then the table should stop, like in the case where the button “s” had been
pressed.
Overall, we have the following operational buttons and limit switches:
s = STOP button
m = motion continuation button
a = S
L
motion button
d = S
R
motion button
z = limit switch of the S
R
motion
w = limit switch of the S
L
motion
The corresponding state diagram is indicated in Figure 4.38, where the STOP state of S
0L
and
S
0R
is noted, with a previous S
L
or S
R
motion correspondingly.
Based on this remark, we have the following Turn ON and Turn OFF sets for the auxiliary
variables:
w
z
Worktable
Lead screw
Motor
Motion
reverse
Motion
reverse
Figure 4.37 The movable carrier (lead screw worktable) of a machine tool.
S
0L
S
L
m
s+zw
S
R
a+z
d+w
S
0R
m
s
AB
00
01
11
10
Figure 4.38 State diagram for application in Section 4.4.2, shown in Figure 4.37.
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Introduction to Industrial Automation
Turn ON A S S d w
d w B
Turn OFF A S
L R
B
=
+
= +
=
=
(
)
(
) ,
1
R
R L
B
L L
S a z
a z B
Turn ON B S S m
(
)
(
(
)
+
= +
=
=
1
0
))
(
)
A
L
L
A
R R
Turn OFF B S S s zw
S S
=
=
=
+
+
0
0
0
0
( )
( )
(
)
m
s
mA mA m
S S
s zw A sA z
A
R
R
A
=
=
=
+
=
+
= +
+
=
1
0
1
w
wA s
+
Applying the logical Equation (1) to the A and B auxiliary variables, we obtain,
A (a z)B (d w)B A
a z B (d w)B A
= +
+
+
(
)
=
+
+
+
(
)
(
)
B
zwA s m B
z w A s(m B)
=
+
(
)
+
= + +
+
(
) (
)
,
and also,
S
AB S
AB
L
R
=
=
,
The implementation of these logical expressions is presented in the automation circuit shown in
Figure 4.39.
N
R
B
A
z
B
w
s
m
d
A
A
B
w
a
z
B
S
R
Α
Β
Β
Α
S
L
Figure 4.39 Automation circuit for application in Section 4.4.2 based on the state diagram of
Figure 4.38.
Logical Design of Automation Circuits
◾
151
4.4.3 Operation of N Machines with Pause under Specific Conditions
Let’s assume that we have a set of n identical machines, which we would like to start and stop
manually with a corresponding n number of START-STOP pairs of buttons. For the START
operation of the machines no specific condition is needed. However, for the STOP operation, due
to some functional specifications, it is important that the STOP action is applied immediately to
all the machines, except for the last in operation machine, which should terminate its operation
only when a sensor is energized. The operation of the rest of the machines, except the last one, must
stop independently of the sensor’s state. The difficult part of this problem is the fact that the last
machine in operation is not predefined, rather it is randomly selected from the n of total machines.
In the case that the sensor is activated, and the STOP button of the final operation machine is not
pressed; then the machine continues to operate. To summarize, every machine from the n total can
act as the last machine in operation, where we would like to stop it in cooperation with a sensor. In
this case, it is assumed that the rest of the machines will have been stopped already.
At this point is should be mentioned that this problem is not an abstract example for tutorial
purposes; it occurs frequently in the central autonomous heating systems of multiple apartments.
In this case, the machines are replaced from the central electrovalves of the apartments (heating
or cooling of the apartment). In these systems, every inhabitant can stop the heating at any time
it is desired. In the case that the inhabitant is the last one who switches off the heating, in order
not to have hot water trapped in specific areas of the pumps’ network, the automation system
should prevent the electrovalve of the last apartment to close, even if the inhabitant keeps it open
until all the thermal heating of the apartment is reduced to an acceptable level (based on a specific
temperature sensor) before closing the final electrovalve.
Since the construction of the state diagram for 1, 2, 3,…, n-1,…, n machines is very complicated,
we will only represent the case of three machines, but in a way that the expansion of the diagram to
more machines would be straightforward. In Figure 4.40, this state diagram is presented with all the
potential operational combinations of the machines; with the indications of the machines (A, B, C) and
the three states (S
1
, S
2
, S
3
), where only the last machine is in operation, and from where the transition
to S
0
requires the logical condition for the sensor to be energized. In this automation system, the sensor
signal, which is also the transition event, is represented by “t”. Additionally, we denote with “s
i
” and “p
i
”
the START and STOP buttons of the i
th
machine, with i=1, 2, 3 for the illustrated example.
Based on this analysis, the Turn ON and Turn OFF logical expressions for the auxiliary vari-
ables A, B, and C are defined as:
Turn ON A
S S s
S S s
0 1
B 0, C 0
3 2
B
=
+
=
=
=
( )
( )
1
1
1,, C 0
7 6
B , C 1
4 5
B ,
S S s
S S s
=
=
=
=
+
+
( )
( )
1
1
1
0 C
C
1
s BC s BC s BC s BC s B s B s
=
=
+
+
+
=
+
=
1
1
1
1
1
1
1
Turn OFF A
S S p t
S S p
1
B 0, C 0
1 B
=
+
=
=
1 0
5 4
( )
( )
==
=
=
=
=
+
+
0, C 1
1 B 1, C 0
1 B
S S p
S S p
2 3
6 7
1
( )
( )
,, C 1
p tBC p C p BC p BC p BC p Bt p B
p BC
=
=
+
+
+
=
+
+
=
+
1
1
1
1
1
1
1
1
Β
pp B p t p B p C p t p B C t
1
1
1
1
1
1
+
=
+
+
=
+ +
(
)
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Introduction to Industrial Automation
Turn ON B
S S s
S S s
1 2
A 1, C 0
0 3
A
=
+
=
=
=
( )
( )
2
2
0,, C 0
5 6
A , C 1
4 7
A ,
S S s
S S s
=
=
=
=
+
+
( )
( )
2
1
2
0 C
C
2
s AC s AC s AC s AC s C s C s
=
=
+
+
+
=
+
=
1
2
2
2
2
2
2
Turn OFF B
S S p
S S p t
2 A 1, C 0
2
A
=
+
=
=
1 2
3 0
( )
(
)
==
=
=
=
=
+
+
0, C 0
2 A , C 1
2 A
S S p
S S p
7 4
0
6 5
1
( )
( )
,, C 1
p AC p tAC p AC p AC p CA p Ct p C
p CA
=
=
+
+
+
=
+
+
=
+
2
2
2
2
2
2
2
2
pp C p t p C p A p t p C A t
2
2
2
2
2
2
+
=
+
+
=
+ +
(
)
Turn ON C
S S s
S S s
0 4
A 0, B 0
1 5
A
=
+
=
=
=
( )
( )
3
3
1,, B 0
2 6
A , B 1
3 7
A ,
S S s
S S s
=
=
=
=
+
+
( )
( )
3
1
3
0 BB
3
s AB s AB s AB s AB s B s B s
=
=
+
+
+
=
+
=
1
3
3
3
3
3
3
S
4
S
5
s
3
p
1
S
6
S
7
S
1
ABC
000
101
111
011
100
S
2
110
S
0
S
3
Machine A
Machine B
010
001
Machine C
p
3
•t
p
2
•t
p
1
•t
s
1
s
2
s
1
p
1
p
2
s
2
p
2
s
2
p
2
s
2
s
1
p
1
s
1
s
3
s
3
s
3
p
3
p
3
p
3
Figure 4.40 State diagram for the operation of three machines with pause under specific con-
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