Advanced analysis algorithm notes

1. Lecture 8
Clock-Mode Sequential Machines
Gas burner start up (application example)

2. Clock-Mode Sequential Machines
• 8.1 Introduction
• 8.2 Mealy and Moore machine
• 8.3 State table
• 8.4 State diagram

3. Gas burner start up
(application example)
• 8.5 Introduction
• 8.6 Technological conditions
• 8.7 Variable list
• 8.8 Block diagram of the whole system
• 8.9 Minimal HW configuration of a PLC
• 8.10 State diagram

4. 8.1 Introduction
The various flip-flops, counters and shift
registers are all examples of sequential
machines (automatons).
All these circuits contain memory elements.
The flip-flops are the elementary memory
elements. The counters and shift registers
are composed of more than one such
element.

5. Introduction -2
All the circuit are capable of assuming more
than one state.
Their outputs do not depend only on the
inputs but also on the state in which the
circuit is at the time when the input is
acting on it.
If we note carefully the circuits of all these
elements, they have a feedback from the
output to the input.

6. 8.2 Mealy and Moore machine
In general, a sequential machine will have the
following:
1. A set S containing a finite number, say p, of
internal states, so that
S={S1, S2,……Sp}
2. A set X having a finite number, say n, of
inputs, so that
X={X1, X2,……Xn}
3. A set Z containing a finite number, say m, of
outputs, so that
Z={Z1, Z2,……Zm}

7. Mealy and Moore machine-2
4. A characterizing function f that uniquely
defines the next state St+1
as a function of
the present state St
and the present input
Xt
, so that
St+1
= f(St
, Xt
)

8. Mealy and Moore machine-3
5.A Mealy machine
A characterizing function g that uniquely
defines the output Zt
as a function of the
present input Xt
and the present internal
state St
, so that
Zt
= g(St
, Xt
)

9. Mealy and Moore machine-4
5.B Moore machine
A characterizing function g that uniquely
defines the output Zt
as a function of the
present internal state St
, so that
Zt
= g(St
)

10. Mealy and Moore machine-5
A sequential machine can therefore formally
be defined as follows:
Definition:
A sequential machine is a quintuple,
M=(X,Z,S,f,g), where X, Z and S are the
finite and nonempty sets of inputs,
outputs, and states respectively.

11. Mealy and Moore machine-6
f is the next-state function, such that
St+1
= f(St
, Xt
)
and the g is the output function such that
Zt
= g(St
, Xt
) for a Mealy machine
Zt
= g(St
) for a Moore machine
To describe a sequential machine, either a
state table or a state diagram is used.

12. 8.3 State table
Table1 is a state table describing an
example sequential machine M1. It can be
seen that machine M1 has a set of four
internal states A,B,C and D, a set of two
inputs I1 and I2 and a set of outputs O1 ,O2
The characterizing functions f and g are
depicted in tabular form, which is the state
table.

13. State table-2
• State table of a Mealy machine M1
Present state Next state, output
Input
I1 I2
A A,O1 B,O2
B D,O2 A,O1
C B,O1 D,O2
D A,O1 C,O1

14. State table-3
For example, for the present state B when the
input is I1, the next state is D and the output is
O2. If the input is I2, the next state is A and the
output is O1.
Thus the table shows the next state and the output
for each combination of the present state and
the input.
Since the output of the machine M1 depends on
both the present state and the input, it is a Mealy
machine.

15. State table-4
Table2 shows the state table of a Moore
machine. Here the output is independent
of the input and depends only on the
present state of the machine.
Therefore, this table has a separate column
defining the outputs, and two input
columns defining the next state without
having any output associated with it.

16. State table-5
• State table of a Moore machine M2
Present state Next state
Input
I1 I2
Output
A B C O1
B C D O2
C A C O1
D A C O2

17. State table-6
Another interesting property of of the
machines M1, M2 which we have depicted
in the two state tables is that for all
combinations of present state and input,
the next state and the output are
completely specified. Such machines are
therefore called completely specified
sequential machines (CSSMs).

18. State table-7
There is another clas of sequential
machines, where sometimes the next
state or the output or both may remain
unspecified. Such machines are known as
incompetely specified sequential
machines (ISSMs).

19. 8.4 State diagram
The information contained in the state table
can also be shown in a graphical manner
with the help of nodes conected by
directed graphs. Such diagrams are called
state diagrams.
Folowing figures show the state diagrams of
machines M1 and M2 respectively.

20. State diagram-2
State diagram of the Mealy machine M1

21. State diagram-3
State diagram of the Moore machine M2

22. Literature
• Nripendra N. Biswas: Logic Design
Theory,Prentice Hall
International,1993,ISBN 0-13-010695-X

23. Gas burner start up
(application example)

24. 8.5 Introduction
• Both startup and shut down of a gas burner is
rather complicated by safety reason
• There is a risk of explosion for example at gas
escape, premature ignition (firing), lighting out of
the flame when the gas valve is open etc.
• The right startup sequence given by standards
• Simplified in our example
• Moore machine application

25. 8.6 Technological conditions
At the beginning waiting for Start signal from
thermostat
Initial checking:
• Air pressure sensor checking
– (there must not be the air overpressure)
• Gas pressure sensor checking
– (there must be sufficient gas pressure)

26. Technological conditions-2
After the initial checking:
Startup of the combustion air compressor
and after it the delay τ2=3 s (air compressor is
running with sufficient performance)
Ventilating of the combustion chamber during
τ1=30 s (to prevent creating of detonating
mixture from the rest of gas and the air)
Checking of sufficient ventilating of the combustion
chamber(sufficient high value at the air pressure
sensor)

27. Technological conditions-3
After the sufficient ventilating the burner
firing startup:
• Gas valve opening
• Firing signal generation (e.g. pulses)
• Continuing with these conditions during
τ3=4 s
• After this delay expiration standard
operating checking starts

28. Technological conditions-4
Standard operating checking sequence
Gas pressure sensor checking
-(there must be sufficient gas pressure)
Air pressure sensor checking
-(there must be sufficient air overpressure)
Flame presence sensor checking
-(the flame must not disappear when gas valve is open)
Thermostat checking
-(is there a need for heating, that is for running the
burner?)

29. Technological conditions-5
Shut down of the gas burner
• Similar sequence as with start up
• Here not in detail, only one macro state „shut
down“
Errors
• When any error occures during start up,standard
operating or shut down, then it is necessary to
assure properly transition to the error state (shut
down and the error message)

30. 8.7 Variable list
Inputs of PLC
• Sta…..thermostat
(there is a need for heating: Sta=1)
• Vzd …air pressure sensor
(sufficient pressure : Vzd=1)
• Ply … gas pressure sensor
(sufficient pressure : Ply=1)
• Pla …. flame presence sensor
(flame is burning: Pla=1)

31. Variable list-2
Outputs of PLC
• Sdv ……air compressor
(Sdv=1: air compressor start up!)
• Opp ….. gas valve
(Opp =1: gas valve open!)
• Zps …. firing signal
(Zps=1: firing signal generation!)

32. Variable list-3
Internal variables – technological
parameters
• τ1 …delay for ventilating of the
combustion chamber (τ1=30s )
• τ2…delay for combustion air compressor
starting (τ2=3s )
• τ3… delay for firing signal generation
(τ3=4s )

33. 8.8 Block diagram of the whole
system
TP Sta
Vzd
Ply
Pla
PLC
OI
TP ……technological process ( gas burner )

34. Block diagram of the whole
system-2
TP Sta
Vzd
Ply
Pla
PLC
OI

35. Block diagram of the whole
system-3
ŘS TP
Opp
Zps
Sta
Vzd
Ply
PlaSdv
PLC
OI

36. Block diagram of the whole
system-4
ŘS TP
Opp
Zps
Sta
Vzd
Ply
PlaSdv
PLC
OI
τ1, τ2, τ3

37. Block diagram of the whole
system-5
ŘS TP
Opp
Zps
Sta
Vzd
Ply
PlaSdv
PLC
OI
τ1, τ2, τ3
OP ErrRest
OP Operator panel

38. Variable list
- inputs and outputs of PLC
Inputs of PLC
• Sta…..thermostat (there is a need for heating:
Sta=1)
• Vzd …air pressure sensor (sufficient pressure :
Vzd=1)
• Ply … gas pressure sensor (sufficient pressure :
Ply=1)
• Pla …. flame presence sensor (flame is burning:
Pla=1)
• Rest …..OP – restarting command (command
for restarting from operator panel: Rest=1)

39. Variable list
- inputs and outputs
Outputs of PLC
• Sdv ……air compressor (Sdv=1: air
compressor start up!)
• Opp ….. gas valve (Opp =1: gas valve
open!)
• Zps …. firing signal (Zps=1: firing signal
generation!)
• Err …..OP – error indication lamp (Err=1:
lamp is on!)

40. 8.9 Minimal HW configuration
of a PLC
• 5 binary inputs +20% reserve…6 DI
• 4 binary outputs +20% reserve..5 DO
– DI ..Digital Input
– DI ..Digital Output
• real configuration: 8/8 IO [ajou]
• binary inputs and outputs of PLC often
organised in groups of 4, 8, 16
• specific addresses are HW dependend,
(IEC 1131: inputs - I, outputs – Q)

41. 8.10 State diagram
K07
ODS
K06
K07
K05
K06
C1
C2
K05
ZAP
C2
C1
K01
ERR
CNS
K02
Vzd
Vzd
Ply
Ply
Sdv
Tau2Vzd
Opp,Zps
Tau1
Tau1
K04
Tau3
Ply
Tau3
Ply
Vzd
Vzd
Pla
Pla
Sta
Opp, Sdv En?
Sta
Sta
Zps
1
2
34
5
6
Rest
Start up:
CNS to ZAP
Tau2
Ordinary operation:
K04 až K07
Shut down:
„makrostate“ ODS
Errors:
„macrostate“ ERR

42. State diagram-2
CNS
K01
Sta
CNS..waiting for start
K01..first checking
State names:

43. State diagram-3
CNS
K01
Sta
K01
ERR
CNS
K02
Vzd
Vzd
State names :
K02..second checking
ERR..error
Vzd ... direct variable (=1)
Vzd ...inverse variable (=0)

44. State diagram-4
CNS
K01
Sta
K02
C1
K01
ERR
CNS
K02
Vzd
Vzd
Ply
Ply
Sdv
State names :
C1…first waiting loop
blue ..outputs, only when
changing

45. State diagram-5
CNS
K01
Sta
ERR
CNS
K01
K02
C1
C2
C1
K01
ERR
CNS
K02
Vzd
Vzd
Ply
Ply
Sdv
Tau2
Tau2
State names:
C2…second waiting loop
green auxiliary binary
variables (with the
relation to the
technological parametres)
t< τ2: Tau2=0 …. Tau2
t≥ τ2: Tau2=1 …. Tau2
Implementation in PLC
with „timers“

46. State diagram-6
ZAP
C2
C1
K01
ERR
CNS
K02
Vzd
Vzd
Ply
Ply
Sdv
Tau2Vzd
Tau2
Opp,Zps
Tau1
Tau1
Sta
State names :
ZAP...burner firing

47. State diagram-7
ZAP
C2
C1
K01
ERR
CNS
K02
Vzd
Vzd
Ply
Ply
Sdv
Tau2Vzd
Tau2
Opp,Zps
Tau1
Tau1
K04 Tau3
Tau3
Sta
State names :
K04…fourth checking
Zps

48. State diagram-8
C1
C2
K05
ZAP
C2
C1
K01
ERR
CNS
K02
Vzd
Vzd
Ply
Ply
Sdv
Tau2Vzd
Tau2
Opp,Zps
Tau1
Tau1
K04
Tau3
Ply
Tau3
Ply
Sta
State names:
K05…fifth checking
Zps

49. State diagram-9
K05
K06
C1
C2
K05
ZAP
C2
C1
K01
ERR
CNS
K02
Vzd
Vzd
Ply
Ply
Sdv
Tau2Vzd
Tau2
Opp,Zps
Tau1
Tau1
K04
Tau3
Ply
Tau3
Ply
Vzd
Vzd
Sta
State names:
K06…sixth checking
Zps

50. State diagram-10
K06
K07
K05
K06
C1
C2
K05
ZAP
C2
C1
K01
ERR
CNS
K02
Vzd
Vzd
Ply
Ply
Sdv
Tau2Vzd
Tau2
Opp,Zps
Tau1
Tau1
K04
Tau3
Ply
Tau3
Ply
Vzd
Vzd
Pla
Pla
Sta
State names :
K07…seventh checking
Zps

51. State diagram-11
K07
ODS
K06
K07
K05
K06
C1
C2
K05
ZAP
C2
C1
K01
ERR
CNS
K02
Vzd
Vzd
Ply
Ply
Sdv
Tau2Vzd
Tau2
Opp,Zps
Tau1
Tau1
K04
Tau3
Ply
Tau3
Ply
Vzd
Vzd
Pla
Pla
Sta
Sta
Opp, Sdv
Sta State names:
ODS…shut down
(macrostate-sequention
of states similar
to the stating up)
Zps

52. State diagram-12
K07
ODS
K06
K07
K05
K06
C1
C2
K05
ZAP
C2
C1
K01
ERR
CNS
K02
Vzd
Vzd
Ply
Ply
Sdv
Tau2Vzd
Tau2
Opp,Zps
Tau1
Tau1
K04
Tau3
Ply
Tau3
Ply
Vzd
Vzd
Pla
Pla
Sta
Opp, Sdv En?
Sta
Sta
Zps
Another input:
En?..main power
switch ????

53. State diagram-13
K07
ODS
K06
K07
K05
K06
C1
C2
K05
ZAP
C2
C1
K01
ERR
CNS
K02
Vzd
Vzd
Ply
Ply
Sdv
Tau2Vzd
Tau2
Opp,Zps
Tau1
Tau1
K04
Tau3
Ply
Tau3
Ply
Vzd
Vzd
Pla
Pla
Sta
Opp, Sdv En?
Sta
Sta
Zps
1
2
34
5
6
ERR…. Error
„ macrostate “:
1,2,…,6 various types of
errors – it is possible to
distinquish via previous
state and the cause of the
errror occurence)
E.g.: Err4:„there is
not sufficient gas
pressure during
ordinary operation“

54. State diagram-14
K07
ODS
K06
K07
K05
K06
C1
C2
K05
ZAP
C2
C1
K01
ERR
CNS
K02
Vzd
Vzd
Ply
Ply
Sdv
Tau2Vzd
Tau2
Opp,Zps
Tau1
Tau1
K04
Tau3
Ply
Tau3
Ply
Vzd
Vzd
Pla
Pla
Sta
Opp, Sdv En?
Sta
Sta
Zps
1
2
34
5
6
Rest
Rest:
• only authorized
operator
• confirming
of error removing
• special safety switch
on the operator panel