lecture 8 clock-mode sequential machines gas burner start up (application example)

Lecture 8

Clock-Mode Sequential Machines

Gas burner start up (application example)

Clock-Mode Sequential Machines

• 8.1 Introduction

• 8.2 Mealy and Moore machine

• 8.3 State table

• 8.4 State diagram


• 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

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.

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.

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}

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 )


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 )


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 )


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.


f is the next-state function, such thatSt+1 = f(St , Xt )and the g is the output function such that Zt = g(St , Xt ) for a Mealy machineZt = g(St ) for a Moore machine

To describe a sequential machine, either a state table or a state diagram is used.

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.

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

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.

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.

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

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).

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).

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.

State diagram-2

State diagram of the Mealy machine M1

State diagram-3

State diagram of the Moore machine M2

Literature

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

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

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)

Technological conditions-2After 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)

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


Standard operating checking sequenceGas 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?)


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)

8.7 Variable listInputs 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)

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!)

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 )

8.8 Block diagram of the whole system

TP StaVzd

Ply

Pla

PLCOI

TP ……technological process ( gas burner )

Block diagram of the whole system-2

TP StaVzd

Ply

Pla

PLCOI


ŘS TPOpp

ZpsStaVzd

Ply

PlaSdv

PLCOI


ŘS TPOpp

ZpsStaVzd

Ply

PlaSdv

PLCOI

τ1, τ2, τ3


ŘS TPOpp

ZpsStaVzd

Ply

PlaSdv

PLCOI

τ1, τ2, τ3

OP ErrRestOP Operator panel

Variable listinputs 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)

Variable listinputs 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!)

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)

8.10 State diagram

K07

ODS

K06

K07

K05

K06C1

C2K05

ZAP

C2

C1

K01

ERR

CNS

K02

VzdVzd

Ply

Ply

Sdv

Tau2Vzd

Opp,Zps

Tau1Tau1

K04Tau3

Ply

Tau3

Ply

VzdVzd

PlaPla

Sta

Opp, Sdv En?

Sta

Sta

Zps

12

345

6

Rest

Start up:CNS to ZAP

Tau2

Ordinary operation:K04 až K07

Shut down:„makrostate“ ODS

Errors:„macrostate“ ERR

State diagram-2

CNSK01

Sta

CNS..waiting for start

K01..first checking

State names:

State diagram-3

CNSK01

Sta

K01

ERR

CNS

K02

VzdVzd

State names :

K02..second checking

ERR..error

Vzd ... direct variable (=1)

Vzd ...inverse variable (=0)

State diagram-4

CNSK01

Sta

K02

C1

K01

ERR

CNS

K02

VzdVzd

Ply

Ply

Sdv

State names :

C1…first waiting loop

blue ..outputs, only when changing

State diagram-5

CNSK01

Sta

ERR

CNSK01

K02

C1

C2

C1

K01

ERR

CNS

K02

VzdVzd

Ply

Ply

Sdv

Tau2Tau2

State names:

C2…second waiting loop

green auxiliary binary variables (with the relation to the technological parametres)

t< τ2: Tau2=0 …. Tau2t τ2: Tau2=1 …. Tau2Implementation in PLC with „timers“

State diagram-6

ZAP

C2

C1

K01

ERR

CNS

K02

VzdVzd

Ply

Ply

Sdv

Tau2VzdTau2

Opp,Zps

Tau1Tau1

Sta State names :

ZAP...burner firing

State diagram-7

ZAP

C2

C1

K01

ERR

CNS

K02

VzdVzd

Ply

Ply

Sdv

Tau2VzdTau2

Opp,Zps

Tau1Tau1

K04 Tau3

Tau3

Sta State names :

K04…fourth checking

Zps

State diagram-8

C1

C2K05

ZAP

C2

C1

K01

ERR

CNS

K02

VzdVzd

Ply

Ply

Sdv

Tau2VzdTau2

Opp,Zps

Tau1Tau1

K04Tau3

Ply

Tau3

Ply

StaState names:

K05…fifth checking

Zps

State diagram-9

K05

K06C1

C2K05

ZAP

C2

C1

K01

ERR

CNS

K02

VzdVzd

Ply

Ply

Sdv

Tau2VzdTau2

Opp,Zps

Tau1Tau1

K04Tau3

Ply

Tau3

Ply

VzdVzd

Sta State names:

K06…sixth checking

Zps

State diagram-10

K06

K07

K05

K06C1

C2K05

ZAP

C2

C1

K01

ERR

CNS

K02

VzdVzd

Ply

Ply

Sdv

Tau2VzdTau2

Opp,Zps

Tau1Tau1

K04Tau3

Ply

Tau3

Ply

VzdVzd

PlaPla

Sta State names :

K07…seventh checking

Zps

State diagram-11

K07

ODS

K06

K07

K05

K06C1

C2K05

ZAP

C2

C1

K01

ERR

CNS

K02

VzdVzd

Ply

Ply

Sdv

Tau2VzdTau2

Opp,Zps

Tau1Tau1

K04Tau3

Ply

Tau3

Ply

VzdVzd

PlaPla

Sta

Sta

Opp, Sdv Sta State names:

ODS…shut down(macrostate-sequention of states similar to the stating up)

Zps

State diagram-12

K07

ODS

K06

K07

K05

K06C1

C2K05

ZAP

C2

C1

K01

ERR

CNS

K02

VzdVzd

Ply

Ply

Sdv

Tau2VzdTau2

Opp,Zps

Tau1Tau1

K04Tau3

Ply

Tau3

Ply

VzdVzd

PlaPla

Sta

Opp, Sdv En?

Sta

Sta

Zps

Another input:

En?..main power switch ????

State diagram-13

K07

ODS

K06

K07

K05

K06C1

C2K05

ZAP

C2

C1

K01

ERR

CNS

K02

VzdVzd

Ply

Ply

Sdv

Tau2VzdTau2

Opp,Zps

Tau1Tau1

K04Tau3

Ply

Tau3

Ply

VzdVzd

PlaPla

Sta

Opp, Sdv En?

Sta

Sta

Zps

12

345

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“

State diagram-14

K07

ODS

K06

K07

K05

K06C1

C2K05

ZAP

C2

C1

K01

ERR

CNS

K02

VzdVzd

Ply

Ply

Sdv

Tau2VzdTau2

Opp,Zps

Tau1Tau1

K04Tau3

Ply

Tau3

Ply

VzdVzd

PlaPla

Sta

Opp, Sdv En?

Sta

Sta

Zps

12

345

6

Rest

Rest:• only authorized operator• confirming of error removing• special safety switch on the operator panel

lecture 8 clock-mode sequential machines gas burner start up (application example)

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