Lecture 8
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This document summarizes a lecture about clock-mode sequential machines and provides an example application of starting a gas burner. It includes: 1) An overview of clock-mode sequential machines including Mealy and Moore machines, state tables, and state diagrams. 2) Details of the gas burner startup application including a list of inputs, outputs, technological conditions, and block diagram of the system. 3) A 13-state Moore machine state diagram modeling the gas burner startup and shutdown sequences including states for initialization, checking conditions, firing startup, normal operation, and errors.
![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)](https://image.slidesharecdn.com/lecture8-150318150359-conversion-gate01/85/Lecture-8-40-320.jpg)
Lecture 8
- 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
- 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