Ladder Diagram Example

et438b-7.pptx 1

Lecture Notes Part 7ET 438B Sequential Control and Data Acquisition

et438b-7.pptx 2

Ladder Diagram Example

A manual mixing operation is to be automated using sequential process control methods. The process composed of three steps:

a.) filling a tank to a predetermined level b.) agitating the liquid for 30 minutes c.) draining the tank for use in another part of process

Does the ladder logic schematic that follows perform this function correctly?

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Ladder Diagram Example

Press startEnergized

Solenoid Aenergizedtank begins tofill

Tank fills tolimit

closed

open

Timer energizedMotor starts

Timer goesTo 30 minutes

closed

open

Mixer motor offSolenoid B on

When tankdrains flow switchresets. Timer resets

open

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Combinational and Sequential Logic with Relays and Contacts

Let contact state represent a logical value

Implement AND gate

= Logic 0 Called Form A Contact

= Logic 1 Called Form B Contact

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Combinational and Sequential Logic with Relays and Contacts

inputs

output

potential grd

A B = C

Conditions A AND B must be present to energizeoutput CNote: all contacts are considered instantaneousand not held unless modified

With electromechanical relays fan-in and fan-out limited by number of contacts in relays

Energized

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More Logic Functions

potential grd

Either A OR B will cause coil C to be energizedContacts A, B represent conditions or states inthe sequential process

ORFunction

A + B = C Boolean expression

Energized

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More Logic Functions

NOT Function

Boolean ExpressionB = A

Contact of opposite state creates inversion

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Constructing Other Logic Functions

120 Vac grd

Combine the AND function with the NOT function to get a NAND operation.

Rung 1 implements the AND functionRung 2 implements the NOT function

Any contact associated with coil D will changestate like a NAND TTL gate.

Energized

open

De-energized

et438b-7.pptx 9

Multiple Input AND/NAND

Can add a memory action to the above by includinga feedback from the output coil to the inputs

A B C = E and A B C = E

Energized

open

Close AND

NAND

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Memory Action AND/NAND

Can add a memory action to the above by includinga feedback from the output coil to the inputs

B andC are notsealed

Energized

open

Close

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All Inputs Latched AND/NAND

Contact E in rung 2 is a feedback from the output that makes circuit ignore state changes of A, B and Cafter the condition A B C is detected.

The output can not change unless the circuit is de-energized.

Energized

open

Close

et438b-7.pptx 12

Motor Control ExampleThree-wire control- used for manual and automatic motor starting.

motor

M1 seals-in the start PB. Motor stops when power lost

Thermal overloads actuate the control contacts OL1 to OL3

Powerwiring

120 Vac GRDControl wiring

M1

STOPSTART

OL1

OL2

OL3

Motor Runs

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Multiple Input OR/NOR Function

Notice that Relay logic is similar to TTL. Can useTruth tables and Boolean expressions to do designs

OR

ORoutput

NORoutput

Outputs A+B+C = E

A+B+C = E

A OR B OR CEnergize E

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Ladder Logic Memory ElementsMechanically latched relay - maintains state even when power removed. Has two coils (operate, reset)

Typical wiring

Inputs A and B set the output contacts E andreset then respectively. This give toggle actionthat “remembers” the last input state even whenpower is removed

Typical Applications Reversing Motor starters. Reclose Relay Cut-out

OperateLatched

Close

Close

ResetLatched

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Off-Return Memory

Remember all contacts are drawn with the coilsde-energized

Press B: continuity rung 4 Both loads off

2

1

1

2

3

4

5

6

Energize and re-energize circuit - Load 2 onNo continuity in rungs 1-4Continuity in rung 6

Press A: continuity rung 2 Both loads on

Close

EOn

E1On

Open

Load1 off

Load 2 off

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Timer Sub-Circuits

Schematic indicates that this is a on-delay timer. After defined interval TR-E in rung 2 opens and TR-E in rung 3 closes

Rung 1: when input A is energized timer TR-E starts

Load 1 is deactivated after time delayLoad 2 is activated after time delay

Load 3 is instantaneously deactivated by TR-E

TR-EOn

Open Load off

Open Load off

Close Load on

1

2

3

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Form “C” ContactLoads are toggled between a common point

Contact A creates a remote control toggle switch

Typical “Form C” contacts include both a NO and NCcontact arrangement.

Used in some sensors formore flexibility

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Designing Sequential Control Systems

• Detect patterns of inputs• Use true tables, Boolean Algebra• Multiple inputs and/or outputs• Sum of Products or product of sums Boolean

Implementations• Reduce to minimum implementation

Combinational Systems

• Follow steps, transition from one step to another.• Use state transition diagrams or tables with Boolean

Algebra• State Machine implemented in software or hardware• Decisions made base on current condition of system

and input information

Sequential Systems

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Review of Logic Gates and Boolean Algebra

False =0 True =1Boolean Variables

BooleanOperators

EOR=XOR

AlternateImplementation

BABAX

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Axioms of Boolean Algebra

AAA

AAA

Idempotent Associative

)CB(AC)BA(

)CB(AC)BA(

Distributive

)CA()BA()CB(A

)CA()BA()CB(A

Identity Complement DeMorgan’s Theorem

AA

A

A

AA

1

00

11

0

01

0

1

A)A(

AA

AA

BA)BA(

BA)BA(

Absorption

ABAA

BABAA

Order of Operations1. NOT2. AND3. OR

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Example: Simplify the following expression using the axioms ofBoolean Algebra.

)CB(A)CBA(X

)CB(A)CB()A(X Add

Parentheses

Apply DeMorgans’s Theorem to first term

)CB()A()CB(A

)CB(A)CB(AX

Apply DeMorgan’s

Here

)CB()CB( )CB(A)CB(AX

CABACABAX Expand

ExpressionsCollect common terms and factor

CACA)AA(C

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Example Continued

)AA(CBABAX

1 AA

Use Complement

Axiom

1 CBABAX

CBABAX

Use Identity Axiom

CC 1

Simplified Expression

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Logic Design

1.) Obtain description of process2.) Define control action3.) Define Inputs and Outputs4.) Develop Truth Table or Boolean Equation of Process

Process control description

A heating oven with two bays can heat one ingot in each bay. When the heater is on it provides enough heat for two ingots. If only one ingot is present, the oven may overheat so a fan is used to cool the oven when it exceeds a set temperature.

Control Action

When only one ingot is in the oven and the temperature exceeds the setpoint, turn on the fan

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Logic DesignDefine I/O variables Inputs: B1 = bay1 ingot present

B2 = bay2 ingot present T = temperature sensor

Output: F= fan startCreate Truth Table

T B2

B1

F

0 0 0 0

0 0 1 0

0 1 0 0

0 1 1 0

1 0 0 1

1 0 1 1

1 1 0 1

1 1 1 1

If there is no over temperature don’t start the fan

Over temperature in empty oven: safety fan start

Over temperature in full oven: safety fan start

Start fan in lightly load ovens with over temp.

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Logic Design

Select elements from truth table in SOP (sum-of-products) form then simplify.

T B2

B1

F

0 0 0 0

0 0 1 0

0 1 0 0

0 1 1 0

1 0 0 1

1 0 1 1

1 1 0 1

1 1 1 1

21 BBTF 21 BBT 21 BBT 21 BBT

TF

)BB(TF

))BB(B)BB(B(TF

)BBBBBBBB(TF

22

112112

21212121

Ignore unloaded and full load cases and try again

Requires only Temp control

et438b-7.pptx 26

Logic Design

T B2

B1

F

0 0 0 0

0 0 1 0

0 1 0 0

0 1 1 0

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 0

21 BBTF 21 BBT

)BBBB(TF 2121

FT

B1 B2

B1 B2

Ladder Logic Representation

Revised Truth Table

et438b-7.pptx 27

Simplified Forms of Functions

Avoid multiple complemented variables in ladder logic (No NAND, NOR)

BABAX BABAX

NAND NOR

NAND/NOR can not be implemented effectively using software. (Programmable Logic Controllers)

et438b-7.pptx 28

State-Based DesignsDefinitionsState - current operational mode of system

Examples: On/Off, Idle, Tank filling, dispensing product.

Conditions (inputs) - inputs required for leaving thecurrent state and moving to another state

Examples: Coins inserted, button pressed, OL activated

Actions (outputs) - actions performed by system whenthe transition from one state to another take place

Examples: Start motor, turn on light, sound alarm.

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State-Based DesignsWhen a set of inputs (conditions) become valid for leaving a state, the system is directed to the destination state

CurrentState

NextState

State entry inputconditions

State exit inputconditions

To other states

State outputs

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State Transition Diagrams

State transition diagrams allow designers to examine the interaction between desired conditions and find their logical relationships and sequence. Use in digital computer design

State1

State2

State3

Else

Else

Else

A

B

C

If Condition A true go to State 2Else stay in State 1 If B true go to State 3

Else State 2

If C true go to State 1Else State 3

et438b-7.pptx 31

State EquationsInformal: State X =(State X +Arrival from another state) and has not

left for another state

Statei

State1

State2

Statej

.

.

.

Staten

set1

set2

seti

setn

Seti =logical condition to set state variable i and enter state

.

.

State1

State2

Statek

Statem

.

.

.

.

.

reset1

reset2

reseti

resetm

Re-seti,= logical condition to reset state variable i and leave

et438b-7.pptx 32

State Equations

Formal Definition:

m

1kki

n

1jiji

1i )I,state(reset)I,state(setstatestate

Where:statei = a variable that reflects state i is onstatei

+1 = next value of state variableouti = desired outputs of state ihi( ) = output function of state variablesn = number of transitions into state im = number of transitions out of state iN = total number of system statesseti= logical condition to set state variable i reseti = logical condition to reset state variable i

)state,...state,state(hout N21ii

SetConditions

Functions of state and inputs

ResetConditions

Functions of state and

inputs

et438b-7.pptx 33

Example

S0(Stop)X1=0

S1(Start)X1=1

Write the state equation for a motor starting control described in the state diagram below with the following input and outputs

I0=pressed stop button (PB1)I1= pressed start button (PB2)I2 = motor overload condition (OL)

O1 = start motor (M)

1I

2I0I Only 1 state variable requiredfor two conditions X1=0 or X1=1

1Iset

2I0Ireset

1

1

111 11 resetsetXX

2I0I1I1X1X 1

2I0I1I1X1X 1

Output equation

11 XOM

et438b-7.pptx 34

ExampleBoolean Equation to ladder logic diagram

2I0I1I1X1X 1 Substitute variable names

Overload OLI2

Start PB2I1

Stop PBI

MX

10

1OLPB1PB2)(MM

STOPPB1

OL

STARTPB2

M

M

ConstructLadder

et438b-7.pptx 35

Design Example: Reciprocating Motion Process

A work piece must travel back and forth on a conveyor. The locationof the work piece is determined by two limit switches. When the location is detected control signal are sent to a reversing motorcontactor. The machine is started and stopped from a local set of push button switches. Develop a ladder logic diagram to implementthis control.

et438b-7.pptx 36


Determine the inputs, outputs and states of system

I0: press startI1: press stopI2: Table at reverse limit (1LS)I3: Table at forward limit (2LS)

I0

I1

I2I3

Inputs:

O0: Start motor forward (2CR)O1: Start motor reverse (3CR)

Outputs:

O0

O1

States:

S0: offS1: on-forward, S2: on reverse,

et438b-7.pptx 37


S0(Stop)

S1(on-

forward)

S2(on-

reverse)

Assume machine starts at reverse limit. (1LS changes state)

I0: press startI1: press stopI2: Table at reverse limit (1LS)I3: Table at forward limit (2LS)

0IT 1,0

O0 start forwardaction

3IT 2,1

O1 start reverseaction

2IT 1,2 101 IT ,

et438b-7.pptx 38


Define set and reset conditions

Define 2 state variables X1 and X2

X2 X1 Condition

0 0 Off (S0)

0 1 On-Forward (S1)

1 0 On-Reverse (S2)

1 1 Not allowed

S1(on-

forward)

S2(on-

reverse)

0IT 1,0

2IT 1,2

2X2I0Iset 1X

X1=1X2=0

S0(Stop)

X1=0X2=1

3IT 2,1

101 IT ,

3I1Ireset 1X

1X3Iset 2X 2Ireset 2X

)3I1I))(2X2I0I(1X(1X

)3I1I))(2X2I0I(1X(1X

)reset)(set1X(1X

1

1

1x1x1

)2I)(1X3I2X(2X

)reset)(set2X(2X1

2x2x1

OutputsO0 O1 O1X2 ,0O1X

et438b-7.pptx 39


Convert state equations into ladder diagram 2CR = O03CR =O1I0=startI1=stopI2=1LSI3=2LS

)LS2Stop)(CR3LS1StartCR2(CR2 1

)LS1)(CR2LS2CR3(CR3 1

STOP2LS

START

3CR

2CR

2CR

1LS

1LS

2CR

3CR

3CR

2LS

et438b-7.pptx 40

States With PrioritizationSystems with multiple entries and exits from a state require blocking ofAlternatives.

S0

S1

S2

A

B

C

D

A or C can occur independently to exit S1.Must give one transition priority over other.Block setting of conflicting state

Two ChoicesIF A THEN block CIF C THEN block A

)1SC1SA())2SD0SB(1S(1S 1

)0SB()1SA0S(0S 1

)2SD()A1SC2S(2S 1

A given priority to C

)2SD()1SC2S(2S

)0SB()C1SA0S(0S1

1

C over A

et438b-7.pptx 41

Prioritization Example

Inputs OutputsA PB QC RDEFFS

S0

S2

S1

)DC(A

EF

AB

)FDC(E

FS

State

P Q R

S0 0 1 1

S1 1 0 1

S2 1 1 0

Output Map

Write state equationsfor this system. Give stateS2 priority over S0

0S))DC(A(T01

1S)EF(T10

FST1 1SABT12

2S))FDC(E(T21

et438b-7.pptx 42

Prioritization ExampleWrite state equations using transitions

2112101 T)TT0S(0S

)TT()TTT1S(1S 1210121011

)TT()TTT1S(1S 1210121011

21121 T)T2S(2S

S0 blocked if S2 is active

State

P Q R

S0 0 1 1

S1 1 0 1

S2 1 1 0

Output Map

Simplify using DeMorgam’s Theorem

Output Equations

2S1SP 2S0SQ 1S0SR

Documents

Ladder Diagram Example