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Home / notes / Industrial Automation and Control Unit 3 Notes – AKTU B.Tech 5th Semester

Industrial Automation and Control Unit 3 Notes – AKTU B.Tech 5th Semester

Study Industrial Automation and Control Unit 3 notes for AKTU B.Tech. Learn PLC I/O, ladder logic, SFC, timers, counters and math with diagrams.

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Industrial Automation and Control Unit 3 Notes explain how a programmable logic controller connects field signals with a stored control program. This unit, Automation using PLC, covers digital and analog interfaces, sinking and sourcing circuits, ladder programming, sequential function charts, timers, counters and numerical calculations.

These notes are for AKTU B.Tech 5th Semester EE and EN students studying BEE053. The explanations include labelled diagram positions, worked examples and revision questions for understanding the unit and preparing examination answers.

Topics Covered

Topic Topic
3.1 PLC input and output foundation 3.13 Off-delay timer: TOF
3.2 Digital inputs and outputs 3.14 Retentive timer
3.3 Analog inputs, outputs and scaling 3.15 Cyclic timers
3.4 Sinking and sourcing concepts 3.16 Timer selection and problems
3.5 Sinking and sourcing outputs 3.17 Counters and pulse interpretation
3.6 Ladder diagram fundamentals 3.18 Up-counter: CTU
3.7 Start–stop holding logic 3.19 Down-counter: CTD
3.8 Programming practices and scan effects 3.20 Up/down counting
3.9 Sequential function chart 3.21 Math instructions and data types
3.10 Fill, hold and drain sequence 3.22 Comparison and worked math problems
3.11 Timer instruction foundation 3.23 Integrated carton-batching example
3.12 On-delay timer: TON 3.24 Revision and examination practice

3.1 PLC Input and Output Foundation

A PLC input supplies information about a field condition. A PLC output supplies a command to an appropriate device or interface. The electrical circuit determines how a signal reaches the controller; the program determines how the stored signal is used.

Four Basic Signal Classes

Signal class Information carried Example
Digital input: DI Discrete state Pushbutton or presence sensor
Digital output: DO Discrete command Lamp or contactor interface
Analog input: AI Variable measurement Temperature or tank level
Analog output: AO Variable command Valve-position or drive-speed reference
PLC Digital and Analog Interfaces
Inputs provide process feedback, while outputs provide commands to suitable load interfaces.

A transmitter sends its measurement toward a PLC input. An output sends a command toward a load. A networked drive can exchange both commands and status, so command information must still be distinguished from feedback.

Process Image and Physical Signals

A conventional cyclic program reads stored input information, executes its logic and updates output information. A physical input can change between scans. Consequently, a stored input bit is a sampled representation of the field signal.

Before connecting I/O, check:

  • Voltage and current requirements.
  • AC or DC operation and polarity.
  • Common connections and isolation.
  • Input filtering and permitted load duty.

Matching connectors do not establish electrical compatibility. Software cannot repair an incompatible current path.

3.2 Digital Inputs and Outputs

Digital Input Operation

A digital input classifies its electrical signal using the module’s defined thresholds. The input may receive current through a switch or a transistor sensor output. Filtering can reject brief disturbances, but it can also delay a valid change.

Physical NO/NC Contacts and Program Bits

Consider a physical normally closed stop switch wired so that the input is energized while the switch is healthy and unpressed.

Physical condition Stop contact StopOK input bit
Released and healthy Closed 1
Pressed Open 0

The program should test StopOK for TRUE when this bit means permission to run. A ladder symbol tests stored information; its appearance does not have to match the physical contact type.

Physical NC Stop and StopOK Bit
A released NC stop supplies the input, producing StopOK = 1 for a ladder TRUE test.

Output Technologies

Feature Relay output Transistor output
Switching element Mechanical contact Semiconductor
Supply suitability AC/DC within contact ratings Specified DC arrangement
Switching speed Limited by mechanical operation Often faster within specified limits
Main considerations Contact wear and condition Leakage current and voltage drop

A triac output generally serves suitable AC loads. Output technologies have different current, frequency, isolation and load limits.

A PLC output can operate a small lamp or coil within its rating. A motor normally requires suitable switching equipment, such as a contactor or drive. Protection and inductive suppression must match the hardware.

Pulse Detection Limit

A short sensor pulse can occur completely between ordinary input samples. High-speed counting, interrupts or suitable pulse conditioning may be required. Changing ladder logic cannot recover an event that the input system never captured.

3.3 Analog Inputs, Outputs and Scaling

Analog Input Conversion

An analog input converts an electrical measurement into a numerical value using analog-to-digital conversion. The program must interpret the configured range, numerical format and diagnostic status.

Typical industrial signals include 0–10 V and 4–20 mA, subject to module support. Temperature measurement may require a dedicated sensor and conversion arrangement.

Analog Measurement Path
A transmitter signal passes through an analog input and ADC before the program converts raw counts into engineering units.

Resolution and Accuracy

Resolution describes the representable increment. Accuracy describes closeness to the true or accepted value under stated conditions. More bits do not automatically remove sensor error, calibration error or noise.

An ideal n-bit conversion has 2ⁿ codes. If codes 0 to 2ⁿ − 1 map exactly to both range endpoints:

One code interval = Measurement span / (2ⁿ − 1)

Use the module’s convention because specifications may define quantization steps differently.

Linear Scaling Formula

Engineering value = E_min + (Raw − R_min) × (E_max − E_min) / (R_max − R_min)

Symbol Meaning
Raw Measured numerical input
R_min, R_max Configured raw endpoints
E_min, E_max Corresponding engineering endpoints

Do not assume that every PLC uses the same raw count range.

Worked Scaling Examples

Example 1: Raw counts to tank level

Raw 0–4000 represents level 0–100%. At Raw = 2600:

Level = (2600 / 4000) × 100 = 65%

Example 2: Current to tank level

For an ideal 4–20 mA signal representing 0–100%, at 12 mA:

Level = [(12 − 4) / (20 − 4)] × 100 = 50%

Raw-count scaling and current scaling use different numerical endpoints even when they describe the same process quantity.

Linear 4–20 mA Scaling
A current of 4 mA represents 0%, 12 mA represents 50% and 20 mA represents 100% in this example.

Analog Output

An analog output converts a programmed value into an electrical reference through a digital-to-analog output stage. The connected drive or valve must accept the selected range and common arrangement. A command value alone does not prove that the actuator reached the requested position.

3.4 Sinking and Sourcing Concepts

Sourcing supplies conventional current from the positive supply toward a connected circuit. Sinking receives current and provides its return toward 0 V or the negative side.

Feature Sourcing device Sinking device
Current role Supplies current from positive supply Returns current toward 0 V
Typical DC sensor output PNP NPN
Usual matching PLC input Sinking input Sourcing input

A complete loop must connect the supply, field output, input sensing circuit and common in the correct direction.

PNP Sensor with a Sinking Input

An active PNP output supplies current from +24 V toward the PLC input. The sinking input returns this current through its sensing circuit and common to 0 V.

PNP Sensor Connected to a Sinking Input
The PNP output sources current, and the PLC input common provides the 0 V return.

NPN Sensor with a Sourcing Input

A sourcing input supplies current from its positive common through the sensing circuit toward the input terminal. An active NPN output provides the return to 0 V.

NPN Sensor Connected to a Sourcing Input
The sourcing input supplies current toward the NPN sensor’s switching return.

Commons and Terminology

  • State which device is being called sinking or sourcing.
  • Some modules permit different arrangements through their common connection; others have a fixed design.
  • Several points may share one common. Do not assume independent polarity or isolation for every point.
  • Sinking and sourcing describe electrical current paths, not subtraction or software data sources.
  • Conventional current direction is opposite to electron motion in a simple metal conductor.

3.5 Sinking and Sourcing Output Circuits

The same reasoning applies to transistor outputs operating DC loads.

Feature Sourcing PLC output Sinking PLC output
Switched side Positive supply side Return side
Load connection Output point to 0 V Positive supply to output point
Enabled current path Supply, output switch, load, 0 V Supply, load, output switch, 0 V
Sourcing and Sinking Output Paths
The electronic switch is placed on different sides of the load in the two output arrangements.

Interface Selection Steps

  1. Identify whether the field output sources or sinks current.
  2. Identify the PLC input’s current role.
  3. Trace the complete supply-to-return loop.
  4. Check commons, voltage, current and isolation.
  5. Confirm how the active electrical signal changes the program bit.

Worked Wiring Diagnosis

A PNP sensor appears active, but its PLC input does not change. Check sensor power, the signal terminal, the 0 V reference and whether the input supports sinking operation before editing the ladder program.

Also verify output voltage drop, leakage sensitivity and inductive suppression. A transistor output cannot automatically replace a relay output simply because their nominal supply voltages match.

3.6 Ladder Diagram Fundamentals

Ladder diagram, or LD, represents logical conditions and operations through rungs between graphical rails. Contact-style instructions test bits; coils assign results; function instructions perform operations.

The rails represent logical flow in the program. They are not field supply connections to the CPU.

TRUE and FALSE Tests

Instruction Logical continuity exists when
Test TRUE Addressed bit = 1
Test FALSE Addressed bit = 0
Normal output coil Assigns its bit according to the executed rung result
Ladder Bit Tests and Output Coil
Contact-style symbols test stored bit states, while a normal coil assigns a result.

AND, OR and NOT Logic

  • Series conditions implement AND.
  • Parallel branches implement OR.
  • A FALSE test implements NOT of the addressed bit.

For Q = (A OR B) AND C, A and B form parallel branches, while C is in their common series path.

AND and OR Ladder Logic
Series tests require both conditions; parallel branches allow either condition.

Evaluation, Tags and Coils

A typical rung evaluates conditions toward its output instructions. Rungs commonly execute in program order, subject to task scheduling and instruction behaviour.

Use descriptive tags such as StartPB, StopOK, RunCmd and TankLevel. Address formats vary by platform, so document the assignments used.

A normal coil assigns a bit whenever it executes. Set/reset or latch/unlatch instructions retain state differently and need defined reset, initialization and priority rules.

3.7 Ladder Programming: Start–Stop Memory

Input and State Assignment

Tag Meaning when TRUE
StartPB Start button active
StopOK NC stop circuit healthy and unpressed
OL_OK Overload permission healthy
RunCmd Stored running command

Holding-Rung Equation

Place StopOK and OL_OK in the common series path. Place StartPB and RunCmd in parallel.

RunCmd(next) = StopOK AND OL_OK AND [StartPB OR RunCmd(previous)]

Stop-Priority Holding Rung
Stop and overload permissions apply to both the start branch and the maintained-run branch.

Operating Sequence

  1. With both permissions TRUE, pressing start makes RunCmd TRUE.
  2. Releasing start leaves the RunCmd holding branch TRUE.
  3. Pressing stop makes StopOK FALSE.
  4. Loss of StopOK or OL_OK breaks the common path and clears RunCmd when the rung executes.

The physical stop contact is NC, but the program tests StopOK for TRUE because TRUE means the stop circuit permits running.

Restart and Set/Reset Behaviour

A software holding bit’s startup value depends on memory configuration and initialization. Define the restart policy after power loss.

Set/reset instructions can provide another form of memory. If both commands occur together, execution order or instruction priority determines the result. Document the required reset priority.

3.8 Programming Practices and Scan Effects

Translate Requirements into Logic

  1. List physical inputs, outputs and internal states.
  2. Define what TRUE means for each signal.
  3. Specify permissions and stop behaviour.
  4. Identify timing and counting requirements.
  5. Write the logic with clear state ownership.
  6. Test normal operation, faults and recovery.

Avoid conflicting assignments to the same tag. A later executed normal assignment can overwrite an earlier result in the same cycle.

Rising-Edge Detection

A rising edge is a FALSE-to-TRUE transition. A one-execution pulse can be defined as:

Pulse = Input(now) AND NOT Input(previous)

Update the previous-state memory after evaluating the pulse in the chosen execution arrangement.

Rising-Edge Pulse Detection
A pulse occurs when the present input is TRUE and the stored previous input is FALSE.

Mechanical bounce can create several transitions for one intended event. Filtering or debouncing should reject unwanted changes without hiding valid events.

Program Verification Matrix

Test Expected verification
Normal start and stop Correct command and state changes
Permission loss Defined output response
Input held TRUE No unintended repeated event action
Short pulse Event captured or limitation identified
Reset with active command Correct priority and recovery
Power or network recovery Defined initialization and data quality

3.9 Sequential Function Chart

A sequential function chart, or SFC, organizes operation into steps, transition conditions and actions. It gives a more specific sequence model than a general-purpose flowchart.

Element Meaning
Initial step Starting stage of the sequence
Step A process stage that can be active
Transition Condition permitting progression
Action Work associated with an active step
SFC Step, Action and Transition
An initial step has associated actions, and a satisfied transition transfers activity to the following step.

A transition can fire when its preceding steps are active and its condition is satisfied. The chart structure determines which steps become inactive and which become active.

Output behaviour depends on the action definition and qualifiers. An action is not automatically retained after its step ends, nor does every qualifier necessarily clear every output.

Ladder Diagram and SFC Comparison

Feature Ladder diagram SFC
Main organization Boolean rungs and instructions Steps, transitions and actions
Strong application Interlocks and Boolean logic Staged operating sequences
Sequence memory Internal tags or state logic Step activity
Combined use Implements conditions and actions Can use ladder for associated logic

Define the initial state, reset destination and fault recovery. Returning to the initial step is insufficient if actuators or retained actions remain inconsistent with it.

3.10 SFC Example: Fill, Hold and Drain

The required process starts idle with both valves closed, fills to high level, waits for a defined interval, drains to low level and returns to idle.

Fill, Hold and Drain SFC
Level conditions and timer completion advance the tank through its operating stages.
Step Action Transition
S0: Idle Both valves closed Start AND Ready
S1: Fill Inlet commanded ON High level reached
S2: Hold Valves closed; timer active Hold interval complete
S3: Drain Outlet commanded ON Low level reached; return to S0

Outputs must also satisfy the required machine permissions. Define responses to contradictory level signals, timeouts, unavailable actuators and interrupted operation. Fault or Manual states may be needed.

Alternative and Simultaneous Branches

An alternative branch selects one path. Define priority or mutual exclusion when more than one transition can be TRUE.

A simultaneous branch activates parallel sequences. Its join must wait for the stated completion conditions.

Simultaneous SFC Branches and Join
Parallel actions begin together and join when their required completion conditions are satisfied.

Ladder can implement the same sequence using state bits or an integer state tag. Maintain intended state exclusivity and clear entry, exit and recovery rules.

3.11 Timer Instruction Foundation

A PLC timer connects a controlling condition to elapsed time and an output condition. It is a software instruction rather than necessarily a separate timing relay.

Parameter Meaning
IN or enable Timing control condition
PT or preset Required time interval
ET or accumulated value Elapsed time under the instruction’s rules
Q or completion output Defined timer output condition
Reset Clears retained state where applicable
Conceptual Timer Interface
IN, PT, Q and ET describe the timer model used in these notes; actual platform fields may differ.

Time Base

For a count-based timer:

Requested time = Preset count × Time base

A 5 s interval with a 10 ms base requires:

Preset count = 5 / 0.01 = 500

Some implementations accept a time value directly. Physical response also depends on task execution, input capture, output updating and actuator behaviour.

Use separate timer instances for unrelated operations. Reusing one timer structure through conflicting paths can change its elapsed value and status unexpectedly.

3.12 On-Delay Timer: TON

A non-retentive TON delays the rising edge of Q.

  1. IN becomes TRUE and timing starts.
  2. IN must remain continuously TRUE for PT.
  3. Q becomes TRUE when the qualifying interval completes.
  4. IN becoming FALSE clears Q and elapsed time in this model.
TON Timing Diagram
Q rises after the preset interval and falls when IN becomes FALSE.

Fan-Proof Example

A fan-run proof must remain TRUE for 3 s before a conveyor permission is granted. FanProof enables TON T1 with PT = 3 s. A separate test of T1.Q supplies Permit.

TON Instruction and Permission Rung
A three-second fan-proof condition qualifies the downstream permission.

Interrupted Timing Example

PT = 5 s. IN is TRUE for 2 s, FALSE for 1 s and TRUE again for 5 s. The first 2 s are discarded. Q becomes TRUE after the later uninterrupted 5 s interval.

An input pulse shorter than PT does not generate the delayed-on output in this model.

Common errors include using the input instead of Q for the delayed action, assuming retention after IN falls, mixing time units and sharing one timer between unrelated operations.

3.13 Off-Delay Timer: TOF

A TOF delays the falling edge of Q.

  1. While IN is TRUE, Q is TRUE.
  2. When IN becomes FALSE, the off-delay begins.
  3. Q remains TRUE for PT.
  4. Q becomes FALSE when that interval finishes.

If IN returns TRUE before expiry, Q stays TRUE and the falling-delay sequence is cancelled or reinitialized according to the instruction model.

TOF Timing Diagram
Q rises immediately and remains TRUE for the preset interval after IN falls.

Extraction-Fan Example

An extraction fan must run for 4 s after RunRequest disappears. RunRequest enables the TOF; its delayed-falling Q provides FanCmd through the required permission logic.

TOF Instruction and Fan Command
The off-delay output maintains the fan command after the process request ends.

Worked Timing Example

IN is TRUE from t = 0 to t = 10 s, with PT = 4 s. Q stays TRUE until approximately t = 14 s in the ideal model.

A TOF status bit called “done” may remain TRUE during the input-on and delay periods, then clear at expiry. Interpret the actual instruction rather than assuming every done bit rises at the end of timing.

A delayed process stop must not unintentionally delay a stop that requires immediate command removal. Permission placement must reflect the required stopping behaviour.

3.14 Retentive Timer

A retentive timer accumulates enabled operating time across interruptions. In the illustrated model, disabling the input holds the accumulated value; a separate reset clears it.

Retentive Accumulation Diagram
Enabled intervals add to accumulated time, while disabled intervals hold the existing value.

Worked Example

For PT = 10 s, enabled intervals of 3 s, 4 s and 3 s give:

Accumulated enabled time = 3 + 4 + 3 = 10 s

Completion occurs during the third interval. Disabled intervals do not contribute to the total.

Retentive Timer with Explicit Reset
Reset clears accumulated timing; retention through power loss depends on separate controller and data settings.

TON and Retentive Timer Comparison

Feature Non-retentive TON Retentive model
Input becomes FALSE Elapsed value resets Accumulated value remains
Later enable Starts a new interval Continues accumulation
Clearing time Normal disabling resets it Explicit reset required
Application Continuous-condition delay Cumulative run-time monitoring

Retention during input interruption does not guarantee retention through power loss, restart, memory clear or program download.

For maintenance monitoring, define actual operation carefully. A motor command alone may not establish that the motor ran; use suitable feedback where actual operating time is required.

3.15 Cyclic Timers and Repeating Operation

A cyclic timing function repeatedly alternates between defined ON and OFF states while enabled. It can use a dedicated instruction or timer-based state logic. Parameter names and mnemonics vary across PLCs.

Cyclic Timing Relationships

Period T = T_on + T_off

Frequency f = 1 / T

Duty cycle = (T_on / T) × 100%

For a lamp ON for 2 s and OFF for 3 s:

  • Period = 5 s.
  • Frequency = 0.2 Hz.
  • Duty cycle = 40%.
Repeating ON/OFF Timing
The example repeats a two-second ON phase after a three-second OFF phase.

Two-State Implementation

  1. Initialize to OFF and keep the lamp command FALSE.
  2. Run the OFF timer for 3 s.
  3. Change to ON when the OFF interval completes.
  4. Command the lamp and run the ON timer for 2 s.
  5. Return to OFF when the ON interval completes.
  6. Reset inactive timing state according to the instruction’s behaviour.
Explicit Two-State Cyclic Control
Separate timed OFF and ON states define the repeating cycle and its restart behaviour.

In this example, disabling removes the lamp command and re-enabling starts a fresh OFF phase.

Ordinary task-based transitions include execution latency. For precise pulse generation, select suitable hardware or high-speed facilities. An unexplained self-resetting timer rung may create a one-scan pulse or implementation-dependent oscillation.

3.16 Timer Selection and Timing Problems

Requirement Timer concept
Wait before enabling an output TON
Keep output ON after input falls TOF
Accumulate time over separate runs Retentive timing
Repeat defined ON/OFF phases Cyclic timing

TON and TOF Comparison

Feature TON model TOF model
Delayed output edge Rising Falling
IN becomes TRUE Qualifying interval starts Q becomes TRUE
IN becomes FALSE Q clears and elapsed resets Off-delay starts
Typical use Delayed permission Fan overrun

Worked Time-Base Problem

Preset count = 250 and time base = 20 ms:

Time = 250 × 20 ms = 5000 ms = 5 s

For an 8 s interval with the same base:

Preset count = 8000 / 20 = 400

Worked TOF Reactivation

PT = 4 s. IN falls at 10 s, then returns TRUE at 12 s. The delay has not expired, so Q remains TRUE. A later falling input begins another off-delay under this model.

Verify short enables, threshold crossing, reactivation, reset during timing and reset while enable remains TRUE. State units and the assumed instruction model.

3.17 Counters and Pulse Interpretation

A software counter changes a numerical value in response to recognized events. Common PLC counters respond to rising edges, not every scan containing a TRUE input.

Parameter Meaning
CU / CD Up-count / down-count event input
PV Threshold or preset value to load
CV Current count
R Reset, where defined
LD Load preset into a down-counter
Q Status defined by the counter model
Rising-Edge Counting
Holding a sensor TRUE does not create a new rising edge in every scan.

One carton holding a sensor TRUE for six scans should normally generate one event. Another event requires a recognized return to FALSE followed by a new rising edge.

Define priority when reset or load coincides with a count edge. These examples use reset priority for CTU and load priority for CTD. Check counting frequency, numerical range and overflow behaviour as well as the input circuit.

Accurate counting depends on event capture, pulse width, bounce control and the meaning assigned to each detected transition. Ordinary scanning may miss fast events; a high-speed counter or other capture facility may be necessary.

3.18 Up-Counter: CTU

In the illustrative IEC-style CTU model, each recognized rising edge at CU increments CV. Reset clears the count. Q indicates CV ≥ PV within the instruction’s defined range.

CTU Interface
CU supplies count events, R clears the count, and Q indicates that the preset threshold has been reached.

Five-Carton Worked Example

With PV = 5 and CV initially zero, five distinct sensor rising edges give counts 1, 2, 3, 4, 5. At CV = 5, Q becomes TRUE and can request BatchComplete. Reset clears CV and Q in this simplified model; count edges are accepted while reset is inactive.

Ten-Part Batch

Set PV = 10. Each recognized part event increments CV. When CV reaches 10, the program can use the completion condition to remove feed permission and indicate BatchReady.

Ten-Part Batch Counter and Feed Permission
The completion flag interrupts further feed permission through separate control logic.

Q becoming TRUE does not universally stop counting. Define whether additional events are accepted, inhibited, limited or followed by a reset.

Held-Input Example

For sensor samples 0, 1, 1, 1, 0, 1, there are two rising edges. The count increases by two if both events are recognized. Repeated TRUE samples do not represent repeated new events.

3.19 Down-Counter: CTD

In the illustrated IEC-style CTD model:

  • LD loads PV into CV.
  • Each recognized rising edge at CD decrements CV while load is inactive.
  • Q indicates CV at or below zero according to the instruction’s defined limits.
CTD Interface
Load establishes the starting quantity; down-count events reduce the remaining count toward zero.

Remaining-Items Example

Load PV = 4. Four recognized dispensing events produce CV values 3, 2, 1, 0. At zero, Q becomes TRUE in this model. The program can then inhibit dispensing or request refill.

Loading a preset is different from resetting to zero. Holding LD TRUE in a load-priority model can reload the quantity every execution and prevent intended counting.

CTU and CTD Comparison

Feature CTU example CTD example
Event input Rising edge at CU Rising edge at CD
Count direction Increasing Decreasing
Initialization Reset to zero Load PV into CV
Completion CV reaches PV CV reaches zero
Typical interpretation Items produced Items remaining

Some controller families use different CTU/CTD accumulated values and status-bit rules. Do not transfer zero-detection or done-bit equations unchanged between platforms.

3.20 Up/Down Counting and Application Design

An up/down counter tracks additions and removals, such as stock, occupancy or parts in a buffer.

New count = Old count + Accepted entry events − Accepted exit events

With initial stock 8, three entries and two exits:

New stock = 8 + 3 − 2 = 9

Entry and Exit Stock Counting
Separate event streams increase and decrease the stored quantity.

Simultaneous Events and Bounds

Define how simultaneous entry and exit events are handled. A no-net-change policy must be supported by the selected instruction or implemented explicitly.

Prevent or diagnose negative stock and quantities above physical capacity. Reset should establish a verified starting condition. Missed, repeated or bypassed events can cause drift and require reconciliation.

Counter and Timer Comparison

Feature Counter Timer
Measures Recognized events Elapsed time under stated conditions
Main trigger Input transitions Timing enable or edge condition
Units Parts, cartons or cycles Seconds or milliseconds
Common mistake Counting scans instead of events Incorrect time base or retention assumption

3.21 Math Instructions and Numerical Data

Math instructions calculate measurements, quantities and commands. Exact instruction names and operand rules depend on the platform.

Operation Illustrative expression
ADD Destination = A + B
SUB Destination = A − B
MUL Destination = A × B
DIV Destination = A / B, provided B is valid and nonzero
Guarded Scaling Calculation
Validate the range and divisor, calculate with suitable precision, and assign the result with its quality status.

Data Types and Integer Division

Integers represent whole numbers within a finite range. Real or floating-point values permit fractions with finite precision. Signedness, conversions and intermediate-result types affect the answer.

In a truncating integer-division model:

7 / 2 = 3

With suitable real arithmetic:

7 / 2 = 3.5

A real destination alone does not necessarily make earlier intermediate calculations real.

Scaling Order and Error Handling

For raw 0–4000 mapped to 0–100%, integer division of Raw / 4000 first can produce zero across much of the range. Multiplying first can preserve more information but may overflow. Use a correctly sized or real intermediate.

Before calculation, check:

  • Operand and intermediate types.
  • Numerical ranges and overflow risk.
  • Units and conversion factors.
  • A valid, nonzero denominator.
  • Destination type and result validity.

Define an error response for invalid arithmetic rather than executing division by zero or assuming overflow behaves identically on every PLC.

3.22 Comparison, Scaling and Worked Math Problems

Comparisons create Boolean conditions from numerical values. Examples include Level ≥ 80% and Count ≥ 20. The comparison supplies a condition; separate control logic determines the actuator command.

Use hysteresis or state logic when noise near a threshold would cause repeated switching.

Example 1: Pressure Scaling

Raw 1000–5000 represents pressure 0–10 bar. At Raw = 3400:

Pressure = [(3400 − 1000) / (5000 − 1000)] × 10 = 6 bar

Example 2: Production Rate

A machine produces 120 parts in 2 minutes:

Rate = 120 / 2 = 60 parts/min

Using 120 s instead:

Rate = (120 / 120) × 60 = 60 parts/min

Keep the time units consistent.

Example 3: Average Temperature

For readings of 24°C, 26°C and 28°C:

Average = (24 + 26 + 28) / 3 = 26°C

For a variable number of valid readings N, calculate only when N > 0. Define the result when no readings are valid.

Example 4: Rejection Percentage

Rejected parts = 9; total inspected = 300:

Rejection percentage = (9 / 300) × 100 = 3%

Use suitable precision and guard the total against zero.

Result Quality

Check measurement quality before displaying a precise-looking value. Define whether out-of-range data is clamped, alarmed, substituted or handled as a fault. Arithmetic alone cannot establish sensor validity.

3.23 Integrated PLC Example: Carton Batching

Requirement

Start a conveyor only with valid StopOK and drive permissions. Qualify drive-run proof continuously for 2 s. Count 10 distinct carton detections, then stop feeding and indicate BatchReady. Reset prepares another batch under defined operating conditions.

Timed Carton-Batching System
A photo sensor supplies carton events, while timed drive proof and batch completion govern feed permission.

Functional Allocation

Function Signals or instruction
Digital inputs StartPB, StopOK, DriveOK, DriveRunProof, CartonSensor, ResetPB
Digital outputs ConveyorCmd and BatchReady indicator
Internal states RunRequest, qualified permission and batch state
Timer TON with PT = 2 s for run-proof qualification
Counter CTU with PV = 10 for recognized carton edges

Program Sequence

  1. Evaluate operating permissions and reset conditions.
  2. Establish RunRequest from an allowed start.
  3. Qualify continuous drive-run proof using TON.
  4. Enable the conveyor under the intended state and permissions.
  5. Accept carton events while counting is permitted.
  6. On count completion, end feeding and indicate BatchReady.

Fault and Recovery Checks

  • Missing drive proof must prevent the intended feed permission.
  • A sensor held TRUE must not generate ten counts by repeated scanning.
  • Reset must not silently produce an unexpected running command.
  • Stop handling must interrupt the required output path even if timer or counter values remain stored.

Trace start, a held sensor, permission loss, the ninth carton, the tenth carton, extra events, reset and recovery. Define whether reset clears RunRequest as well as the count.

3.24 Quick Revision and Examination Practice

Essential Revision Points

  • DI/DO carry discrete states; AI/AO carry variable measurements and commands.
  • Sourcing provides current; sinking returns it toward 0 V.
  • Typical PNP sensor outputs match sinking inputs; NPN outputs match sourcing inputs.
  • Physical contacts establish input states; ladder contacts test stored bits.
  • Series and parallel ladder paths implement AND and OR.
  • A holding branch maintains a command while common permissions remain TRUE.
  • SFC organizes steps, actions and transition conditions.
  • TON delays a rising output; TOF delays a falling output.
  • Retentive timing accumulates enabled time across input interruptions.
  • Cyclic timing requires defined ON/OFF phases and initialization.
  • Counters commonly respond to edges rather than every TRUE scan.
  • Math needs suitable types, ranges, units and guarded calculations.

Important Formulas

Relationship Application
Time = Preset count × Time base Count-based timer setting
T = T_on + T_off Cyclic period
f = 1 / T Cycle frequency
Duty = (T_on / T) × 100% ON percentage
Scaled value = E_min + (Raw − R_min) × E_span / R_span Linear scaling
New stock = Old stock + Entries − Exits Inventory counting
Pulse = Now AND NOT Previous Rising-edge detection

Numerical Practice with Answers

Problem Answer
Preset count 150; time base 20 ms 3 s
TON PT = 4 s; enable for 2 s, disable, then enable for 3 s Q remains FALSE in the non-retentive model
Retentive PT = 7 s; enabled intervals 2 s and 5 s without reset Accumulated time 7 s; completion reached
Cyclic output ON 1 s and OFF 3 s Period 4 s; frequency 0.25 Hz; duty 25%
CTU samples 0, 1, 1, 0, 1, 0, 1 Three rising edges if recognized
CTD loaded with 6; four accepted down-count events CV = 2 in the illustrated model
Raw 3000 within 1000–5000 mapped to 0–10 bar 5 bar

Long-Answer Questions

  1. Classify PLC I/O and explain digital and analog operation.
  2. Draw sourcing and sinking input and output current paths.
  3. Explain ladder symbols, rung continuity and start–stop holding logic.
  4. Develop an SFC for fill, hold and drain with its transitions.
  5. Explain TON, TOF, retentive and cyclic timers with timing diagrams.
  6. Compare CTU and CTD and solve a batch-count problem.
  7. Explain arithmetic instructions, data types and scaling errors.
  8. Develop a timed carton-batching sequence using a counter.

Short-Answer Questions

  1. Why can a physical NC stop use a ladder TRUE test?
  2. Why does retentive timing not automatically survive every power loss?
  3. Why does a sensor held TRUE commonly produce only one count?
  4. How does a sourcing PLC input differ from a sourcing sensor output?
  5. Why must a divisor be checked before calculation?

Frequently Asked Questions

What does Industrial Automation and Control Unit 3 cover?

Unit 3 covers automation using PLCs: I/O interfaces, sink/source wiring, ladder logic, SFC, timers, counters and numerical instructions.

What is the difference between TON and TOF?

TON delays Q becoming TRUE. TOF makes Q TRUE with its input and delays Q becoming FALSE after the input falls, under the models used here.

Why are PLC counters normally driven by events?

An event represents a new occurrence. Counting every scan of a held input would measure its sampled duration rather than the intended number of parts.

What should be specified before solving a PLC program?

State the electrical current path, the meaning of each bit, the instruction model, the initial state and the reset behaviour. Then trace sequence, timing, counting and calculation together.

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