Comparison, Math, and Data-Handling Instructions

Comparison, Math, and Data-Handling Instructions in PLC Programs

PLC programs do more than switch outputs on and off. In mechatronics applications — filling tanks, mixing materials, controlling conveyors — the controller must perform arithmetic, compare values to setpoints, and move data between memory locations. This lesson covers the comparison and math instructions defined in IEC 61131-3 and implemented in common industrial PLCs (such as Allen-Bradley Logix platforms, where the instruction names below apply).

Safety Before You Touch the Trainer

Before energizing any PLC trainer, review the hazards present:

• NFPA 70E requires you to verify absence of voltage before making or breaking any wiring connection. Even trainer voltages can cause injury.
• OSHA 29 CFR 1910.147 (lockout/tagout) applies whenever you access the interior of industrial control panels. On a trainer, follow your site's de-energize-and-lock procedure if you must open the enclosure.
• NFPA 79 governs the electrical design of industrial machinery, including control panels you will work on as a technician.
• When using force/override functions in PLC software, outputs can energize unexpectedly. Confirm no personnel are in the machine's work envelope (see ANSI/RIA R15.06 / ISO 10218 for robot and automated system safeguarding principles that extend to any automated machinery).
• Always wear appropriate PPE as required by your lab's safety policy.

Comparison Instructions

Comparison instructions examine two values and pass power (logic continuity) when the condition is true. The most common are:

| Mnemonic | Condition that passes power |

|----------|-----------------------------|

| EQU | Source A equals Source B |

| NEQ | Source A does not equal Source B |

| GRT | Source A greater than Source B |

| LES | Source A less than Source B |

| GEQ | Source A greater than or equal to Source B |

| LEQ | Source A less than or equal to Source B |

In a tank-level program, you might use GEQ to turn on a high-level alarm when the accumulated count reaches or exceeds a setpoint, and a second GEQ at a higher setpoint to close the inlet valve. The setpoint can be stored in a data tag, so the operator can change it at the HMI without editing the ladder logic — this is the concept of an indirect data reference.

Math Instructions

Math instructions read one or two source values, perform an operation, and write the result to a destination tag.

• ADD: Dest = Source A + Source B
• SUB: Dest = Source A − Source B
• MUL: Dest = Source A × Source B
• DIV: Dest = Source A ÷ Source B (integer division truncates; use REAL tags if fractions matter)
• MOV: Dest = Source (copies a value with no arithmetic)
• CPT (Compute): Evaluates a full expression written as a formula — for example, `((LevelTag - Offset) * ScaleFactor)` — and writes the result to the destination. CPT reduces rungs when a calculation requires multiple steps.

All math instructions are output instructions placed on the right side of a rung. They execute every scan when the rung is true (or unconditionally if there are no conditions on the rung).

Data Types and Overflow

Choose your tag data type carefully:

• INT (16-bit signed): range −32,768 to 32,767. Can overflow silently if a result exceeds the range.
• DINT (32-bit signed): range ±2.1 billion. Preferred for counters and accumulated values in industrial programs.
• REAL (32-bit floating point): use when you need decimal precision, such as scaling a 4–20 mA analog input to engineering units.

In this lab, level counts are DINT tags to prevent overflow at high accumulated values.

The Tank-Level Program Logic

The simulated tank uses a CTU (count-up counter) accumulator tag as a proxy for tank level, where each count represents one gallon. The program logic works as follows:

1. When the inlet valve output (`Inlet_Valve`) is ON, an ADD instruction increments the level tag each scan — or more realistically, the CTU increments on a timed pulse so the count rate represents a fill rate.

2. A GEQ comparison checks `Level_Tag >= High_Alarm_SP`. When true, it sets a `High_Alarm_Bit` output.

3. A second GEQ checks `Level_Tag >= Shutoff_SP`. When true, it opens (de-energizes) the inlet valve by resetting the valve output coil.

4. A drain pushbutton resets the level counter to simulate emptying the tank.

The instructor can change the setpoint values in the data table during a live run. The comparison instruction reads the setpoint tag every scan, so the program responds to the new value immediately without any change to the ladder logic. This is the power of storing setpoints in data tags rather than hard-coding constants in the instruction.

Manual Forcing

Forcing allows you to override the state of an input or output bit in software for testing. Use it carefully:

• Forces can cause real outputs to energize. Confirm the physical load (valve, motor) is in a safe state before forcing.
• Always remove all forces before returning the system to automatic operation.
• Document every force applied in your lab log.

CPT Expression Syntax

A CPT expression uses standard arithmetic operators (`+`, `-`, `*`, `/`) and may include parentheses for order of operations. The PLC follows standard mathematical precedence (multiplication and division before addition and subtraction). Always verify your expression result in the online data monitor before relying on it in the program.

Connecting to PMMI and Siemens Credentials

The PLC 1 and PLC 2 knowledge areas of the PMMI Mechatronics certification include comparison and math instruction usage. The Siemens SMSCP Level 1 covers digital fundamentals and PLCs, including data handling. Mastering these instructions prepares you for both credentials.