Off-delay timer (TOF) behavior in PLC Programming - Time & Space Complexity

Time Complexity: Off-delay timer (TOF) behavior

O(n)

Understanding Time Complexity

We want to understand how the time a PLC program takes changes when using an off-delay timer (TOF).

Specifically, how the timer's behavior affects the number of operations as input changes.

Scenario Under Consideration

Analyze the time complexity of the following TOF timer logic.

// Off-delay timer (TOF) example
IF input_signal = TRUE THEN
  timer.Q := TRUE;
  timer.ET := 0;
ELSE
  IF timer.ET < timer.PT THEN
    timer.ET := timer.ET + 1;
    timer.Q := TRUE;
  ELSE
    timer.Q := FALSE;
  END_IF;
END_IF;

This code keeps the output on while input is true, then delays turning off for a preset time.

Identify Repeating Operations

Look for loops or repeated steps in the timer logic.

• Primary operation: Incrementing the elapsed time (timer.ET) each cycle when input is off.
• How many times: Up to the preset time (timer.PT) cycles, once input turns off.

How Execution Grows With Input

The timer counts up to the preset time each cycle after input turns off.

Input Size (preset time PT)	Approx. Operations (increments)
10	10 increments
100	100 increments
1000	1000 increments

Pattern observation: The number of increments grows linearly with the preset time.

Final Time Complexity

Time Complexity: O(n)

This means the timer's off-delay steps grow in direct proportion to the preset delay time.

Common Mistake

[X] Wrong: "The timer turns off instantly, so no extra steps happen after input off."

[OK] Correct: The timer counts each cycle until the preset time, so it does extra steps proportional to that delay.

Interview Connect

Understanding timer behavior helps you explain how automation systems handle delays and timing, a key skill in PLC programming.

Self-Check

What if the timer increments by 2 each cycle instead of 1? How would the time complexity change?

Practice

1. What does an Off-delay timer (TOF) do in a PLC program?

easy

A. Delays turning the output ON after the input turns ON

B. Turns the output ON immediately when the input turns ON

C. Keeps the output ON for a set time after the input turns OFF

D. Turns the output OFF immediately when the input turns OFF

Solution

1. Step 1: Understand TOF basic function

   An Off-delay timer keeps the output ON even after the input signal goes OFF, but only for a preset delay time.

2. Step 2: Compare options with TOF behavior

   Keeps the output ON for a set time after the input turns OFF matches this behavior exactly, while others describe different timer types or immediate actions.

3. Final Answer:

   Keeps the output ON for a set time after the input turns OFF -> Option C

4. Quick Check:

   TOF delays OFF after input OFF = D [OK]

Hint: Remember TOF delays turning OFF, not ON [OK]

Common Mistakes:

• Confusing TOF with On-delay timer (TON)
• Thinking output turns OFF immediately
• Mixing input and output timing

2. Which of the following is the correct syntax to declare an Off-delay timer (TOF) named T1 with a preset time of 5 seconds in a typical PLC ladder logic?

easy

A. TOF T1, 5s

B. TIMER_OFF T1, 5

C. TON T1, 5s

D. OFF_DELAY T1, 5000

Solution

1. Step 1: Identify correct timer type keyword

   TOF is the standard abbreviation for Off-delay timer in many PLC languages.

2. Step 2: Check syntax format

   TOF T1, 5s uses TOF with timer name and preset time in seconds, matching typical syntax.

3. Final Answer:

   <code>TOF T1, 5s</code> -> Option A

4. Quick Check:

   TOF keyword with timer and time = C [OK]

Hint: Look for TOF keyword and time unit seconds [OK]

Common Mistakes:

• Using TON instead of TOF
• Wrong time format or units
• Using non-standard timer names

3. Given the following PLC code snippet using an Off-delay timer (TOF):

INPUT = ON (for 10s)
TOF T1, 5s
OUTPUT = T1.Q
Then INPUT turns OFF at time 10s.
What is the OUTPUT state at time 12s?

medium

A. Undefined

B. OFF

C. Flashing ON/OFF

D. ON

Solution

1. Step 1: Understand TOF timing

   When INPUT turns OFF at 10s, TOF keeps OUTPUT ON for 5 seconds delay.

2. Step 2: Calculate OUTPUT state at 12s

   12s is 2 seconds after INPUT OFF, which is less than 5s delay, so OUTPUT remains ON.

3. Final Answer:

   ON -> Option D

4. Quick Check:

   TOF delay not expired at 12s = ON [OK]

Hint: Check if delay time passed after input OFF [OK]

Common Mistakes:

• Assuming OUTPUT turns OFF immediately
• Confusing ON-delay with OFF-delay
• Ignoring preset delay time

4. You wrote this PLC code using an Off-delay timer (TOF):

TOF T1, 3s
OUTPUT = T1.Q
INPUT turns OFF at 5s
But OUTPUT turns OFF immediately at 5s instead of delaying.
What is the most likely error?

medium

A. TOF timer is used instead of TON timer

B. Preset time for TOF is set to zero or missing

C. OUTPUT is assigned incorrectly to INPUT instead of T1.Q

D. INPUT signal never turned OFF

Solution

1. Step 1: Analyze timer preset time effect

   If preset time is zero or missing, TOF will not delay turning OFF output.

2. Step 2: Match symptom with cause

   Immediate OFF at input OFF means no delay, likely due to zero preset time.

3. Final Answer:

   Preset time for TOF is set to zero or missing -> Option B

4. Quick Check:

   Zero preset time causes no delay [OK]

Hint: Check if preset time is properly set [OK]

Common Mistakes:

• Confusing TOF with TON timer
• Assigning output to wrong variable
• Ignoring input signal changes

5. In a safety system, you want a motor to keep running for 10 seconds after the stop button is released to allow smooth shutdown. Which PLC timer setup using Off-delay timer (TOF) is correct?

1) TOF MotorTimer, 10s
2) TON MotorTimer, 10s
3) TOF MotorTimer, 0s
4) TON MotorTimer, 0s

hard

A. Option 1 only

B. Option 2 only

C. Options 1 and 3

D. Options 2 and 4

Solution

1. Step 1: Identify timer type for delayed OFF

   TOF timer delays turning OFF output after input OFF, perfect for smooth shutdown.

2. Step 2: Check preset time correctness

   Only option 1 uses TOF with 10s delay, matching requirement.

3. Final Answer:

   Option 1 only -> Option A

4. Quick Check:

   TOF with 10s delay = smooth shutdown [OK]

Hint: Use TOF with correct delay time for shutdown [OK]

Common Mistakes:

• Using TON instead of TOF for delayed OFF
• Setting delay time to zero
• Selecting multiple options incorrectly