Latching circuit (seal-in logic) in PLC Programming - Time & Space Complexity

Time Complexity: Latching circuit (seal-in logic)

O(1)

Understanding Time Complexity

We want to understand how the time it takes to run a latching circuit program changes as the input size changes.

Specifically, we ask: How does the program's execution time grow when the number of inputs or cycles increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

// Simple latching circuit (seal-in logic)
IF StartButton THEN
  Motor := TRUE;
ELSIF StopButton THEN
  Motor := FALSE;
ELSE
  Motor := Motor; // Keep previous state
END_IF;

This code keeps a motor running after pressing start until stop is pressed, using seal-in logic.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The program runs this logic once every scan cycle.
• How many times: It repeats continuously, once per cycle, but no loops inside the code.

How Execution Grows With Input

The program checks inputs and updates output once per cycle, regardless of input size.

Input Size (n)	Approx. Operations
10	2 checks + 1 assignment
100	2 checks + 1 assignment
1000	2 checks + 1 assignment

Pattern observation: The number of operations stays the same no matter how many cycles or inputs, because the logic is simple and fixed.

Final Time Complexity

Time Complexity: O(1)

This means the program takes about the same time to run each cycle, no matter how many times it runs or how many inputs it has.

Common Mistake

[X] Wrong: "The program takes longer as the motor runs longer because it keeps checking forever."

[OK] Correct: Each cycle runs the same simple checks quickly; the length of running time does not add more work per cycle.

Interview Connect

Understanding how simple control logic runs efficiently helps you explain how automation programs handle real-time tasks smoothly.

Self-Check

"What if we added a loop inside the logic to check multiple sensors? How would the time complexity change?"

Practice

1. What is the main purpose of a latching circuit (seal-in logic) in PLC programming?

easy

A. To keep a device ON after pressing start until stop is pressed

B. To immediately turn off a device when start is pressed

C. To reset all outputs when the PLC powers on

D. To count the number of times a button is pressed

Solution

1. Step 1: Understand the function of latching circuits

   Latching circuits keep an output ON even after the start input is released.

2. Step 2: Identify the stop input role

   The stop input breaks the latch, turning the output OFF safely.

3. Final Answer:

   To keep a device ON after pressing start until stop is pressed -> Option A

4. Quick Check:

   Latching circuit = Keeps device ON until stopped [OK]

Hint: Remember: latch holds output ON until stop breaks it [OK]

Common Mistakes:

• Thinking latch turns device OFF immediately after start
• Confusing latch with reset logic
• Ignoring the stop input function

2. Which of the following is the correct ladder logic rung for a latching circuit using a start pushbutton Start, stop pushbutton Stop, and output coil Motor?

easy

A. |---[Stop]---[Start]---(Motor)---|
| +----(Motor)---------|

B. |---[Start]---[Stop]---(Motor)---|
| | |
| +----(Motor)---------|

C. |---[Stop]---[Start]---(Motor)---|
| | |
| +----(Motor)---------|

D. |---[Start]---[Stop]---(Motor)---|
| +----(Motor)---------|

Solution

1. Step 1: Check the order of stop and start contacts

   Stop is normally closed and should be first to allow breaking the circuit; start is normally open and second.

2. Step 2: Confirm the seal-in contact

   The output coil Motor is used as a contact in parallel with Start to latch the circuit.

3. Final Answer:

   Stop first, then Start, with Motor contact in parallel to Start -> Option C

4. Quick Check:

   Stop before Start, Motor seals in [OK]

Hint: Stop contact always first; Motor seals in after Start [OK]

Common Mistakes:

• Placing Start before Stop contact
• Missing Motor contact in parallel
• Confusing normally open and normally closed contacts

3. Given this ladder logic snippet:

|---[Stop]---[Start]---(Motor)---|
|          |                   |
|          +----(Motor)---------|

If the Start button is pressed and released, then the Stop button is pressed, what is the state of Motor output?

medium

A. Motor toggles ON and OFF with each Start press

B. Motor remains ON after Start is released and turns OFF when Stop is pressed

C. Motor never turns ON because Stop is first

D. Motor turns ON only while Start is pressed and OFF immediately after release

Solution

1. Step 1: Analyze pressing Start

   Pressing Start energizes Motor coil, which closes Motor contact in parallel, latching the circuit ON.

2. Step 2: Analyze pressing Stop

   Pressing Stop opens the circuit, breaking the latch and turning Motor OFF.

3. Final Answer:

   Motor stays ON after Start release, OFF when Stop pressed -> Option B

4. Quick Check:

   Latching holds Motor ON until Stop breaks it [OK]

Hint: Start latches ON, Stop breaks latch OFF [OK]

Common Mistakes:

• Thinking Motor turns OFF immediately after Start release
• Ignoring Stop button effect
• Confusing latch with toggle

4. Identify the error in this ladder logic for a latching circuit:

|---[Start]---[Stop]---(Motor)---|
|          |                   |
|          +----(Motor)---------|

medium

A. Start contact should be normally closed

B. Motor coil is missing from the rung

C. Motor contact is not in parallel with Stop

D. Start and Stop contacts are in wrong order; Stop should be first

Solution

1. Step 1: Check contact order

   Stop contact should be first and normally closed to allow breaking the circuit safely.

2. Step 2: Confirm Start contact position

   Start contact should be after Stop and normally open to energize Motor.

3. Final Answer:

   Start and Stop contacts are in wrong order; Stop should be first -> Option D

4. Quick Check:

   Stop first, then Start for correct latch [OK]

Hint: Stop contact always first to break circuit safely [OK]

Common Mistakes:

• Placing Start before Stop
• Confusing normally open/closed contacts
• Missing Motor contact in parallel

5. You want to control a motor with a latching circuit but add a safety feature: the motor should only latch ON if a safety switch Safety is closed. Which ladder logic modification correctly adds this condition?

hard

A. Add Safety contact in series before Start and Motor contacts

B. Add Safety contact in parallel with Start

C. Add Safety contact in parallel with Stop

D. Add Safety contact in series after Motor coil

Solution

1. Step 1: Understand safety switch role

   Safety must be closed to allow motor start; it should be in series to block power if open.

2. Step 2: Place Safety contact correctly

   Putting Safety in series before Start and Motor ensures motor cannot latch if Safety is open.

3. Final Answer:

   Add Safety contact in series before Start and Motor contacts -> Option A

4. Quick Check:

   Safety in series blocks motor if open [OK]

Hint: Series Safety contact blocks motor if open [OK]

Common Mistakes:

• Placing Safety in parallel, bypassing it
• Putting Safety after Motor coil, ineffective
• Confusing series and parallel placement