Cascading timers for long delays in PLC Programming - Time & Space Complexity

Time Complexity: Cascading timers for long delays

O(n)

Understanding Time Complexity

When using cascading timers in PLC programming, it is important to understand how the execution time grows as the delay length increases.

We want to know how the number of timer checks or steps changes when we set longer delays.

Scenario Under Consideration

Analyze the time complexity of the following cascading timers code snippet.

// Initialize timers
Timer1.Preset := 1000; // 1 second
Timer2.Preset := 1000; // 1 second

// Start Timer1
IF NOT Timer1.Done THEN
  Timer1.Start := TRUE;
ELSE
  Timer2.Start := TRUE;
END_IF

This code uses two timers in sequence to create a longer delay by starting Timer2 only after Timer1 finishes.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Checking timer completion status repeatedly.
• How many times: Timer1 runs for its preset time, then Timer2 runs for its preset time.

How Execution Grows With Input

As the total delay increases by adding more timers or longer presets, the total checks grow proportionally.

Input Size (total delay in seconds)	Approx. Operations (timer checks)
2 (2 timers x 1s)	About 2000 checks
10 (10 timers x 1s)	About 10,000 checks
100 (100 timers x 1s)	About 100,000 checks

Pattern observation: The number of timer checks grows linearly with the total delay length.

Final Time Complexity

Time Complexity: O(n)

This means the time to complete the delay grows directly in proportion to the total delay length set by cascading timers.

Common Mistake

[X] Wrong: "Using more timers in cascade does not affect execution time much because each timer runs independently."

[OK] Correct: Each timer must complete before the next starts, so total execution time adds up linearly with each timer's delay.

Interview Connect

Understanding how cascading timers affect execution time helps you design efficient control systems and explain timing behavior clearly in real projects.

Self-Check

"What if we replaced cascading timers with a single timer set to the total delay? How would the time complexity change?"

Practice

1. What is the main purpose of using cascading timers in PLC programming for long delays?

easy

A. To combine multiple short timers to achieve a longer delay

B. To run multiple timers simultaneously for faster operation

C. To reset timers automatically after each cycle

D. To reduce the number of timers used in a program

Solution

1. Step 1: Understand the limitation of single timers

   Single timers have a maximum delay limit, so they cannot handle very long delays alone.

2. Step 2: Explain cascading timers concept

   Cascading timers link several short timers in sequence, where each starts after the previous finishes, to create a longer total delay.

3. Final Answer:

   To combine multiple short timers to achieve a longer delay -> Option A

4. Quick Check:

   Cascading timers extend delay by chaining short timers [OK]

Hint: Think of timers as building blocks for longer delays [OK]

Common Mistakes:

• Assuming timers run at the same time
• Believing timers reset automatically
• Thinking cascading reduces timer count

2. Which of the following is the correct way to start the second timer in a cascading timer setup?

easy

A. Start the second timer when the first timer is running

B. Start the second timer when the first timer's done bit is ON

C. Start the second timer when the first timer's preset value is reached

D. Start the second timer immediately after the first timer starts

Solution

1. Step 1: Identify the trigger for the second timer

   The second timer should start only after the first timer finishes, indicated by its done bit being ON.

2. Step 2: Eliminate incorrect options

   Starting the second timer while the first is running or immediately after it starts is incorrect because it breaks the cascade logic.

3. Final Answer:

   Start the second timer when the first timer's done bit is ON -> Option B

4. Quick Check:

   Second timer triggers on first timer done bit [OK]

Hint: Second timer waits for first timer done bit [OK]

Common Mistakes:

• Starting second timer too early
• Using preset value instead of done bit
• Starting timers simultaneously

3. Given the following cascading timers setup:

Timer1: PT=10s, DN bit set after 10s
Timer2: PT=20s, starts when Timer1.DN is ON
Timer3: PT=30s, starts when Timer2.DN is ON

What is the total delay before Timer3.DN becomes ON?

medium

A. 60 minutes

B. 30 seconds

C. 10 seconds

D. 60 seconds

Solution

1. Step 1: Calculate each timer's delay

   Timer1 delays 10 seconds, Timer2 delays 20 seconds, Timer3 delays 30 seconds.

2. Step 2: Add delays in cascade

   Total delay = 10s + 20s + 30s = 60 seconds.

3. Final Answer:

   60 seconds -> Option D

4. Quick Check:

   Sum of all timer delays = 60 seconds [OK]

Hint: Add all timer delays in sequence for total delay [OK]

Common Mistakes:

• Taking only last timer delay
• Multiplying delays instead of adding
• Confusing seconds with minutes

4. In a cascading timer setup, the second timer never starts even after the first timer finishes. What is the most likely cause?

medium

A. The first timer's done bit is not used as a start condition for the second timer

B. The first timer's preset time is too short

C. The second timer's preset time is longer than the first timer's

D. The second timer's start condition is incorrectly linked to the first timer's running bit

Solution

1. Step 1: Analyze the start condition for the second timer

   The second timer must start when the first timer's done bit is ON; if not, it won't start.

2. Step 2: Identify the error

   If the done bit is not used as the start condition, the second timer never triggers, causing the issue.

3. Final Answer:

   The first timer's done bit is not used as a start condition for the second timer -> Option A

4. Quick Check:

   Second timer needs first timer done bit to start [OK]

Hint: Check if second timer triggers on first timer done bit [OK]

Common Mistakes:

• Confusing running bit with done bit
• Blaming preset times for start issues
• Ignoring start condition linkage

5. You need a delay of 5 minutes in a PLC program, but the maximum timer preset is 1 minute. How can you use cascading timers to achieve this delay?

hard

A. Use a single timer set to 5 minutes, ignoring the max preset limit

B. Use 1 timer set to 1 minute and loop it 5 times without cascading

C. Use 5 timers in sequence, each set to 1 minute, starting the next when the previous timer's done bit is ON

D. Use 2 timers set to 2.5 minutes each, starting simultaneously

Solution

1. Step 1: Understand timer preset limit

   The timer cannot be set above 1 minute, so a single timer cannot create a 5-minute delay.

2. Step 2: Apply cascading timers to extend delay

   Use 5 timers of 1 minute each, starting each next timer when the previous timer's done bit is ON, to sum up to 5 minutes.

3. Final Answer:

   Use 5 timers in sequence, each set to 1 minute, starting the next when the previous timer's done bit is ON -> Option C

4. Quick Check:

   Cascade multiple 1-minute timers to reach 5 minutes [OK]

Hint: Chain timers equal to max preset to reach total delay [OK]

Common Mistakes:

• Trying to set timer above max preset
• Starting timers simultaneously instead of cascading
• Looping single timer without done bit control