PID function block for process control in PLC Programming - Time & Space Complexity

Time Complexity: PID function block for process control

O(1)

Understanding Time Complexity

We want to understand how the time to run a PID function block changes as the process runs longer or with more data.

Specifically, we ask: How does the work inside the PID block grow with input size?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

FUNCTION_BLOCK PID
VAR_INPUT
  SetPoint : REAL;
  ProcessValue : REAL;
  Kp : REAL;
  Ki : REAL;
  Kd : REAL;
END_VAR
VAR
  Integral : REAL := 0;
  PreviousError : REAL := 0;
END_VAR

METHOD Run : REAL
VAR
  Error : REAL;
  Derivative : REAL;
END_VAR
  Error := SetPoint - ProcessValue;
  Integral := Integral + Error;
  Derivative := Error - PreviousError;
  PreviousError := Error;
  Run := Kp * Error + Ki * Integral + Kd * Derivative;
END_METHOD
END_FUNCTION_BLOCK

This code calculates the control output using the PID formula each time it runs.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The PID calculation steps inside the Run method.
• How many times: Each time the Run method is called, it performs a fixed number of calculations.

How Execution Grows With Input

The number of calculations stays the same no matter how many times the PID runs.

Input Size (n)	Approx. Operations
10	About 5 calculations each run, total 50
100	About 5 calculations each run, total 500
1000	About 5 calculations each run, total 5000

Pattern observation: The work grows linearly with the number of times the method runs, but each run is constant work.

Final Time Complexity

Time Complexity: O(1)

This means each PID calculation takes the same amount of time no matter what.

Common Mistake

[X] Wrong: "The PID calculation time grows as the process runs longer because it stores past errors."

[OK] Correct: The PID here only keeps the sum of errors and the last error, not all past errors, so the calculation steps stay the same.

Interview Connect

Understanding that PID calculations run in constant time helps you explain how control systems stay efficient even when running continuously.

Self-Check

"What if the PID stored all past errors in a list and summed them each time? How would the time complexity change?"

Practice

1. What is the main purpose of a PID function block in process control?

easy

A. To keep a process variable close to a desired target value

B. To store data for later analysis

C. To display process values on a screen

D. To manually adjust valves and switches

Solution

1. Step 1: Understand the role of PID blocks

   PID blocks automatically adjust outputs to keep a process variable near a setpoint.

2. Step 2: Compare options to this role

   Only To keep a process variable close to a desired target value describes this automatic control function; others describe unrelated tasks.

3. Final Answer:

   To keep a process variable close to a desired target value -> Option A

4. Quick Check:

   PID controls process variable = keep near target [OK]

Hint: PID blocks control variables automatically, not manually [OK]

Common Mistakes:

• Thinking PID stores data instead of controlling
• Confusing PID with display or manual control
• Assuming PID only measures values

2. Which of the following is the correct way to declare a PID function block instance named pid1 in a PLC program?

easy

A. pid1 : PID;

B. pid1 = PID();

C. PID pid1;

D. pid1 -> PID();

Solution

1. Step 1: Recall PLC function block declaration syntax

   In PLC languages like Structured Text, function blocks are declared with name : Type;.

2. Step 2: Match options to this syntax

   pid1 : PID; matches the correct syntax; others use incorrect assignment or C-like syntax.

3. Final Answer:

   pid1 : PID; -> Option A

4. Quick Check:

   Function block declaration uses colon and semicolon [OK]

Hint: Use colon and semicolon to declare function blocks [OK]

Common Mistakes:

• Using equal sign instead of colon
• Using C or Java style declarations
• Using arrow operator incorrectly

3. Given the following PLC code snippet using a PID block:

pid1.Kp := 2.0;
pid1.Ki := 0.5;
pid1.Kd := 0.1;
pid1.SetPoint := 100;
pid1.ProcessVariable := 90;
pid1();
Output := pid1.ControlOutput;

What is the expected behavior of Output after this code runs once?

medium

A. Output will be negative to decrease the process variable

B. Output will be zero because PID needs multiple cycles

C. Output will be a positive value to increase the process variable

D. Output will equal the SetPoint value

Solution

1. Step 1: Analyze PID inputs and error

   The error is SetPoint (100) minus ProcessVariable (90) = 10, positive error.

2. Step 2: Understand PID output direction

   Positive error means output should increase to raise the process variable, so output is positive.

3. Final Answer:

   Output will be a positive value to increase the process variable -> Option C

4. Quick Check:

   Positive error -> positive output to correct [OK]

Hint: Positive error means output pushes variable up [OK]

Common Mistakes:

• Assuming output is zero on first run
• Confusing output direction with error sign
• Thinking output equals setpoint directly

4. Identify the error in this PID block usage snippet:

pid1.Kp := 1.5;
pid1.Ki := 0.3;
pid1.Kd := 0.05;
pid1.SetPoint := 50;
pid1.ProcessVariable := 55;
Output := pid1.ControlOutput;
pid1();

medium

A. Assigning ProcessVariable before SetPoint

B. Setting Kp, Ki, Kd values too low

C. Missing declaration of pid1

D. Calling the PID block function pid1() after reading output

Solution

1. Step 1: Check order of function call and output read

   The PID block must be called (executed) before reading ControlOutput to update output.

2. Step 2: Identify the mistake in code order

   Here, Output is assigned before pid1() is called, so output is stale or invalid.

3. Final Answer:

   Calling the PID block function pid1() after reading output -> Option D

4. Quick Check:

   Call PID block before reading output [OK]

Hint: Always call PID block before reading output [OK]

Common Mistakes:

• Reading output before calling PID block
• Confusing parameter order
• Ignoring function block declaration

5. You want to tune a PID block to control temperature in a tank. The temperature rises too slowly and overshoots the target. Which tuning change should you make to reduce overshoot and improve response?

hard

A. Decrease Kp and increase Ki

B. Decrease Kp and increase Kd

C. Increase Kp and decrease Kd

D. Increase Ki and Kd equally

Solution

1. Step 1: Understand overshoot and slow rise causes

   High Kp causes overshoot; low Kd means less damping; slow rise means Kp might be too low.

2. Step 2: Choose tuning to reduce overshoot and improve speed

   Decreasing Kp reduces overshoot; increasing Kd adds damping to reduce oscillations and overshoot.

3. Final Answer:

   Decrease Kp and increase Kd -> Option B

4. Quick Check:

   Lower Kp + higher Kd = less overshoot, better control [OK]

Hint: Lower Kp and raise Kd to reduce overshoot [OK]

Common Mistakes:

• Increasing Kp causes more overshoot
• Ignoring derivative gain effect
• Changing Ki without addressing overshoot