PID controller basics for power electronics - Step-by-Step Execution

Concept Flow - PID controller basics for power electronics

Measure Output

↓

Calculate Error = Setpoint - Output

↓

Compute P term: Kp * Error

↓

Compute I term: I_prev + Ki * Error * dt

↓

Compute D term: Kd * (Error - Error_prev) / dt

↓

Sum PID Output = P + I + D

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Apply Output to Power Electronics Device

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Update Error_prev and I_prev

↩Back to Measure Output

The PID controller measures output, calculates error, computes proportional, integral, and derivative terms, sums them, applies the control signal, then updates for the next cycle.

Execution Sample

Power Electronics

Setpoint = 10
Output = 7
Error = Setpoint - Output
P = Kp * Error
I = I_prev + Ki * Error * dt
D = Kd * (Error - Error_prev) / dt
Control = P + I + D

This code calculates the PID control output based on the current error between desired and actual output.

Analysis Table

Step	Setpoint	Output	Error	P term	I term	D term	Control Output	Notes
1	10	7	3	3.0	0.3	0.0	3.3	Initial error calculation, I_prev=0, Error_prev=0
2	10	8	2	2.0	0.5	-0.5	2.0	Error decreased, I accumulates, D negative due to error drop
3	10	9	1	1.0	0.6	-0.5	1.1	Error smaller, integral grows slowly, derivative negative
4	10	9.5	0.5	0.5	0.65	-0.25	0.9	Error small, integral near steady, derivative smaller
5	10	10	0	0.0	0.65	-0.25	0.4	Error zero, integral steady, derivative negative
6	10	10	0	0.0	0.65	0.0	0.65	No error change, derivative zero, control stabilizes
Exit	10	10	0	-	-	-	-	Error zero, system stable, control output steady

💡 Error reaches zero and remains stable, control output stabilizes, ending the control adjustment cycle.

State Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6
Error	N/A	3	2	1	0.5	0	0
P term	N/A	3.0	2.0	1.0	0.5	0.0	0.0
I term	0	0.3	0.5	0.6	0.65	0.65	0.65
D term	0	0.0	-0.5	-0.5	-0.25	-0.25	0.0
Control Output	N/A	3.3	2.0	1.1	0.9	0.4	0.65

Key Insights - 3 Insights

Why does the derivative term become negative when the error decreases?

Because the derivative term measures the rate of change of error. When error drops from 3 to 2, the difference (Error - Error_prev) is negative, making the derivative term negative as seen in step 2 of the execution_table.

Why does the integral term keep increasing even when the error is small?

The integral term sums all past errors over time. Even small errors add up gradually, so the I term grows slowly as shown from step 1 to step 5 in the variable_tracker.

What happens to the control output when the error reaches zero?

When error is zero, the proportional and derivative terms become zero, but the integral term remains steady, so the control output stabilizes as shown in steps 5 and 6.

Visual Quiz - 3 Questions

Look at the execution_table at step 2. What is the value of the derivative term?

A -0.5

B 0.5

C 0.0

D 0.3

💡 Hint

Check the 'D term' column in the execution_table row for step 2.

At which step does the error first become zero?

A Step 4

B Step 6

C Step 5

D Step 3

💡 Hint

Look at the 'Error' column in the execution_table to find when it reaches zero.

If the integral gain Ki was zero, how would the I term change across steps?

A It would increase faster

B It would stay zero at all steps

C It would become negative

D It would equal the P term

💡 Hint

Refer to the variable_tracker row for 'I term' and recall that I term depends on Ki.

Concept Snapshot

PID Controller Basics for Power Electronics:
- Measures error = setpoint - output
- Calculates P = Kp * error (instant response)
- Calculates I = sum of past errors * Ki (eliminates steady error)
- Calculates D = rate of error change * Kd (predicts future error)
- Control output = P + I + D applied to device
- Updates error history each cycle for continuous control

Full Transcript

A PID controller in power electronics works by continuously measuring the output and comparing it to the desired setpoint. It calculates the error and uses three terms: proportional (P), integral (I), and derivative (D). The proportional term reacts to the current error, the integral term sums past errors to remove steady-state error, and the derivative term predicts future error by looking at how fast the error changes. These three terms are added to produce the control output, which adjusts the power electronics device. After applying the control, the controller updates its stored error values to prepare for the next measurement cycle. This process repeats continuously to maintain the desired output level.

Practice

1. What does the P in a PID controller stand for in power electronics?

easy

A. Proportional

B. Predictive

C. Power

D. Process

Solution

1. Step 1: Understand PID components

   The PID controller has three parts: Proportional, Integral, and Derivative.

2. Step 2: Identify the meaning of P

   The letter P stands for Proportional, which adjusts output based on current error.

3. Final Answer:

   Proportional -> Option A

4. Quick Check:

   P in PID = Proportional [OK]

Hint: Remember PID parts: P=Proportional, I=Integral, D=Derivative [OK]

Common Mistakes:

• Confusing P with Predictive
• Thinking P means Power
• Mixing P with Process

2. Which of the following is the correct formula for the output of a PID controller?

easy

A. Output = Kp * error + Ki * integral(error) + Kd * derivative(error)

B. Output = Kp + Ki + Kd

C. Output = error / (Kp + Ki + Kd)

D. Output = Kp * Ki * Kd * error

Solution

1. Step 1: Recall PID output formula

   The PID output combines proportional, integral, and derivative terms multiplied by their gains.

2. Step 2: Match formula to options

   Output = Kp * error + Ki * integral(error) + Kd * derivative(error) correctly shows Output = Kp * error + Ki * integral(error) + Kd * derivative(error).

3. Final Answer:

   Output = Kp * error + Ki * integral(error) + Kd * derivative(error) -> Option A

4. Quick Check:

   PID output formula = Output = Kp * error + Ki * integral(error) + Kd * derivative(error) [OK]

Hint: PID output sums weighted error terms, not just adds gains [OK]

Common Mistakes:

• Adding gains without error terms
• Multiplying all gains and error directly
• Dividing error by sum of gains

3. Given a PID controller with Kp=2, Ki=1, Kd=0.5, and error=3, integral(error)=4, derivative(error)=2, what is the output?

medium

A. 15

B. 13

C. 11

D. 14

Solution

1. Step 1: Calculate each term

   Proportional = Kp * error = 2 * 3 = 6
   Integral = Ki * integral(error) = 1 * 4 = 4
   Derivative = Kd * derivative(error) = 0.5 * 2 = 1

2. Step 2: Sum all terms for output

   Output = 6 + 4 + 1 = 11

3. Final Answer:

   11 -> Option C

4. Quick Check:

   2*3 + 1*4 + 0.5*2 = 11 [OK]

Hint: Multiply gains by errors, then add all results [OK]

Common Mistakes:

• Adding gains instead of multiplying
• Ignoring derivative term
• Mixing integral and derivative values

4. A PID controller is not stabilizing a power converter. Which of these is a likely error in tuning?

medium

A. Setting Kp to zero to remove proportional action

B. Setting Ki too high causing integral windup

C. Ignoring derivative term completely

D. Using too small sampling time

Solution

1. Step 1: Understand integral windup

   Integral windup happens when Ki is too high, causing output to saturate and instability.

2. Step 2: Evaluate options

   Setting Ki too high causing integral windup correctly identifies high Ki causing windup, which destabilizes the system.

3. Final Answer:

   Setting Ki too high causing integral windup -> Option B

4. Quick Check:

   High Ki can cause windup and instability [OK]

Hint: Watch for high Ki causing output to saturate [OK]

Common Mistakes:

• Thinking zero Kp always stabilizes
• Ignoring derivative term is always safe
• Assuming smaller sampling time fixes tuning

5. In a power electronics system, how does increasing the derivative gain (Kd) affect the controller's response?

hard

A. It slows down the response by adding delay

B. It increases steady-state error by ignoring past errors

C. It eliminates the need for proportional gain

D. It reduces overshoot by reacting to error changes quickly

Solution

1. Step 1: Understand derivative action

   Derivative gain reacts to the rate of error change, helping reduce overshoot and oscillations.

2. Step 2: Analyze effects of increasing Kd

   Increasing Kd makes the controller respond faster to error changes, reducing overshoot.

3. Final Answer:

   It reduces overshoot by reacting to error changes quickly -> Option D

4. Quick Check:

   Higher Kd reduces overshoot by quick error change response [OK]

Hint: Higher Kd means faster reaction to error changes, less overshoot [OK]

Common Mistakes:

• Thinking Kd increases steady-state error
• Believing Kd slows response
• Assuming Kd replaces proportional gain