PID controller basics for power electronics - Mini Project: Build & Apply

PID Controller Basics for Power Electronics

📖 Scenario: You are designing a simple PID controller to regulate the output voltage of a power converter. The PID controller adjusts the control signal based on the error between the desired voltage and the actual voltage.

🎯 Goal: Build a step-by-step understanding of how to set up a PID controller by defining the error, setting PID gains, calculating the control signal, and applying the control signal limits.

📋 What You'll Learn

Define the error as the difference between the reference voltage and the measured voltage

Set the PID gains: proportional (Kp), integral (Ki), and derivative (Kd)

Calculate the control signal using the PID formula with error, integral of error, and derivative of error

Apply saturation limits to the control signal to keep it within allowed bounds

💡 Why This Matters

🌍 Real World

PID controllers are widely used in power electronics to regulate voltages and currents precisely, ensuring stable and efficient operation of converters and inverters.

💼 Career

Understanding PID basics is essential for engineers working in power electronics design, control systems, and automation to develop reliable and optimized control solutions.

1

Define the error variable

Create two variables: V_ref with value 12.0 (volts) and V_meas with value 10.5 (volts). Then create a variable called error that is the difference between V_ref and V_meas.

Power Electronics

# Define reference and measured voltages
# Your code here

Hint

Subtract the measured voltage from the reference voltage to get the error.

2

Set PID gain constants

Create three variables called Kp, Ki, and Kd and set them to 1.2, 0.01, and 0.05 respectively.

Power Electronics

V_ref = 12.0
V_meas = 10.5
error = V_ref - V_meas
# Set PID gains
# Your code here

Hint

Assign the exact values to each gain variable.

3

Calculate the PID control signal

Create variables integral_error and derivative_error with values 0.2 and -0.1 respectively. Then calculate the control signal u using the formula: u = Kp * error + Ki * integral_error + Kd * derivative_error.

Power Electronics

V_ref = 12.0
V_meas = 10.5
error = V_ref - V_meas
Kp = 1.2
Ki = 0.01
Kd = 0.05
# Define integral and derivative errors
# Your code here

Hint

Use the PID formula combining proportional, integral, and derivative terms.

4

Apply saturation limits to the control signal

Create variables u_min and u_max with values 0 and 15 respectively. Then update u so it is limited between u_min and u_max using conditional statements.

Power Electronics

V_ref = 12.0
V_meas = 10.5
error = V_ref - V_meas
Kp = 1.2
Ki = 0.01
Kd = 0.05
integral_error = 0.2
derivative_error = -0.1
u = Kp * error + Ki * integral_error + Kd * derivative_error
# Define saturation limits and apply them to u
# Your code here

Hint

Use if-elif statements to keep u within the limits.

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