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

Concept Flow - PID controller basics for power electronics

Measure Output

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Calculate Error = Setpoint - Output

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Compute P term: Kp * Error

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Compute I term: I_prev + Ki * Error * dt

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

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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.