Calculation
u = u₀ + Kp · e
A P controller responds immediately and proportionally: doubling the control error doubles the output change.
Zacher/Reuter 2024, Abschnitt 4.3.1: P-Regler
P controller: output from control error
A P controller responds immediately and proportionally: doubling the control error doubles the output change.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Controller output u — Value sent by the controller to the actuator, such as a normalised valve opening or drive command.
- Controller gain Kp — Controller-output change per unit of error. Kp comes from controller design or cautious tuning; an excessive value promotes oscillation.
- Control error e — Instantaneous setpoint minus measured value on the same scale. Its sign sets controller action; verify it on the real process.
- Bias u₀ — Controller output that holds the desired operating point at e=0. Obtain it from steady plant operation; use 0 if no bias is required.
Example
Kp=2, e=6 and u₀=20 give u=32. With an actuator range of 0 to 100, this value is not yet saturated.
Assumptions and limits
Ideal continuous P controller without output saturation, deadband, sampling or actuator dynamics; all signals must use consistent scaling.
Understand P controller: output from control error
Calculate a proportional controller output from controller gain, instantaneous control error and bias.
What does this quantity describe?
A P controller responds immediately and proportionally: doubling the control error doubles the output change. This calculator represents a clearly bounded technical relationship between the displayed quantities. The definition helps put inputs into the same reference state before interpreting the result.
Formula and variables
u = u₀ + Kp · e
| Symbol / input | Meaning |
|---|---|
| Controller output u | Value sent by the controller to the actuator, such as a normalised valve opening or drive command. |
| Controller gain Kp | Controller-output change per unit of error. Kp comes from controller design or cautious tuning; an excessive value promotes oscillation. |
| Control error e | Instantaneous setpoint minus measured value on the same scale. Its sign sets controller action; verify it on the real process. |
| Bias u₀ | Controller output that holds the desired operating point at e=0. Obtain it from steady plant operation; use 0 if no bias is required. |
Choose the inputs correctly
Controller output u: Value sent by the controller to the actuator, such as a normalised valve opening or drive command. Controller gain Kp: Controller-output change per unit of error. Kp comes from controller design or cautious tuning; an excessive value promotes oscillation. Control error e: Instantaneous setpoint minus measured value on the same scale. Its sign sets controller action; verify it on the real process. Bias u₀: Controller output that holds the desired operating point at e=0. Obtain it from steady plant operation; use 0 if no bias is required.
How to use the calculator
Select the target quantity, enter the other known values with units, then check the result against the worked example and model limits.
Worked example
Kp=2, e=6 and u₀=20 give u=32. With an actuator range of 0 to 100, this value is not yet saturated.
Understand the result and units
A P controller responds immediately and proportionally: doubling the control error doubles the output change. Read the result as a model value for the selected operating point and check units, sign, order of magnitude and application boundary conditions.
Use the displayed units and convert afterwards. Prefixes such as k-, m- and µ- are common sources of mistakes.
Typical applications
P controller: output from control error: Such basic calculations support plausibility checks, early component selection and preparation of a complete verification.
Assumptions, limits and common mistakes
Ideal continuous P controller without output saturation, deadband, sampling or actuator dynamics; all signals must use consistent scaling.
Common mistake: A formally correct result can still be unsuitable when load case, reference state or units do not match the application.
Frequently asked questions
How do I check the result?
Compare unit and order of magnitude with a second calculation and vary inputs one at a time.
Are assumptions automatically satisfied?
No. The calculator exposes a model; real boundary conditions require separate review.
Can I mix arbitrary units?
Only when the calculator converts within the same physical quantity type.