Pid Output⚠ unverified
Physics / Controls · Compute the PID controller output
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| kp | kp | — | 1.0 | Proportional gain |
| ki | ki | — | 1.0 | Integral gain |
| kd | kd | — | 1.0 | Derivative gain |
| error | error | — | 1.0 | Current error signal (setpoint minus measurement) |
| integral | integral | — | 1.0 | Accumulated integral of the error over time |
| derivative | derivative | — | 1.0 | Rate of change of the error |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | u | — | Controller output (control effort) |
The science & history
Understanding the Parameters
- $k_p, k_i, k_d$ — tuning knobs (Ziegler–Nichols, IMC, etc. choose them).
- error / integral / derivative — must be consistent in time base with $k_i$, $k_d$.
- $u$ — linear combination; no saturation, anti-windup, or filtering modelled here.
Derivation (Approaching a Proof)
By definition of the parallel PID: proportional on error, integral on accumulated error, derivative on error rate. Laplace form $U(s) = (K_p + K_i/s + K_d s) E(s)$ is the same law in the $s$-domain.
History
PID control dominates industrial process control; the three-term structure dates to early 20th-century governors and pneumatic controllers.
Related Concepts: Phase Margin, Lead Compensator Phase, Lag Compensator Attenuation, Velocity Error Constant
Notes: Registry calculator pid-output (unverified). Snapshot evaluation only — not a dynamic
simulator.