OPEN CONTROL LAB / LIVE MODELFOPDT · RK4 · PIDF

INPUT → RESPONSE → FEEDBACK → UNDERSTANDING

PID LOOP LAB

Interactive PID Tuning & Control-System Simulator

Change the controller.
Watch the loop respond.

Enter lab Learn PID

LIVE RESPONSE / y(t)0.00 s

SP1.000PV0.000ERROR1.000OUTPUT1.271

PKp 1.250present errorIKi 0.420error memoryDKd 0.080rate of change

1.250Kp e(t)+0.021Ki ∫ e(t)dt+0.000Kd de(t)/dt=1.271u(t)

01Setpoint

02Error+1.000

03PID1.25 + 0.02 + 0.00

04Actuator1.271

05Planty 0.000

06Sensor

Every trace and value above comes from the same deterministic simulation engine used in the laboratory.

PID MISSIONS

Don’t just move sliders. Solve a loop.

Start with a failure mode, meet measurable constraints, and get an explanation tied to the signals that caused the result.

01 · StarterBuild your first stable loop

Tune a delayed first-order process without trading stability for speed.

Start mission 02 · IntermediateReject an unexpected load

A process disturbance arrives after five seconds. Recover without violent actuator movement.

Start mission 03 · IntermediateStop integral windup

The actuator is tightly limited. Recover cleanly from saturation using an anti-windup strategy.

Start mission

See all five missions

THE CENTRAL IDEA

See what the controller is thinking.

A response curve tells you what happened. PID Loop Lab also shows why: error, individual P/I/D contributions, the unclamped command, actuator limits, plant state, disturbance, and measurement path.

Setpoint + process valueP / I / D contributionUnclamped + applied outputNoise + disturbance markers

FROM EQUATION TO MOTION

What is PID?

e(t)=r(t)-y(t)

u(t)=K_p e(t)+K_i\int e(t)\,dt+K_d\frac{de(t)}{dt}

PROPORTIONAL

React to the error now.

Scales the present weighted error. More gain is not universally better; stability depends on the plant.

Isolate this term

INTEGRAL

Remember error from the past.

Accumulates error to remove offset, but saturation can produce windup without protection.

Isolate this term

DERIVATIVE

React to how quickly the signal changes.

Adds rate information. Measurement mode and filtering limit setpoint kick and noise amplification.

Isolate this term

ENGINEERING, NOT THEATRE

Built around the loop.

Every feature exists to answer a control question: What caused the response? Which assumption does a tuning rule make? What did the actuator actually receive?

Practical PIDDerivative filter, setpoint weighting, saturation, slew limits, and two anti-windup modes.

Validated tuningFOPDT and ultimate-cycle methods with eligibility checks, controller forms, warnings, and references.

Numerical guardsSeparate plant step and controller sample time, RK4 integration, seeded noise, and divergence stops.

01—08

Build a loop. Stress it. Explain it.

Start from a stable FOPDT process, then add noise, delay, saturation, and slow sampling one effect at a time.

Open the lab

CONTROL FIELD NOTES

Search it. Understand it. Try it.

Focused guides turn common PID questions into indexable explanations and reproducible experiments.

FOUNDATIONSPID controller: the complete visual guide THE PRESENTProportional control without the guesswork THE MEMORYIntegral windup and how to stop it THE DIRECTIONDerivative control, filtering and noise