PID Controller Tuner

Interactive PID Parameter Optimization

SimulationControl systems

PID Controller Tuner

Tune closed-loop proportional, integral, and derivative gains, then compare them with the physical mass-spring-damper response that underpins sensor dynamics.

5 presetsClosed-loop cases

3 processesThermal, motor, flow

10 sResponse window

Rank-8Dynamics self-test

Workbench mode

Mass-Spring-Damper Sensor Response

Move from a physical acceleration step to proof-mass displacement, poles, overshoot, rise, and settling. Change damping alone to separate transient behavior from final sensitivity.

TryLoad Proof mass: underdamped, then press Play or Step through the four evidence stages.

ObserveChange only Damping from 2.00 to 20.0 N*s/m: overshoot disappears while final displacement stays 10.0 mm.

ExplainDamping moves poles and changes the transient; mass and spring set static acceleration sensitivity m/k.

Physical model

Scenario preset Underdamped

Mass (log scale) 1.00 kg

Damping 2.00 N*s/m

Spring (log scale) 100 N/m

Acceleration step (log scale) 1.00 m/s^2

Response evidence Stage 1 of 4

1. ApplyIdeal acceleration step drives the proof mass.

2. MoveDisplacement approaches its static value.

3. Read polesPole position explains ringing or monotonic decay.

4. QualifyRise, peak, and exact-grid settling bound the reading.

Fundamentals identity (pale only)Current responseFinal reference2% success band

Natural frequency

Damping ratio

Poles

Sensitivity m/k

Final displacement

Overshoot

Peak / rise

Exact 2% settle

m*x'' + c*x' + k*x = m*a0*u(t)
omegaN = sqrt(k/m); zeta = c/(2*sqrt(k*m))

accelerationSensitivity = m/k
xInfinity = (m/k)*a0; envelope estimate 4/(zeta*omegaN)

Transient and static behavior are separate.At 2.00 N*s/m the response overshoots, while the final displacement is 10.0 mm.

Deterministic fixture assertions (relative tolerance 1e-6)

Fixture	Computed	Expected	Result

Technical boundaries. This is a linear time-invariant, one-degree-of-freedom lumped model with constant positive mass/spring values, viscous damping, zero initial conditions, and an ideal acceleration step. It does not model nonlinear springs, Coulomb friction, stops, cross-axis motion, mode shapes, temperature, electronics, sampling, feedback saturation, or structural failure. The 2% settling readout is a deterministic teaching metric, not a component qualification.

TryStart with Motor Balanced at Kp 2.0, Ki 0.50, and Kd 0.2, then compare Aggressive Motor.

ObserveOvershoot rises as Kp increases, Ki drives steady-state error toward 0%, and Kd damps the transient peak.

ExplainThe 3 gain terms separate roles: Kp reacts to current error, Ki accumulates persistent error, and Kd opposes rapid error change.

Guided Investigation

Use Motor Balanced and inspect how the response approaches the setpoint.
Switch to Slow Temperature and notice why a large Kp can still settle slowly.
Try Aggressive Motor and use the diagnosis to decide which gain to reduce.

Scenario Focus

Motor Balanced is a moderate loop where proportional action gives speed, integral removes final error, and derivative adds damping.

Process and Gains

Process

Test Mode

Kp: Proportional4.0

Responds to present error. More Kp usually improves speed but can create overshoot.

Ki: Integral0.80

Accumulates error. More Ki removes bias but can cause slow oscillation or windup.

Kd: Derivative1.6

Responds to rate of change. More Kd damps overshoot but can amplify noisy measurements.

Tuning Snapshot

Process

Style

Stability

Score

Step Response

Fundamentals identity (pale only)Current responseSetpoint reference2% success band

Overshoot

Settling

SS Error

Rise Time

Peak Time

Tuning Diagnosis

Run a response to see the tuning diagnosis.

Preset Comparison

Preset	Metrics	Signal

Gain Effect Check

Gain	Current Signal	What To Try

Process Notes

Motor speed has medium dynamics and is a good starting point for PID learning.

Question	Current Signal	Why It Matters

Technical boundaries. This deterministic teaching model uses a saturated PID controller and simplified second-order process families over a 10-second window. It does not model sample jitter, actuator dead band, transport delay, sensor noise, derivative filtering, anti-windup schemes beyond a bounded integral, nonlinear plant behaviour, hardware limits, or safety certification. Treat the scores and Ziegler-Nichols estimate as comparative evidence, not commissioning advice.