Dynamics & feedback

Control Systems

Interactive simulations of feedback and signal processing — how a controller tames a system's response, what happens when you sample a signal too slowly to trust it, and the classic balancing problem that shows why proportional control alone often isn't enough.

Integral Windup & Anti-Windup

The loop is tuned correctly, the valve is fully open, and the controller keeps asking for more — then makes you pay for it.

overshoot with no tuning fault
Open

On-Off Control & Hysteresis

Why a bigger boiler cycles faster, why short-cycling wrecks compressors, and why the worst day for your heating is a mild one.

peak cycling at 50% duty
Open

First-Order Lag & Dead Time

Get a plant model out of one step test — time constant, dead time and gain — then see whether PID can control what you measured.

63.2% at one τ · L/τ decides it
Open

PID Control

Tune proportional, integral, and derivative gains and watch the closed-loop step response settle, overshoot, or oscillate — live.

u = Kₚe + Kᵢ∫e dt + Kₐ·de/dt
Open

Sampling & Aliasing

See the Nyquist limit in action — sample a signal too slowly and a fast frequency masquerades as a slow one.

Nyquist: fs > 2·f
Open

Ball and Beam Control Simulator

The classic PID teaching plant — see exactly why proportional-only control fails and derivative action is required.

x″ = (5/7)g·sinθ
Open

Bode Plot

Build a transfer function from gain, poles, zeros and integrators — see the magnitude and phase plots live, with gain and phase margins.

20·log|G(jω)| dB · ∠G(jω)°
Open
Results from every tool here are for reference only. These are teaching simulations of idealised systems — check against other sources before relying on them.