🚗 Cruise Control: PI Controller and Integral Windup

About this simulation

Modern cruise control is a feedback loop: a sensor reads the car's actual speed, compares it to the driver's target speed, and a controller decides how much throttle (or brake) to apply. This simulation implements a classic PI controller — proportional plus integral — driving a physically simulated car up and down a road whose grade you control directly.

How it works

• Proportional term (K_p) — pushes the throttle in proportion to the current speed error. Too low and the car responds sluggishly; too high and it oscillates.
• Integral term (K_i) — accumulates past error over time, eliminating the steady-state offset a pure-P controller leaves on a hill. Too high and it overshoots.
• Integral windup — when the actuator saturates (full throttle climbing a steep hill), the integral term keeps growing even though the output can't increase any further. When the hill ends, that stored error has to "unwind," causing a big overshoot.
• Anti-windup clamp — stops the integral from accumulating further once the actuator is saturated, so the controller recovers cleanly instead of overshooting.

Controls

• Target speed — the speed the cruise control tries to hold (km/h).
• K_p / K_i — proportional and integral gains of the controller.
• Road grade — tilts the road uphill (+) or downhill (−), the main disturbance to the loop.
• Anti-windup clamp — toggle the anti-windup protection on or off to compare behaviour.
• ↺ Reset run — clears the speed/time chart and resets the car to a standing start.

Try this

Turn anti-windup off, set K_i high (around 2.0), and push the grade slider to +12% for a few seconds, then back to 0%. Watch the integral term climb off the chart and the car blow past its target speed once the hill ends — classic windup. Turn anti-windup back on and repeat: the overshoot almost disappears.