Hot Air Balloon Flight Control Panel: PID Altitude Autopilot (2D)

Autopilot Gains (PID)

Proportional K_p 0.060

Integral K_i 0.006

Derivative K_d 0.35

Flight Plan

Target altitude 60 m

Wind gust strength 1.0

Live Readout

Altitude

0.0 m

Error

0.0 m

Vertical speed

0.0 m/s

Envelope temp

288 K

Actuator

idle

Elapsed

0.0 s

How it works

The plant is real physics, not a scripted flight path. Internal envelope air obeys the ideal gas law at roughly constant pressure, so its density falls as it heats:

ρ_gas = ρ0 · T0 / T_gas
F_buoy = ρ0 · V · g            (Archimedes, displaced ambient air)
F_weight = (m_struct + ρ_gas·V) · g
a = (F_buoy − F_weight) / m_total − k_drag·v·|v| / m_total

A real PID controller (derivative computed on measured altitude, not on the error, so a setpoint step does not "kick" the burner) drives a single bidirectional actuator — burner when positive, vent valve when negative:

e = target − h
u = Kp·e + Ki·∫e dt − Kd·(dh/dt)
dT_gas/dt =  k_heat·u  − k_cool·(T_gas − T0)   if u ≥ 0
dT_gas/dt = −k_vent·|u| − k_cool·(T_gas − T0)   if u < 0

The integral term uses conditional (anti-windup) accumulation: it stops accumulating while the actuator is already saturated at ±100%, which is what keeps a high K_i from producing runaway overshoot after a long saturated climb. Try raising K_i alone to see slow settling become a slow oscillation, and raising K_d too far to see the response go sluggish as it fights its own rate term. Horizontal drift (background wind arrow) is a pure disturbance — a balloon has no rudder, so the autopilot only ever manages altitude, exactly like a real one.

Balloon altitude Target setpoint Burner / vent output