Proportional Feedback Control: Depth Tracking

Based on HMC E79 Practicum 5 — Underwater Robot Depth Control

Mode

System Parameters

Set parameters, then press Go

Response Metrics

ωn (rad/s)--
ζ (damping)--
Overshoot Mp--
Rise time tr--
Settling time ts--
Underdamped
m·z" + c·z' + Kp·z = Kp·zd
ωn = √(Kp/m)   ζ = c/(2√(m·Kp))

Underwater Robot Simulation

Step Response z(t)

Pole Locations (s-plane)

How It Works

The robot uses proportional control: thrust = Kp(zd - z)

This creates a 2nd-order system. Increasing Kp speeds up response but may cause oscillation.

The damping ratio ζ determines behavior: ζ < 1 oscillates, ζ = 1 is critically damped, ζ > 1 is sluggish.

Try it: Find the Kp that gives the fastest response with < 20% overshoot!