PD Controller Playground

An interactive Python simulation for exploring Proportional-Derivative (PD) controller behavior with real-world effects.

Quick Start

pip install -r requirements.txt

# Static plots with sliders
python pd_controller_playground.py

# Animated mass-spring-damper visualization (recommended)
python pd_animated_playground.py

# Armature-controlled DC motor with PD loop
python dc_motor_pd_playground.py

What You Can Explore

Slider	What it does	What to observe
Kp	Proportional gain	↑ Kp → faster response but more overshoot/oscillation
Kd	Derivative gain	↑ Kd → more damping, but amplifies sensor noise
dt	Sampling period	↑ dt → poor discretisation, potential instability
Noise σ	Sensor noise std dev	↑ Noise → jittery control signal (derivative amplifies it)
Delay steps	Transport delay	↑ Delay → phase lag → oscillation → instability
Saturation	Actuator limit	↓ Saturation → limited authority, slow response

Phenomena to Observe

• Instability — Crank up Kp with some delay and watch the system diverge
• Oscillation — High Kp with low Kd produces underdamped ringing
• Steady-state error — PD has no integrator; observe residual offset
• Noise amplification — Add noise and increase Kd to see the control signal go wild