DiffEq Temperature Controller¶

Overview¶

The DiffEq Temperature Controller provides first-order proportional-integral (PI) control with automatic gain tuning. It’s ideal for initial temperature stabilization before switching to more sophisticated controllers like LQR.

Key Features¶

Automatic Gain Tuning: Self-tunes based on system dynamics
Robust Stability: First-order response prevents oscillations
Smooth Transitions: Bumpless transfer when switching controllers
Fast Response: Quickly brings system to target temperature

Theory¶

Control Law¶

The controller implements a first-order differential equation:

\[\begin{split}\\tau \\frac{dT_{bath}}{dt} = k_P e + k_I \\int e dt\end{split}\]

where:

\(\\tau\): Time constant (ps)
\(e = T_{target} - T_{measured}\): Temperature error
\(k_P, k_I\): Proportional and integral gains (auto-tuned)

Auto-Tuning¶

The controller automatically computes gains based on:

System time constant \(\\tau\)
Desired closed-loop bandwidth
Stability margins

Usage¶

Basic Usage¶

Example for initial temperature control:

python3 18_unified_cavity_dynamics.py \\
  --enable-diffeq-controller \\
  --diffeq-temperature-method lj_coulombic \\
  --diffeq-time-constant 0.1 \\
  --diffeq-turn-on-time 10.0 \\
  --diffeq-turn-off-time 510.0 \\
  --target-temp 100.0

Key Parameters¶

--diffeq-temperature-method: Which temperature to control (lj_coulombic, kinetic, harmonic)
--diffeq-time-constant: Response time constant in ps (smaller = faster response)
--diffeq-turn-on-time: When to activate controller (ps)
--diffeq-turn-off-time: When to deactivate controller (ps)
--diffeq-output-file: CSV file for logging controller state

API Reference¶

class hoomd.cavitymd.controllers.DiffEqController¶: Bases: object