Step control

cubie.integrators.step_control

The step control package encapsulates the configuration and compilation machinery used to build CUDA device functions that manage integrator time-step selection. Fixed, integral, proportional–integral, proportional–integral– derivative, and Gustafsson-style predictive controllers share a common configuration interface that feeds the cubie.CUDAFactory compilation pipeline.

Controller interfaces

• BaseStepController – abstract base for all controllers.

• BaseAdaptiveStepController – adds adaptive gain handling.

• FixedStepController – returns constant time steps.

• AdaptiveIController – integral-only adaptive controller.

• AdaptivePIController – proportional–integral controller.

• AdaptivePIDController – proportional–integral–derivative controller.

• GustafssonController – Gustafsson PI controller variant.

• get_controller – resolves controller implementations from settings.

Configuration objects

• BaseStepControllerConfig – base attrs configuration shared by all controllers.

• AdaptiveStepControlConfig – configuration used by adaptive controllers.

• FixedStepControlConfig – fixed-step configuration container.

• PIStepControlConfig – proportional–integral gain configuration.

• PIDStepControlConfig – proportional–integral–derivative configuration.

• GustafssonStepControlConfig – Gustafsson controller configuration.

Dependencies

• Relies on cubie.CUDAFactory for compile-time caching of CUDA device functions.

• Requires Numba CUDA support during runtime to JIT the device controllers.

• Pulls validators and clamp helpers from cubie._utils when building device functions.

Suggested controller parameters

The default proportional, integral, and derivative gains mirror the recommendations from Söderlind and Wang while matching the guidance in OrdinaryDiffEq.jl. Common choices include:

Controller	beta1	beta2	beta3
basic	1.00	0.00	0
PI42	0.60	-0.20	0
PI33	2/3	-1/3	0
PI34	0.70	-0.40	0
H211PI	1/6	1/6	0
H312PID	1/18	1/9	1/18