Journey 09 — SolvLRDE-Control

License token: control · Product name: SolvLRDE-Control (resonix-control)

See also: Vertical SKUs overview · Licensing

What this SKU is for

SolvLRDE-Control is the licensed vertical for linear time-invariant (LTI) control and systems engineering — aerospace flight dynamics, automotive chassis/ride models, robotics manipulators, and any team that holds a state-space plant x_dot = A x + B u and needs responses at specific times without running a stiff ODE integrator.

The engineering problem

Step responses, impulse responses, modal decay studies, and many Gramian-style queries reduce to the matrix exponential or resolvent: y(T) = exp(A * T) * y0. Engineers usually integrate x_dot = A x forward with RK or BDF, picking dt for stability and accuracy. That is correct but wasteful when you only need y(T) at a handful of horizons (e.g. settling time, peak overshoot, 20 s modal decay) or when you sweep many T values for a frequency-domain style study derived from the resolvent.

Why Control exists (and why LRDE fits)

Paste A from your linearized plant (or second-order companion form) and call solve(A, x0, T). No timestep selection, no stiffness tolerance tuning for the linear subproblem. Control is the SKU most often adopted through the 30-day trial: engineers verify against known transfer functions or Simulink linearizations before OEM licensing.

Who should buy Control (not another SKU)

Choose Control when…	Choose something else when…
Plant is LTI with constant `A` over the analysis window	Power-network companion form → Grid
You need step/impulse response at arbitrary `T`	Banded heat/diffusion MOL → Thermal
Inputs encoded in `x0` or constant forcing via augmented state	Nonlinear `f(t,y)` → SolvSRK

Typical production integration

Operator: A from linearization Jacobian or canonical second-order form [x, x_dot].
Initial state: encode unit step on position or velocity channel in y0.
Horizons: loop T for settling analysis, or single T for peak-response queries.
License gate: solvlrde.license_has_sku("control") before control-analysis features ship.

This walkthrough

Prerequisites: Core journeys 01–06 complete.

Scenario: Transfer functions, step responses, and Gramian queries reduce to evaluating the resolvent (zI - A)^-1. SolvLRDE gives y(T) for the state-space realization directly.

Key APIs

solvlrde.solve()
state-space A from linearized plant

Concepts to internalize

SolvLRDE-Control — resonix-control SKU.
Resolvent view — step/frequency analysis without time marching.
Trial-led funnel — engineers paste A from their linearization.

Important code

The guided tour script wraps this pattern. Copy the production shape into your pipeline:

A = np.array([[0, 1], [-wn**2, -2*zeta*wn]])
result = lrde.solve(A, [0.0, 1.0], T=5.0)

Act-by-act walkthrough

Act 1 — Linear control analysis

Transfer functions, step responses, and Gramian queries reduce to evaluating the resolvent (zI - A)^-1. SolvLRDE gives y(T) for the state-space realization directly.

Act 2 — Second-order mode in state space

x'' + 2 zeta wn x' + wn^2 x = 0 with state [x, x_dot]. Unit step on velocity channel: y0 = [0, 1]. Compare y(T) at several T without integrating.

Field	Value	Notes
`T`	1.0
`n_solves`	32
`survived`	True
`status`	ok
`y`	[0.271467, -0.344391]
`n_talbot_used`	32
`n_solves`	32
`nu_used`	0.6
`contour_scale`	12.8
`wall_s`	0
`T`	5.0
`n_solves`	32
`survived`	True
`status`	ok
`y`	[-0.00304701, -0.0480967]
`n_talbot_used`	32
`n_solves`	32
`nu_used`	0.6
`contour_scale`	2.56
`wall_s`	0
`T`	20.0
`n_solves`	32
`survived`	True
`status`	ok
`y`	[-1.16073e-10, -1.07562e-10]
`n_talbot_used`	32
`n_solves`	32
`nu_used`	0.6
`contour_scale`	0.64
`wall_s`	0

Act 3 — Self-serve trial path

LRDE-Control is the SKU most often adopted via the 30-day trial: engineers paste A from their linearized plant and verify step/frequency response before OEM licensing.

Guided tour output

Verified console capture from sku_control.py:

-- Act 1 - Linear control analysis --
  -> Transfer functions, step responses, and Gramian queries reduce to evaluating the resolvent (zI - A)^-1. SolvLRDE gives y(T) for the state-space realization directly.

-- Act 2 - Second-order mode in state space --
  -> x'' + 2 zeta wn x' + wn^2 x = 0 with state [x, x_dot]. Unit step on velocity channel: y0 = [0, 1]. Compare y(T) at several T without integrating.
  T: 1.0
  n_solves: 32
  survived: True
  status: ok
  y: [0.271467, -0.344391]
  n_talbot_used: 32
  n_solves: 32
  nu_used: 0.6
  contour_scale: 12.8
  wall_s: 0
  T: 5.0
  n_solves: 32
  survived: True
  status: ok
  y: [-0.00304701, -0.0480967]
  n_talbot_used: 32
  n_solves: 32
  nu_used: 0.6
  contour_scale: 2.56
  wall_s: 0
  T: 20.0
  n_solves: 32
  survived: True
  status: ok
  y: [-1.16073e-10, -1.07562e-10]
  n_talbot_used: 32
  n_solves: 32
  nu_used: 0.6
  contour_scale: 0.64
  wall_s: 0

-- Act 3 - Self-serve trial path --
  -> LRDE-Control is the SKU most often adopted via the 30-day trial: engineers paste A from their linearized plant and verify step/frequency response before OEM licensing.

-- Run complete --
  next_journey: sku_climate.py (Climate SKU)

Run it

cd python
# Guided tour — narrated scenario walkthrough (recommended first run):
python examples/skus/sku_control.py
 
# Production one-liner — same API call you ship:
python -c "import solvlrde,numpy as np;wn,z=2.,0.3;A=[[0,1],[-wn**2,-2*z*wn]];print(solvlrde.solve(np.array(A),[0.,1.],T=5.)['y'])"

What comes next

SolvLRDE-Climate for TLM blocks.

Navigation

← Journey 08 — SolvLRDE-Pricing · Journey 10 — SolvLRDE-Climate →

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