Akreon Tutorial Series
Quarter-Car H∞ Control
From road disturbance to robust ride control in one active-suspension example.
Overview
Shape the worst case, not just the nominal response
This tutorial uses an active quarter-car suspension to connect physical modeling with H∞ control. Road motion becomes the disturbance; ride comfort, suspension travel, road holding, and actuator effort become competing performance channels.
The six-part arc moves from dynamics and open-loop analysis to static weighting, observer-based output feedback, frequency shaping, and mixed-sensitivity synthesis.
Rendered Notebook
Technical reference
The consolidated notebook contains the quarter-car model, generalized plants, scaling, H∞ LMIs, controller and observer synthesis, compensator realizations, and physical step and frequency-response comparisons.
Read the rendered notebookUse the chapter links below to jump directly to each derivation, implementation, and result.
Video Series
Watch the tutorial arc
The six-part companion series walks through the model, robust-control design choices, synthesis steps, and physical performance comparisons developed in the notebook.
Watch the YouTube playlistChapters
Six parts
- Part 01
Quarter-Car Dynamics
Model the sprung mass, wheel mass, suspension, tire, actuator, and road input around static equilibrium.
- Part 02
State Space and Open Loop
Assemble the state-space plant and examine its modes, controllability, observability, and finite-horizon Gramians.
- Part 03
Static-Weight H∞ Feedback
Translate physical ride objectives into a scaled generalized plant and synthesize full-state feedback with the bounded-real LMI.
- Part 04
H∞ Observer and Output Feedback
Estimate the suspension state from measured outputs and realize a practical dynamic compensator using the static H∞ gain.
- Part 05
Frequency-Shaped Performance
Replace static penalties with dynamic weights and synthesize an augmented measured-output compensator across frequency.
- Part 06
Mixed-Sensitivity Synthesis
Shape sensitivity, complementary sensitivity, and control sensitivity, then compare all designs on the same physical plant.