Navier-Stokes visual explainer
Follow a shrinking swirl through five interactive chapters to see how speed can rise while core energy falls.
Building · robotics, AI, machine learning
Building and explaining intelligent systems.
I build interactive projects and write about robotics, AI, and machine learning. Explore the experiments, the code, and the ideas behind them.
Explore the projects
Learn by changing something.
Explore dot products, conditional probability, and gradient descent through interactive examples. Each lesson includes worked problems and exercises with solutions.
Projects
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A file-based publishing foundation for project case studies and technical writing on this site.
Writing
All writingBode plots and loop shaping: place gain and phase together
Read Bode plots and shape a position-control loop with a lead controller. Calculate crossover and phase margin, compare closed-loop tracking, and check what the model leaves out.
Cascade control: let position request velocity and velocity request torque
Build cascade control from nested position and velocity loops. Follow command units, compare finite inner dynamics with ideal velocity tracking, and calculate the effect of an opposing load.
Control bandwidth: tracking speed and physical limits
Calculate closed-loop bandwidth relative to DC gain, then compare sinusoidal tracking with the torque it requires. Separate bandwidth from loop crossover and account for resonance, delay, sampling, and noise.
Controller discretization: sample, compute, and hold
Explore controller discretization with exact held-input dynamics. Compare immediate and delayed commands, calculate discrete poles, and connect sample timing to control stability.
Derivative kick and filtering: choose what D responds to
Explain derivative kick and filtering with a target step and measured noise. Compare derivative on error with derivative on measurement, calculate filtered command peaks, and weigh noise gain against lag.
Feedforward control: predict torque, then correct error
Calculate model-based torque from a smooth speed reference, then add feedback correction. Compare feedforward, proportional feedback, and their combination under inertia error, drag error, and unknown external torque.
Now
The Navier-Stokes explainer is live. Follow a shrinking swirl through five short chapters, then compare its speed with the energy inside it. Each scene includes the assumptions behind the picture.
- Status
- Navier-Stokes interactive explainer is live
About
Interested in how intelligent physical systems work. This site is becoming a record of experiments, technical decisions, and explanations about machine perception, learning, and action. The emphasis is on concrete examples and work that can be examined.
- 01
Choose a question worth making concrete.
- 02
Build the smallest experiment that can expose an assumption.
- 03
Examine what happened and document what changed.
- 04
Publish the result, its limits, and the next useful step.