Learning library

Make the foundations concrete.

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99 lessons to explore

Foundations first

  1. Foundations / 12 min read

    Bode 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.

  2. Foundations / 12 min read

    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.

  3. Foundations / 11 min read

    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.