Writing
Explanations, tutorials, build notes, and essays grounded in work that can be examined. Explore a concept, try an experiment, and follow the reasoning behind it.
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Explore poles and zeros by changing one numerator zero in a stable second-order system. Calculate inverse response, compare real and complex poles, and distinguish canceled factors from hidden internal modes.
Connect the Routh-Hurwitz criterion, Nyquist stability test, and gain and phase margins. Find when a three-lag feedback system settles, sustains oscillation, or becomes unstable.
Read step response characteristics from an exact second-order model. Compare rise time, overshoot, settling time, and steady error without mistaking the end of a plot for the final value.
Derive a robot joint transfer function with the Laplace transform. Separate zero-state and natural responses, calculate a pole and time constant, and compare torque steps with pulses.
Explore actuator dynamics with a DC motor’s current rise, back EMF, and geared load. Compare finite inductance with a reduced model, calculate reflected rotor inertia, and check torque, steady speed, and energy balance.
Fit dynamic parameters from a rotating joint's motion and torque data. Recover inertia, gravity mass moment, and damping, then test excitation, noise, and held-out predictions.
Explore feedback control with a robot joint speed model. Compare proportional correction with feedforward alone, calculate steady error, and test disturbances, sensor bias, and torque limits.
Solve a robot arm’s joint accelerations from torque, configuration, and velocity. Replay gravity release and compensation with RK4, then check energy balance and step-size error.
Compare Coulomb, viscous, and Stribeck friction in a robot joint. Calculate resisting torque and power loss during motion, check static holding at zero speed, and see where friction compensation needs a better model.
Calculate joint torque from a robot arm’s pose, velocity, and requested acceleration. Account for gravity, coupling, friction, and a known tip force, then see how actuator limits change the resulting acceleration.
Explore joint flexibility with two rotary inertias joined by a spring and damper. Calculate transmitted torque, loaded deflection, elastic oscillation, and energy loss, then compare motor and load motion.
Turn uncertain inertia, damping, and disturbance torque into an acceleration range. Compare a nominal command with an actual model, handle negative acceleration correctly, and understand the assumptions behind a worst-case bound.