FixTheRobot Explore Robotics / Guidance, Navigation and Control / M5 / M5-L1

This lab works on phones, but writing code is much easier on a laptop.

Guidance, Navigation and Control · Nonlinear, Scheduled and Adaptive Control · M5-L1 · Intermediate

Schedule the Gains Through the Burn

Bench log · Hopper on the test range

12:30. Hopper's pitch loop was tuned at the pad and is crisp at liftoff. By the end of the burn, 48 kg of propellant later, the same gains give a sluggish, ringing loop. Re-tuning at burnout makes the liftoff jittery.

You will see why, compute the gains for any mass, and write the table lookup that the flight code uses.

Your task

    Simulation
    solution.pyLoading Python…
    Ctrl+Enter runs
    What Python can I use?

    Plain Python 3 with the standard library and the course library gnckit (import gnckit as g: transfer functions and margins, state space and LQR, the Hopper model, quaternions, a convex solver). NumPy is not available in the browser. Your code runs in a background worker: an endless loop is stopped after a few seconds and the page stays usable. It runs in your browser and is never sent anywhere.

    Hints

    What this lab teaches

    Stage 1: the loop gain is proportional to the authority, which is proportional to the mass; fixed gains mean a different loop at every mass, and a schedule in 1/b keeps the damping and the delay margin the same. Stage 2: the gains that place the closed-loop polynomial for a given mass. Stage 3: interpolation in a stored table, with the end values held outside the designed range.

    Grading compares your gains with the exact ones for hidden masses, and your table values with the linear interpolation, including queries outside the table.

    Theory for this lab

    Nonlinear, Scheduled and Adaptive Control labs

    1. M5-L1: Schedule the Gains Through the Burn: this lab.
    2. M5-L2: Fly with One Effector Lost

    Educational simplification: the pitch axis only, with a pitch inertia that does not change and a mass that is known. Module 5 treats the scheduling variable, the interpolation between linear designs and the stability of a slowly varying system.

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