Read the full L0 lesson

L0 · Orientation: what is being identified?

System identification (SysID) means learning a useful model of a system from experiments. In this lesson the system is one rotational degree of freedom. The model boundary is intentionally explicit:

known applied torque u  ->  rotational plant  ->  observed q and qd

The plant follows

$$ J\ddot{q} + b\dot{q} = u $$

Here $q$ is position in radians, $\dot{q}$ is velocity in radians per second, $\ddot{q}$ is acceleration, $u$ is applied torque in N m, $J$ is inertia in kg m^2, and $b$ is viscous damping in N m s/rad. The unknowns are only $J$ and $b$. In code these signals are named q, qd, and qdd.

A simulator with known parameters generates the observations. The estimator receives time, torque, position, and velocity, together with parameter bounds and an initial guess chosen beforehand. The true parameters are used later to check the result.

Three names appear in every plot:

Comparing the initial and identified models shows how fitting changes the prediction. We then test a motion withheld from fitting to see whether the improvement carries over to new data.

Checkpoint

Before opening the plot, predict which model should be closest to the Oracle after fitting. Then open the report and check whether the parameter table agrees with your prediction.

Answer: the identified model should be closest because it is fitted on the Oracle-generated observations. That expectation is a hypothesis to test on held-out data, not proof by itself.