Iterative Learning Control

For a system that repeats the same motion over and over, using last time's tracking error to correct next time's control input.

Iterative learning control targets systems that execute the same task repeatedly — an arm running the same trajectory on every cycle of a production line, for instance. It's generally credited to Arimoto, Kawamura, and Miyazaki's 1984 paper ‘Bettering operation of robots by learning.’ The idea is straightforward: after the k-th run, record the tracking error e_k(t) at every moment, then update the next run's input to u_{k+1}(t) = u_k(t) + L·e_k(t), where u is the control input and L a hand-designed learning gain; in practice a low-pass filter is usually added too, to keep noise from being amplified run after run. Ordinary feedback control can only correct an error after it appears; ILC instead feeds the previous run's error forward into the next run, so repeatable errors from an inaccurate model or friction get squeezed down more and more over successive runs. It requires the initial state and reference trajectory to stay much the same each time, and it offers no help against random disturbances or a task never attempted before — so it's usually paired with PID feedback.

ExampleAn industrial arm repeats the same welding trajectory on every production cycle: run 1 records lag at the corners, run 2 supplies extra torque slightly ahead of time at those same moments, and the tracking error at the corners keeps shrinking run after run.

Also called

ILC

Related

Feedforward Control · Proportional-Integral-Derivative Control · Trajectory Tracking · Adaptive Control · Teach-and-Playback Programming

Sources

Iterative learning control - Wikipedia