An Introduction to Iterative Learning Control - Inside Mines

Interlude: The Two-Dimensional Nature of ILC - 1
• Let the plant be a scalar (and possibly time-varying), discrete-time dynamical system, described
as:
Here:
yk(t + 1) = fS[yk(t), uk(t), t]
– k denotes a trial (or execution, repetition, pass, etc.).
– t ∈ [0, N] denotes time (integer-valued).
– yk(0) = yd(0) = y0 for all k.
• Use a general form of a typical ILC algorithm for a system with relative degree one:
where
uk+1(t) = fL[uk(t), ek(t + 1), k]
– ek(t) = yd(t) − yk(t) is the error on trial k.
– yd(t) is a desired output signal.