An Introduction to Iterative Learning Control - Inside Mines

ILC and One-Step-Ahead Minimum Error Control
Relationship Between u ∗ (t) and uOSA(t)
• Carry out a long-division process on the plant to compute find:
h1 = b0
h2 = b1 − a1b0
b1 − a1h1
h3 = b2 − a2b0 − a1(b1 − a1b0)
b2 − a2h1 − a1h2
• Consider the expressions for uOSA(t) for t = 0, 1, 2, . . ., assuming:
– All initial conditions on the input are equal to zero for t < 0.
– All initial conditions on the output are zero for t ≤ 0.
– yd(0) = y(0) = 0.
For t = 0 (using the fact that b0 = h1):
uOSA(0) = 1
yd(1)
b0
= 1
h1
yd(1)
= u ∗ (0)