An Introduction to Iterative Learning Control - Inside Mines

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A Representation of Discrete-Time Linear ILC - 4 • We may similarly consider time-varying and noncausal filters in the ILC update law: Uk+1 = Uk + LEk • A causal (in time), time-varying filter in the ILC update law might look like, for example: ⎡ n1,0 0 0 . . . 0 ⎢ n2,0 n1,1 0 . . . 0 ⎢ L = ⎢ n3,0 n2,1 n1,2 . . . 0 ⎢ ⎣ .. . . . . . nN,0 nN−1,1 nN−2,2 . . . n1,N−1 • A non-causal (in time), time-invariant averaging filter in the ILC update law might look like, for example: L = ⎡ ⎢ ⎣ K K 0 0 · · · 0 0 0 0 K K 0 · · · 0 0 0 0 0 K K · · · . .. 0 0 0 . . . . 0 0 0 0 · · · K K 0 0 0 0 0 · · · 0 K K 0 0 0 0 · · · 0 0 K • These issues have been described in some detail by Longman. . . . ⎤ ⎥ ⎦ ⎤ ⎥ ⎦
Multi-Loop Approach <strong>to</strong> ILC - 1 • Suppose we use the discrete-time version of Arimo<strong>to</strong>’s ILC algorithm (assume relative degree m = 1): uk+1(t) = uk(t) + γek(t + 1) = uk + γ(yd − Huk) • Then the individual components of uk+1 are: uk+1(0) = uk(0) + γ(yd(1) − h1uk(0)) uk+1(1) = uk(1) + γ(yd(2) − h1uk(1) − h2uk(0)) . �t−1 uk+1(t) = uk(t) + γ(yd(t + 1) − h1uk(t) − . n=0 ht+1−nuk(n))
Page 1 and 2: An Introduction to Iterative Learni
Page 3 and 4: Control Design Problem Reference Er
Page 5 and 6: Systems that Execute the Same Traje
Page 7 and 8: Iterative Learning Control - 1 •
Page 10 and 11: • Consider the plant: A Simple Li
Page 13 and 14: Adaptive ILC for a Robotic Manipula
Page 15: Adaptive ILC for a Robotic Manipula
Page 18 and 19: A Short Overview of ILC - 2 • Pas
Page 21 and 22: ILC Problem Formulation - 1 • Sta
Page 23 and 24: Some Learning Control Algorithms
Page 25 and 26: • General linear algorithm: • C
Page 27 and 28: LTI Learning Control - Nature of th
Page 29 and 30: Interlude: The Two-Dimensional Natu
Page 31 and 32: A Representation of Discrete-Time L
Page 33: A Representation of Discrete-Time L
Page 38 and 39: Multi-Loop Interpretation of ILC
Page 40: ILC Algorithm Design (cont.) Extens
Page 43 and 44: (5) Nonlinear and Time-Varying Syst
Page 45 and 46: Repetition-Domain Frequency Represe
Page 47 and 48: Convergence with Zero Error Converg
Page 49 and 50: ILC and One-Step-Ahead Minimum Erro
Page 51 and 52: ILC and One-Step-Ahead Minimum Erro
Page 53 and 54: For t = 1: We can write uOSA(1) = 1
Page 55 and 56: • Plant: yk(t + 1) = 0.4yk(t) + 0
Page 57 and 58: Concluding Comments - 2 • We have
Page 59: Related References (cont.) 6. “An

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