An Introduction to Iterative Learning Control - Inside Mines

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Relationship Between u ∗ (t) and uOSA(t) (cont.) • The key fact is that, for all t: u ∗ (t) = uOSA(t) • Recall that the one-step-ahead minimum prediction error controller effectively inverts the plant (after discounting the time delay). • Thus, we have reinforced the concept that the ILC technique effectively inverts the plant, as noted above. • The one-step-ahead minimum prediction error controller is a feedback controller. • The ILC technique is an open-loop control scheme that converges to the same input sequence as the one-step-ahead minimum prediction error controller. • Control energy considerations: – A common objection to ILC is that it is often applied without regard to control energy. – This same objection applies to the one-step-ahead minimum prediction error controller. – However, the weighted one-step-ahead controller can be introduced to minimize the cost function J1(t + 1) = 1 2 [y(t + 1) − yd(t + 1)] 2 + λ 2 u2 OSA (t) – This concept can also be applied to ILC design.
• Plant: yk(t + 1) = 0.4yk(t) + 0.7uk(t) • Resulting ILC input sequence (u ∗ (t)): Illustration • Resulting one-step-ahead minimum error predictor output(uOSA(t)): • Actual and desired outputs from each control technique:
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 and 34: A Representation of Discrete-Time L
Page 35 and 36: Multi-Loop Approach to ILC - 1 •
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: For t = 1: We can write uOSA(1) = 1
Page 57 and 58: Concluding Comments - 2 • We have
Page 59: Related References (cont.) 6. “An
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An Introduction to Iterative Learning Control - Inside Mines

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