Experimentally verified point‐to‐point iterative learning control for highly coupled systems

Abstract

Iterative learning control (ILC) is a well-established approach for precision tracking control of systems, which perform a repeated tracking task defined over a fixed time interval. Despite a rich theoretical framework accompanied by a wide array of application studies, comparatively little attention has been paid to the case of multiple input, multiple output (MIMO) systems. Here, the presence of interacting dynamics often correlates with reduced performance. This article focuses on a general class of linear ILC algorithms and establishes links between interaction dynamics and reduced robustness to modeling uncertainty, and slower convergence. It then shows how these and other limitations can be addressed by relaxing the tracking requirement to include only a subset of time points along the time duration. This is the first analysis to show how so-called 'point-to-point' ILC can address performance limitations associated with highly coupled systems. Theoretical observations are tested using a novel MIMO experimental test facility, which permits both exogenous disturbance injection and a variable level of coupling between input and output pairs. Results compare experimental observations with theoretical predictions over a wide range of interaction levels and with varying levels of injected noise.POINT-TO-POINT ITERATIVE LEARNING CONTROL 303Of the small number of practical studies that have been reported, interaction between dynamics has been assumed negligible and is generally not considered [1,19,20]. With mild interaction, one approach is to treat the coupling as an exogenous disturbance and design multiple SISO ILC loops. This has yielded satisfactory results when applied to control each joint of a six degree-offreedom industrial robot [21]. The approach has also been taken in stroke rehabilitation with ILC used to control the electrical stimulation applied to muscles in the upper limb [22]. However, in the foregoing cases, a robustness filter was required to prevent instability and the tracking accuracy was considerably larger than when controlling a single joint (with the remaining joints locked). In the case of more significant multivariable coupling, this approach may therefore be expected to lead to a further loss of tracking accuracy and the likelihood of instability. A similar approach is multiaxis inversion-based ILC, which assumes a square system matrix and employs a diagonal system inverse that contains only the dominant dynamics for each output [23]. Here, omission of non-dominant dynamics leads to lack of convergence at frequencies at which the omitted dynamics have an overly large norm.Other practical studies have employed MIMO ILC to tackle vibration suppression. For example, in [24], an ILC approach is applied to a six degree of freedom LCD substrate transfer robot to reduce end-effector vibration. The reference is modified off-line to reduce link vibration using redundant actuation degrees of freedom. Another MIMO vibration suppression approach is to develop ILC algorithms that have two separate...

A coordinate descent approach to optimal tracking time allocation in point-to-point ILC

“…and the sequence {f (Λ j )} j 0 generated by the update (24) monotonically converges to a limitf * as…”

“…for each coordinate descent trial. From Algorithm 1, the valuer p used in Stage Two update (24) is computed based on the measured data aŝ r p = G Λ u ex ∞ (Λ). (F.2)…”

“…According to the coordinate descent update (24), the cost function r p , (G Λ G Λ * ) −1rp is optimized at each coordinate descent trial. Based on (G.5), the optimized cost function is also proportional tof (Λ) as…”

Generalized Iterative Learning Control Using Successive Projection: Algorithm, Convergence, and Experimental Verification

“…However in many application domains, the output may only be available at certain time instants, or only certain time instants may be relevant to capture the task requirement, e.g. high-acceleration positioning tables [25], robotic manipulators [26], two-mass systems [27], electro-mechanical systems [28], [29] and human motor system [30]. In recent years, the 'classical' ILC problem has been extended to meet the above needs leading to the so-called intermediate point (or point-to-point) ILC.…”

Parameter‐dependent Lyapunov function‐based robust iterative learning control for discrete systems with actuator faults

“…Since this first work, ILC research and applications has broadened and the survey papers [2] and [3] 2 JIAN DING ET AL are one source for an overview of developments up to the time of their publication. This area of control systems research continues to grow both in theory and applications, where recent new applications areas include robotic-assisted stroke rehabilitation for the upper limb [4], large dynamic range nanopositioning control [5], traffic management [6] and highly coupled electromechanical systems [7].…”