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A multiple input, multiple output (MIMO) experimental test facility has been developed for the evaluation, benchmarking and comparison of iterative learning control (ILC) strategies. The system addresses the distinct lack of experimental studies for the multivariable case and enables controller performance and robustness to be rigorously investigated over a broad range of operating conditions. The electromechanical facility is multi-configurable with up to 3 inputs and permits both exogenous disturbance injection and a variable level of coupling to be applied between input and output pairs. To confirm its suitability for evaluation and comparison of ILC, theoretical results are derived for two popular forms of gradient-type ILC algorithm, linking interaction with fundamental performance limitations. The test facility is then used to establish how well theoretical predictions match experimental results. The analysis is then extended to provide solutions to address this performance degradation, and these are again confirmed using the test facility.

Iterative Learning Control (ILC) was formally conceived 30 years ago, and has become an area of considerable research interest in both theoretical and application domains. ILC is suitable for systems which perform a repeated process defined over a finite time interval, termed a trial. It uses data recorded over previous trials to modify the control signal of the subsequent trial with the aim of sequentially improving tracking accuracy. A well established algorithmic framework has emerged for the class of gradient based algorithms whose convergence and robustness properties have been extensively studied by many groups, including Bristow (2008), Butcher, Karimi, and Longchamp (2008), Freeman, Rogers, Hughes, Burridge, and Meadmore (2012), Janssens, Pipeleers, and Swevers (2013a), Mishra, Topcu, and Tomizuka (2011), Ratcliffe, Lewin, Rogers, Hatonen, and Owens (2006), van de Wijdeven, Donkers, and Bosgra (2009) and Wang, Dassau, and Doyle (2010). A prominent member of this class is Norm Optimal ILC (NOILC) which has received considerable attention in the ILC community due to its mature theoretic basis (Amann et al., 1996, Janssens et al., 2013b and Pandit and Buchheit, 1999). The framework has been applied to a range of systems including gantry robots (Ratcliffe et al., 2006), multi-axis robotic testbeds (Barton & Alleyne, 2011), rehabilitation platforms (Rogers et al., 2010), lasers (Rogers et al., 2010) and pneumatic muscle actuators (Schindele & Aschemann, 2011). Extensions have been proposed using a predictive mechanism (Bristow & Alleyne, 2006), constraints (Chu & Owens, 2010), projections (Chu & Owens, 2009), and accelerated learning (Owens & Chu, 2009). Another well established algorithm is ‘gradient ILC’, also termed ‘adjoint ILC’ which has been studied by many groups, including Furuta, Yamakita, and Kobayashi (1991), Jian-Xu and Ji (1998), Owens and Feng (2003) and Owens, Hätönen, and Daley (2009) and found to possess considerable robustness to plant uncertainty (Owens et al., 2009). This has been confirmed in applications to experimental single input, single output (SISO) systems including a non-minimum test facility (Freeman, Lewin, & Rogers, 2007). ILC has a proven ability in providing high performance in the presence of significant modelling uncertainty and exogenous disturbance, leading to uptake within industries such as manufacturing (Freeman et al., 2010 and Kim and Kim, 1996), chemical process engineering (Hui-hai, 2009 and Lee et al., 1996), industrial power systems (Deng et al., 2009 and Zha et al., 2003), robotics (Elci et al., 1994, Chen and Li, 2010, Hui-hai, 2009 and Norrlöf, 2002), biomedical engineering (Freeman et al., 2011) and precision laser and satellite control (Rogers et al., 2010 and Wu et al., 2009). While many such reported applications and cases of detailed experimental comparison and benchmarking exist for the SISO case, there are few instances involving multiple input, multiple output (MIMO) systems (Haurani et al., 2001 and Tyréus, 1979). These are generally more challenging due to interaction dynamics which typically increase controller demand as well as significantly complicating controller design and performance/robustness analysis. A number of studies involve multivariable systems (Barton and Alleyne, 2011, Bristow and Alleyne, 2006 and Ratcliffe et al., 2006), but interaction between dynamics is negligible and is generally not considered. With mild interaction, one approach is to treat the coupling as an exogenous disturbance and to design multiple SISO ILC loops. This has yielded satisfactory results when applied to control each joint of a six degrees-of-freedom industrial robot (Wallén, Norrlöf, & Gunnarsson, 2008). The approach has also been taken in stroke rehabilitation with ILC used to control the electrical stimulation applied to muscles in the lower and upper limb (Freeman et al., 2012). 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. Other practical studies have employed MIMO test facilities to tackle vibration suppression using ILC. For example in Tsai, Chen, Yun, and Tomizuka (2013) an ILC approach is applied to a 6 degree of freedom LCD substrate transfer robot to reduce end-effector vibration. Another MIMO vibration suppression approach is applied experimentally to a 3 input, 3 output flexible beam in van de Wijdeven and Bosgra (2007). In addition to a lack of MIMO application examples with significant input–output coupling there exists no comparative benchmarking between ILC algorithms, critical for thorough performance assessment prior to wider industrial implementation (Ahn et al., 2007 and Bristow et al., 2006). More generally, multivariable test facilities have been developed for the purpose of benchmarking and comparison of control strategies, such as a 2 input, 2 output quadruple-tank process (Johansson, 2000), however, to the authors׳ knowledge no modular facility exists which enables full control over the degree of coupling between input–output pairs, or which enables noise/disturbance injection to be applied. To address this problem, a multi-configurable experimental test facility is developed in this paper to enable MIMO ILC approaches to be rigorously evaluated. This platform provides a variety of possible inputs and outputs, enables disturbance injection and encompasses variable dynamic interaction. In addition, its modular structure will enable principled analysis of many relevant phenomena in a comprehensive manner (e.g. the inclusion of non-minimum phase zeros can be realised by modifying the spring-mass-damper sections to assume the non-minimum phase form used in Freeman et al. (2007)). To confirm the system׳s utility for both benchmarking and for evaluation of new theoretical results, this paper provides novel analysis which links the level of interaction with fundamental performance limitations within both NOILC and gradient ILC. These algorithms are then implemented on the system and experimental results are found to match theoretical predictions over a broad range of operating conditions. To address these limitations, the analysis is extended and it is shown that the performance limitations are directly mitigated by relaxing the tracking requirement to comprise only a subset of points over the trial duration. Using the test facility, these results are then confirmed experimentally over a range of interaction levels. This paper is arranged as follows: Section 2 describes the specification, design and parameter selection of the test facility and Section 3 details its physical realisation. ILC algorithms are derived and summarised in Section 4 together with performance measures, and experimental results follow in Section 5. Conclusions and future work are given in Section 6.

A multivariable test facility has been designed, built and tested for the evaluation of ILC algorithms. This is one of the few multivariable test platforms within the ILC domain (Ahn et al., 2007 and Bristow et al., 2006), and the only benchmarking facility which enables a varying level of interaction between input–output pairs. This paper has hence provided the first experimentally validated results examining the role of MIMO interaction on the performance of ILC. In particular, the MIMO facility enables both the level of interaction and the degree of exogenous noise/disturbance to be adjusted in a transparent fashion. The system has been developed in a systematic manner, initially using simulation studies with lumped parameter models to determine a hardware configuration which yielded desirable interaction characteristics which could be physically realised. Following construction, models were identified using frequency response data to yield low order representations which matched experimentally obtained data over the specified bandwidth. These were also shown to approximate the lumped parameter models, with differences accounted for by the presence of nonlinearities, unmodeled dynamics, and the inclusion of motor and drive dynamics. In parallel with the hardware development, new results have been presented linking the degree of MIMO interaction with the theoretical convergence and input norm properties for two members of a class of gradient based ILC algorithms. These results fuse a rigid connection between the coupling level and resulting performance properties, an association which is subsequently confirmed by experimental results using the MIMO system. A clear insight is hence established into the role of interaction in affecting performance in the MIMO case. The point-to-point framework is then exploited to mitigate the effects of high interaction, and has been found to enable desirable convergence and input norm properties to be recovered in a straightforward manner. These theoretical findings are then confirmed using experimental results. Future work will investigate the effect of additional constraints applied to the point-to-point framework, such as the minimisation of the output acceleration norm (Owens & Chu, 2009) or hard bounds placed on the input signal (Chu & Owens, 2010).