Robust iterative learning control: theory and experimental verification

摘要

Iterative learning control (ILC) is a technique especially developed for application to processes that are required to repeat the same operation over a finite duration. The exact sequence of operation is that the task is completed, the process is reset and then the operation is repeated. Applications are widespread among many industries, e.g. a gantry robot, which is required to place items on a conveyor under synchronization as part of a food manufacturing process. In effect, ILC exploits the fact that once a single execution of the task is complete then the input control action and output response produced are available to update the control input for the next trial and thereby sequentially improve performance. Moreover, it may be possible to undertake the required computations during the time between completing one execution and the start of the next. The fact that it updates the input, i.e. a signal, from trial to trial is the basic difference with other learning-type control schemes such as those based on neural networks, repetitive control and adaptive control, which modify the controller parameters. Since the original idea was first proposed in the 1980s (although the basic idea had seen development previously under other headings), research in ILC theory has seen rapid growth. The most basic problem here is to establish under what conditions an ILC scheme will converge in the trial-to-trial direction. This area continues to see many papers, but it is critical to note that convergence alone is not the complete picture. In fact, convergence in the trial-to-trial direction can conflict with performance along the trials. Another strong feature of the general area is that a range of algorithms have seen at least experimental benchmarking as a necessary next step towards actual application. The diverse range of potential application areas ranges from robotics to aerodynamics and most recently to stroke rehabilitation. One starting point for the literature in this area is the recent survey papers 1, 2 and the references cited in them. In recent years, the literature has seen many papers appearing on ILC for nonlinear systems by a variety of approaches, some of which impose very severe assumptions on the underlying process dynamics. A common feature of these papers, however, is the emphasis on a proof of trial-to-trial error convergence. Consequently, there remains much work to be done in the nonlinear area, but it is equally true that the theory for linear plants, with supporting experimental evidence where appropriate, is far from complete. In particular, the area of robust control has seen relatively little activity and it is not the case that this can be addressed by directly copying over existing tools from, for example, H∞/H2-based robust control theory for standard linear systems. The aims of this special issue are to explain the problems involved in developing a robust control theory for linear model-based ILC and associated algorithms and to provide experimental-based evidence of expected performance. It consists of six papers, which cover major areas of activity where progress has been made and most of them also include the results of experimentally testing the resulting control schemes. In the first of these papers, Moore et al. give new results on robust control based on the H∞ approach for examples where there is uncertainty associated with the plant model and also iteration, i.e. trial-to-trial, domain input–output disturbances (where the latter have no counterparts in non-ILC problems). The second paper by French gives substantial results on the use of the gap-metric in ILC, which results in provable robustness properties and also some insights into how a general solution to the so-called ‘long-term’ stability problem could be achieved by this route. This problem again unique to ILC has been observed in both simulation studies and experimental results. It results in divergence of the trial-to-trial error sequenc