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Iterative learning control is a methodology applicable to systems which repeatedly track a specified reference trajectory defined over a finite time duration. Here the methodology is instead applied to the point-to-point motion control problem in which the output is only specified at a subset of time instants. The iterative learning framework is expanded to address this case, and conditions for convergence to zero point-to-point tracking error are derived. It is shown how the extra design freedom the point-to-point set-up brings allows additional input, output and state constraints to be simultaneously addressed, hence providing a powerful design framework of wide practical utility. Experimental results confirm the performance and accuracy that can be achieved, and the improvements gained over the standard ILC framework.

Iterative Learning Control (ILC) is a technique for controlling systems operating in a repetitive mode with the requirement that a reference trajectory y d(t ) defined over a finite interval 0≤t≤T0≤t≤T is followed to a high precision. Examples of applications include control of wafer scanners ( Heertjes & van de Molengraft, 2009), internal combustion engines ( Heinzen, Gillella, & Sun, 2011) and gantry robots ( Hladowski et al., 2010). Despite substantial developments over the last 25 years, little attention has been paid to the case in which the repeated operation may consist of a more general objective, which need not comprise the tracking of a static pre-defined reference trajectory (see Ahn et al., 2007 and Bristow et al., 2006 for recent overviews of the literature). A small number of ILC schemes do not use a static reference, but these are associated with specific applications, such as gas metal arc welding ( Moore & Mathews, 1997), underwater robotics ( Kawamura & Sakagami, 2002) or liquid slosh in a packaging machine ( Grundelius & Bernhardsson, 1999). In many applications, however, the goal is to repeatedly follow a motion profile in which the error is only critical at certain points. Examples include production line automation, crane control, satellite positioning, robotic ‘pick and place’ tasks, and motion control within a stroke rehabilitation context (Freeman et al., 2009). A commonly applied technique for such tasks is point-to-point motion control, in which the objective is to ensure that, at a finite set of prescribed time instants, the system output equals a corresponding set of desired values. Point-to-point control strategies typically involve the generation of a suitable motion profile in advance, and then the design of a controller to track it. The most common approach to generating such a profile is Input Shaping which has been applied in a wide variety of ways (Dharne and Jayasuriya, 2007, Singh and Singhose, 2002 and Dijkstra et al., 2000), although other approaches have also been used (see Belts, 1998 and Doyle, 1995 and references therein). The application of ILC in the area of point-to-point motion control offers the potential to benefit from the ability to learn from experience gained over previous trials of the task. The problem can clearly be tackled in the standard ILC framework by using any reference which connects the desired points. However, extra freedom is gained by removing the unnecessary constraint that the plant follow a pre-defined output between points, which can be exploited to increase performance. Several cases exist in which ILC has been applied to point-to-point motion control. van de Wijdeven and Bosgra (2008) used Hankel ILC to suppress residual vibrations, where controller matrices are determined through command shaping. An iterative learning scheme is again employed in Park, Chang, Park, and Lee (2006) for vibration suppression, and the control parameters are updated via an input shaping technique. In Ding and Wu (2007) a standard ILC controller is first applied but the control gains are chosen to minimize an error norm motivated by the point-to-point positioning operation rather than the tracking error along the task. These applications of ILC to point-to-point tracking involve the design of an initial reference, which is then static over all trials. Furthermore, they consider only a movement between points. An exception to this is the frequency-domain approach of Freeman, Cai, Rogers, and Lewin (2010) which also requires a predetermined reference trajectory defined over the whole trial duration, but modifies it after each trial, enabling increased convergence and robustness properties compared with using a static trajectory. This approach can also deal with multiple point-to-point movements. However, like the former methods, its performance depends on the initial predetermined reference trajectory which, being based on the nominal plant model, is not optimal with respect to the actual plant. In contrast to the methodologies currently employed within ILC, this paper introduces an approach to the point-to-point problem which dispenses of a reference defined over the entire trial interval, thereby simplifying design and removing unnecessary constraints. Furthermore, for the first time it allows a general class of additional objectives, such as minimising the input energy or output velocity, to be specified by the designer in response to practical considerations and desired performance. This is not possible using the ILC approaches previously formulated. Through use of data collected over repeated executions of the task, these objectives, together with the point-to-point tracking task, can then be achieved robustly in the ILC framework. The paper is organised as follows: Section 2 introduces the control problem and describes the plant, Section 3 applies the gradient descent approach to the point-to-point problem in the ILC framework, and then introduces additional constraints to be satisfied. In Section 4 Newton method based ILC laws are developed, using results derived in the previous section. Experimental results are presented in Section 5, and conclusions are given in Section 6.

The point-to-point motion control problem is of wide applicability within automation, crane positioning, robotics, and stroke rehabilitation. This paper shows how it may be tackled in the iterative learning framework where its novel features include: (1) simplifying design and analysis by only requiring a reference defined at the required points and (2) allowing a general class of additional performance objectives to be simultaneously tackled within the framework of iterative learning. This is achieved by employing the gradient and Newton nonlinear minimization methods within the ILC framework, where the former is used in the implementation of the latter. The practicality, flexibility and robustness of the proposed approach has been verified experimentally. Future work will consider the inclusion of hard constraints on the input and output signals.