Two-dimensional model and algorithm analysis for a class of iterative learning control systems

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Abstract
The iterative learning control system (ILCS) has attracted considerable research interest in recent years. However the theoretical results on some fundamental properties of the ILCS have not yet been established. One of the common drawbacks shared by current approaches is lack of a suitable mathematical model which can clearly describe both the dynamics of the control system itself and the behaviour of the learning process as well. In this paper, a class of iterative learning control systems is analysed from the point of view of two-dimensional (2-D) system theory. The 2-D model for a class of ILCS is established in the form of‘Roessor's model’, based on which a general type of learning controller is proposed. Analysis of the 2-D error equation shows that the 2-D asymptotic stability of the 2-D model guarantees the learning convergence of an ILCS. Design criteria for a learning controller is also suggested. The learning gain matrices are obtained from a recursive 2-D identifier using the input and output of the controlled plant in previous operations; the model transformation method is discussed. An example of applying the proposed learning control method to a parallel link robotic manipulator is given.

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