A Design of Parameter Optimal Iterative Learning Control for Linear Discrete-Time Systems

The iterative learning control algorithm proposed by Owens and Feng, which guarantees the monotonic convergence of the tracking error norms along with the trial, will be modified. The learning gain of the proposed method will be determined through a quadratic cost function. MIMO plant case will be also discussed. Numerical simulations will be presented to confirm the validity of the proposed design. 1. Introduction The iterative learning control (ILC) proposed by Kawamura et al. [1] is a method to control systems operating in a repetitive mode. Examples of such systems include robot manipulator and chemical batch processes reliability testing rigs. The control purpose of ILC is to follow a specified trajectory with high precision. Unlike model matching method [2, 3], it might be useful for the plant with nonminimum phase property. There are many approaches to ILC in the literature [4–6], for example, the method based on the PD control [1], the inverse systems [7–9], control [10, 11], and so on. Although the convergence properties of these algorithms have been analyzed, it is not always clear how to choose the free parameters of the algorithms to attain fast or monotonic convergence. Owens and Feng [12] used parameter optimization through a quadratic cost function as a method to establish the ILC law. The important feature of the algorithm is that the learning gain is to be varied in each trial. The method guarantees the monotonic convergence of tracking error to zero, if a given plant satisfies a definite condition [12]. In the case of nondefinite plants, the behavior of the method was discussed in [13]. In this paper, the method by Owens and Feng will be modified for nondefinite plants. The learning gain is not only for each trial, but also varied at each step. With such modifications, it can be useful for nondefinite plants. Moreover, a special analysis for the tracking error will be shown. The paper is organized as follows. In the next section, the problem statement will be presented and brief review of the method by Owens and Feng will be given. A derivation of the modified learning gain and error analysis with the proposed gain will be presented in Section 3. A determination of the gain matrix will be shown in Section 4. The paper was a modified version of the conference paper, and the most different part will be given in Section 5, that is, an extension to the multi-input, multioutput systems. Some simulation results will be given in Section 6 to confirm the effectiveness of the proposed method. Concluding remarks will be given in Section 7. 2.