Iterative learning control (ILC) schemes can be classified into the previous cycle learning (PCL), the current cycle learning (CCL) and the synergy—previous and current cycle learning (PCCL). In this work, we first present the configurations of various ILC schemes and the corresponding convergence conditions associated with each configuration. As a result of comparison, the PCCL scheme shows the ability of outperforming the PCL and CCL schemes owing to its underlying feature of two degrees of freedom design. Subsequently, we focus on two practical PCCL schemes with analysis and comparisons in frequency domain, substantiate the difference in the learning updating mechanisms, and in the sequel exploit the circumstances where one PCCL scheme can outperform the other. Based on system Bode plots, we can easily check the learning convergence condition, the complementary property of feedback and feedforward compensation, and which PCCL scheme can perform better. For the purpose of comparison and verification, both schemes are applied to a real-time ball-and-beam system.
Numerous iterative learning control (ILC) schemes have been developed in the past two decades with the aim to improve the control performance over a fixed time interval iteratively whenever the control task repeats (Arimoto et al., 1984; Moore et al., 1992; Moore, 1993; Jang et al., 1995; Owens et al., 1996). From practical point of view, many real control systems are modeled and designed in frequency domain (Barton et al., 2000). In such circumstance, the process model is obtained in frequency domain either from a transfer function, or directly from a Bode plot characterizing the process. ILC, analogous to other control methods, needs frequency domain control design and property analysis in order to meet real life requirements (Chen and Wen, 1999; Xu et al., 2001 and Xu et al., 2002; Hu et al., 2001; Norrlof and Gunnarsson, 1999; Moon et al., 1996; Ahn et al., 1995; Lee et al., 1994).
In this work we discuss the schematics of ILC configurations in general, discuss two typical ILC schemes with previous and current cycle learning in particular. We first discuss the representative configurations of several ILC schemes which can be classified into the previous cycle learning (PCL), the current cycle learning (CCL), the previous and current cycle learning (PCCL), as well as PCL with the cascaded structure. The convergence conditions associated with each learning configuration are derived in frequency domain. Next we show, from a frequency perspective, a highly desired property possessed by the PCCL scheme—the complementary role of feedback and learning based feedforward. Being simple and widely applied, PCCL schemes possess the same feedback mechanism but different learning mechanisms. Then we focus on two practical PCCL schemes. In the first step we derive the learning convergence conditions. The difference in learning mechanisms will result in different convergence conditions. In the second step the two PCCL schemes are compared in terms of the convergence speed, which depends on the system types and relative degrees.
Finally two PCCL schemes are implemented on a ball-and-beam platform with detailed discussions on the ILC design and analysis. We will analyze, compare and test the two PCCL schemes in frequency domain using Bode and Nyquist plots intensively. This part serves to provide an illustrative example to researchers and engineers on how to implement ILC schemes, in the sequel shorten the gap between theoretical study and practical implementation of ILC. The experimental results clearly verifies the validity of the conclusions made in the analysis and comparison of the two PCCL schemes.
The paper is organized as follows. In Section 2, the configurations of ILC schemes and several convergence conditions are discussed. In Section 3, the schematics of the two PCCL schemes are discussed and the comparison studies are conducted for certain circumstances. In Section 4, the implementation of two PCCL learning control schemes for a real-time ball-and-beam system is demonstrated with experimental results.
In this work, the characteristics of several representative ILC schemes, and in particular two practical PCCL schemes, have been discussed and compared. It is well known, that the ILC robustness is enhanced by incorporating a current cycle feedback. Here we further demonstrate in frequency domain, that by the combination of both feedback and learning based feedforward, the learning convergence can also be improved in a complementary manner. Through analysis and comparisons, we present a condition under which one PCCL scheme can outperform another. Applying the two schemes to a ball-and-beam platform, which is a type 2 system with relative degree of 2, PCCL scheme II again exhibits the superior performance. Throughout the work, the techniques of Nyquist plots and Bode diagrams are employed, which greatly facilitate the analysis and verification of learning convergence conditions. On the contrary, frequency based analysis reveals the learnability within certain band. This is because the frequency domain analysis can better capture the nature of the control process by treating the system as a band pass filter.
